Calculus, Early Transcendentals, Single Variable Loose-Leaf Edition Plus MyLab Math with Pearson eText - 18-Week Access Card Package
3rd Edition
ISBN: 9780136207764
Author: Briggs, William, Cochran, Lyle, Gillett, Bernard, SCHULZ, Eric
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Textbook Question
Chapter 13.2, Problem 38E
Identifying sets Give a geometric description of the following sets of points.
38. x2 − 4x + y2 + 6y + z2 + 14 = 0
Expert Solution & Answer
![Check Mark](/static/check-mark.png)
Want to see the full answer?
Check out a sample textbook solution![Blurred answer](/static/blurred-answer.jpg)
Students have asked these similar questions
Quadratic Root Solver
For a general quadratic equation y = ax? + bx + c, the roots can be classified into
three categories depending upon the value of the discriminant which is given by
b2 - 4ac
First, if the discriminant is equal to 0, there is only one real root. Then, if the discriminant
is a positive value, there are two roots which are real and unequal. The roots can be
computed as follows:
-b+ Vb? – 4ac
2a
Further, if the discriminant is a negative value, then there are two imaginary roots. In
this case, the roots are given by
b
ь? - 4ас
2a
2a
Programming tasks:
A text file, coeff.txt has the following information:
coeff.txt
3
4
4
4
1
4
Each line represents the values of a, b and c, for a quadratic equation. Write a program
that read these coefficient values, calculate the roots of each quadratic equation, and display
the results. Your program should perform the following tasks:
• Check if the file is successfully opened before reading
• Use loop to read the file from main…
This does not appear to be the answer to this question; Cheese's position is randomly generated in a 5x5 grid. The initial positions are x,y. The position of Cheese is not specified as (3, 4)
Ex: Let A1 ={x, y}, A2 ={1, 2}, and A3 ={a, b},
Find A1 × A2, (A1 × A2) × A3, A1 × A2 × A3.
Chapter 13 Solutions
Calculus, Early Transcendentals, Single Variable Loose-Leaf Edition Plus MyLab Math with Pearson eText - 18-Week Access Card Package
Ch. 13.1 - Describe the length and direction of the vector 5v...Ch. 13.1 - Prob. 2QCCh. 13.1 - Prob. 3QCCh. 13.1 - Given the points P(2.3) and Q(4, 1), find the...Ch. 13.1 - Find vectors of length 10 parallel to the unit...Ch. 13.1 - Verify that the vector 513,1213 has length 1.Ch. 13.1 - Solve 3u | 4v = 12w for u.Ch. 13.1 - Interpret the following statement: Points have a...Ch. 13.1 - What is a position vector?Ch. 13.1 - Given a position vector v, why are there...
Ch. 13.1 - Use the points P(3.1) and Q(7.1) to find position...Ch. 13.1 - If u = u1, u2 and v = v1, v2, how do you find u +...Ch. 13.1 - Find two unit vectors parallel to 2,3.Ch. 13.1 - Is 1,1 a unit vector? Explain.Ch. 13.1 - Evaluate 3,1+2,4 and illustrate the sum...Ch. 13.1 - Prob. 9ECh. 13.1 - Express the vector v = v1, v2 in terms of the unit...Ch. 13.1 - How do you compute |PQ| from the coordinates of...Ch. 13.1 - The velocity of a kayak on a lake is v=2,2,22....Ch. 13.1 - Vector operations Refer to the figure and carry...Ch. 13.1 - Vector operations Refer to the figure and carry...Ch. 13.1 - Vector operations Refer to the figure and carry...Ch. 13.1 - Vector operations Refer to the figure and carry...Ch. 13.1 - Prob. 17ECh. 13.1 - Vector operations Refer to the figure and carry...Ch. 13.1 - Components and magnitudes Define the points O(0,...Ch. 13.1 - Prob. 20ECh. 13.1 - Components and equality Define the points P(3, 1),...Ch. 13.1 - Components and equality Define the points P(3, 1),...Ch. 13.1 - Components and equality Define the points P(3, 1),...Ch. 13.1 - Vector operations Let u = 4, 2, v = 4, 6, and w =...Ch. 13.1 - Vector operations Let u = 4, 2, v = 4, 6, and w =...Ch. 13.1 - Vector operations Let u = 4, 2, v = 4, 6, and w =...Ch. 13.1 - Vector operations Let u = 4, 2, v = 4, 6, and w =...Ch. 13.1 - Vector operations Let u = 3, 4, v = 1, 1, and w =...Ch. 13.1 - Vector operations Let u = 3, 4, v = 1, 1, and w =...Ch. 13.1 - Prob. 30ECh. 13.1 - Vector operations Let u = 3, 4, v = 1, 1, and w =...Ch. 13.1 - Find a unit vector in the direction of v = 6,8.Ch. 13.1 - Prob. 33ECh. 13.1 - Prob. 34ECh. 13.1 - Find the vector v of length 6 that has the same...Ch. 13.1 - Find the vector v that has a magnitude of 10 and a...Ch. 13.1 - Designer vectors Find the following vectors. 73....Ch. 13.1 - Prob. 38ECh. 13.1 - How do you find a vector of length 10 in the...Ch. 13.1 - Let v = 8,15. a. Find a vector in the direction of...Ch. 13.1 - Prob. 41ECh. 13.1 - Prob. 42ECh. 13.1 - Unit vectors Define the points P(4, 1), Q(3, 4),...Ch. 13.1 - Prob. 44ECh. 13.1 - Prob. 45ECh. 13.1 - Prob. 46ECh. 13.1 - Unit vectors a. Find two unit vectors parallel to...Ch. 13.1 - Vectors from polar coordinates Suppose O is the...Ch. 13.1 - Vectors from polar coordinates Find the position...Ch. 13.1 - Prob. 50ECh. 13.1 - Find the velocity v of an ocean freighter that is...Ch. 13.1 - Prob. 52ECh. 13.1 - Airplanes and crosswinds Assume each plane flies...Ch. 13.1 - Prob. 54ECh. 13.1 - Airplanes and crosswinds Assume each plane flies...Ch. 13.1 - A boat in a current The water in a river moves...Ch. 13.1 - Another boat in a current The water in a river...Ch. 13.1 - Prob. 58ECh. 13.1 - Boat in a wind A sailboat floats in a current that...Ch. 13.1 - Prob. 60ECh. 13.1 - Prob. 61ECh. 13.1 - Prob. 62ECh. 13.1 - Prob. 63ECh. 13.1 - Prob. 64ECh. 13.1 - Explain why or why not Determine whether the...Ch. 13.1 - Equal vectors For the points A(3, 4), B(6, 10),...Ch. 13.1 - Vector equations Use the properties of vectors to...Ch. 13.1 - Vector equations Use the properties of vectors to...Ch. 13.1 - Prob. 69ECh. 13.1 - Solving vector equations Solve the following pairs...Ch. 13.1 - Prob. 71ECh. 13.1 - Prob. 72ECh. 13.1 - Prob. 73ECh. 13.1 - Ant on a page An ant walks due east at a constant...Ch. 13.1 - Clock vectors Consider the 12 vectors that have...Ch. 13.1 - Three-way tug-of-war Three people located at A, B,...Ch. 13.1 - Additional Exercises 8185. Vector properties Prove...Ch. 13.1 - Additional Exercises 8185. Vector properties Prove...Ch. 13.1 - Vector properties Prove the following vector...Ch. 13.1 - Vector properties Prove the following vector...Ch. 13.1 - Vector properties Prove the following vector...Ch. 13.1 - Prob. 82ECh. 13.1 - Magnitude of scalar multiple Prove that |cv| = |c|...Ch. 13.1 - Equality of vectors Assume PQ equals RS. Does it...Ch. 13.1 - Linear independence A pair of nonzero vectors in...Ch. 13.1 - Perpendicular vectors Show that two nonzero...Ch. 13.1 - Parallel and perpendicular vectors Let u = a, 5...Ch. 13.1 - The Triangle Inequality Suppose u and v are...Ch. 13.2 - Suppose the positive x-, y-, and z-axes point...Ch. 13.2 - To which coordinate planes are the planes x = 2...Ch. 13.2 - Describe the solution set of the equation (x 1)2...Ch. 13.2 - Which of the following vectors are parallel to...Ch. 13.2 - Which vector has the smaller magnitude: u = 3i j ...Ch. 13.2 - Explain how to plot the point (3, 2, 1) in 3.Ch. 13.2 - What is the y-coordinate of all points in the...Ch. 13.2 - Describe the plane x = 4.Ch. 13.2 - Prob. 4ECh. 13.2 - Let u = 3, 5, 7 and v = 6, 5, 1. Evaluate u + v...Ch. 13.2 - What is the magnitude of a vector joining two...Ch. 13.2 - Which point is farther from the origin, (3, 1, 2)...Ch. 13.2 - Express the vector from P(1, 4, 6) to Q(1, 3, 6)...Ch. 13.2 - Points in 3 Find the coordinates of the vertices...Ch. 13.2 - Points in 3 Find the coordinates of the vertices...Ch. 13.2 - Points in 3 Find the coordinates of the vertices...Ch. 13.2 - Points in 3 Find the coordinates of the vertices...Ch. 13.2 - Plotting points in 3 For each point P(x, y, z)...Ch. 13.2 - Plotting points in 3 For each point P(x, y, z)...Ch. 13.2 - Sketching planes Sketch the following planes in...Ch. 13.2 - Sketching planes Sketch the following planes in...Ch. 13.2 - Sketching planes Sketch the following planes in...Ch. 13.2 - Sketching planes Sketch the following planes in...Ch. 13.2 - Sketching planes Sketch the following planes in...Ch. 13.2 - Sketching planes Sketch the following planes in...Ch. 13.2 - Planes Sketch the plane parallel to the xy-plane...Ch. 13.2 - Prob. 22ECh. 13.2 - Spheres and balls Find an equation or inequality...Ch. 13.2 - Spheres and balls Find an equation or inequality...Ch. 13.2 - Spheres and balls Find an equation or inequality...Ch. 13.2 - Spheres and balls Find an equation or inequality...Ch. 13.2 - Midpoints and spheres Find an equation of the...Ch. 13.2 - Midpoints and spheres Find an equation of the...Ch. 13.2 - Identifying sets Give a geometric description of...Ch. 13.2 - Identifying sets Give a geometric description of...Ch. 13.2 - Identifying sets Give a geometric description of...Ch. 13.2 - Identifying sets Give a geometric description of...Ch. 13.2 - Identifying sets Give a geometric description of...Ch. 13.2 - Prob. 34ECh. 13.2 - Identifying sets Give a geometric description of...Ch. 13.2 - Identifying sets Give a geometric description of...Ch. 13.2 - Identifying sets Give a geometric description of...Ch. 13.2 - Identifying sets Give a geometric description of...Ch. 13.2 - Prob. 39ECh. 13.2 - Prob. 40ECh. 13.2 - Prob. 41ECh. 13.2 - Prob. 42ECh. 13.2 - Prob. 43ECh. 13.2 - Prob. 44ECh. 13.2 - Unit vectors and magnitude Consider the following...Ch. 13.2 - Unit vectors and magnitude Consider the following...Ch. 13.2 - Unit vectors and magnitude Consider the following...Ch. 13.2 - Unit vectors and magnitude Consider the following...Ch. 13.2 - Prob. 49ECh. 13.2 - Unit vectors and magnitude Consider the following...Ch. 13.2 - Flight in crosswinds A model airplane is flying...Ch. 13.2 - Another crosswind flight A model airplane is...Ch. 13.2 - Crosswinds A small plane is flying horizontally...Ch. 13.2 - Prob. 54ECh. 13.2 - Prob. 55ECh. 13.2 - Maintaining equilibrium An object is acted upon by...Ch. 13.2 - Explain why or why not Determine whether the...Ch. 13.2 - Sets of points Describe with a sketch the sets of...Ch. 13.2 - Sets of points Describe with a sketch the sets of...Ch. 13.2 - Sets of points Describe with a sketch the sets of...Ch. 13.2 - Sets of points 61. Give a geometric description of...Ch. 13.2 - Sets of points 62. Give a geometric description of...Ch. 13.2 - Sets of points 63. Give a geometric description of...Ch. 13.2 - Sets of points 64. Give a geometric description of...Ch. 13.2 - Prob. 65ECh. 13.2 - Prob. 66ECh. 13.2 - Write the vector v = 2, 4, 4 as a product of its...Ch. 13.2 - Find the vector of length 10 with the same...Ch. 13.2 - Find a vector of length 5 in the direction...Ch. 13.2 - Prob. 70ECh. 13.2 - Prob. 71ECh. 13.2 - Parallel vectors of varying lengths Find vectors...Ch. 13.2 - Parallel vectors of varying lengths Find vectors...Ch. 13.2 - Collinear points Determine the values of x and y...Ch. 13.2 - Collinear points Determine whether the points P,...Ch. 13.2 - Lengths of the diagonals of a box What is the...Ch. 13.2 - Three-cable load A 500-kg load hangs from three...Ch. 13.2 - Four-cable load A 500-lb load hangs from four...Ch. 13.2 - Possible parallelograms The points O(0, 0, 0),...Ch. 13.2 - Prob. 80ECh. 13.2 - Midpoint formula Prove that the midpoint of the...Ch. 13.2 - Equation of a sphere For constants a, b, c, and d,...Ch. 13.2 - Prob. 83ECh. 13.2 - Medians of a trianglewith coordinates In contrast...Ch. 13.2 - The amazing quadrilateral propertycoordinate free...Ch. 13.2 - The amazing quadrilateral property-with...Ch. 13.3 - Sketch two nonzero vectors u and v with = 0....Ch. 13.3 - Use Theorem 13.1 to computr the dot products i j,...Ch. 13.3 - Let u = 4i 3j. By inspection (not calculations),...Ch. 13.3 - Express the dot product of u and v in terms of...Ch. 13.3 - Express the dot product of u and v in terms of the...Ch. 13.3 - Compute 2, 3, 6 1, 8, 3.Ch. 13.3 - Prob. 4ECh. 13.3 - Prob. 5ECh. 13.3 - Find the angle between u and v if scalvu = 2 and...Ch. 13.3 - Find projvu if scalvu 2 and v 2,1,2.Ch. 13.3 - Use a dot product to determine whether the vectors...Ch. 13.3 - Prob. 9ECh. 13.3 - Prob. 10ECh. 13.3 - Suppose v is a nonzero position vector in the...Ch. 13.3 - Suppose v is a nonzero position vector in...Ch. 13.3 - Prob. 13ECh. 13.3 - Prob. 14ECh. 13.3 - Prob. 15ECh. 13.3 - Prob. 16ECh. 13.3 - Prob. 17ECh. 13.3 - Prob. 18ECh. 13.3 - Prob. 19ECh. 13.3 - Prob. 20ECh. 13.3 - Prob. 21ECh. 13.3 - Prob. 22ECh. 13.3 - Prob. 23ECh. 13.3 - Prob. 24ECh. 13.3 - Prob. 25ECh. 13.3 - Prob. 26ECh. 13.3 - Prob. 27ECh. 13.3 - Prob. 28ECh. 13.3 - Angles of a triangle For the given points P, Q,...Ch. 13.3 - Angles of a triangle For the given points P, Q,...Ch. 13.3 - Sketching orthogonal projections Find projvu and...Ch. 13.3 - Sketching orthogonal projections Find projvu and...Ch. 13.3 - Sketching orthogonal projections Find projvu and...Ch. 13.3 - Sketching orthogonal projections Find projvu and...Ch. 13.3 - Calculating orthogonal projections For the given...Ch. 13.3 - Calculating orthogonal projections For the given...Ch. 13.3 - Calculating orthogonal projections For the given...Ch. 13.3 - Calculating orthogonal projections For the given...Ch. 13.3 - Prob. 39ECh. 13.3 - Calculating orthogonal projections For the given...Ch. 13.3 - Prob. 41ECh. 13.3 - Computing work Calculate the work done in the...Ch. 13.3 - Prob. 43ECh. 13.3 - Computing work Calculate the work done in the...Ch. 13.3 - Computing work Calculate the work done in the...Ch. 13.3 - Prob. 46ECh. 13.3 - Parallel and normal forces Find the components of...Ch. 13.3 - Parallel and normal forces Find the components of...Ch. 13.3 - Prob. 49ECh. 13.3 - Forces on an inclined plane An object on an...Ch. 13.3 - Prob. 51ECh. 13.3 - For what value of a is the vector v = 4,3,7...Ch. 13.3 - For what value of c is the vector v = 2,5,c...Ch. 13.3 - Orthogonal vectors Let a and b be real numbers....Ch. 13.3 - Orthogonal vectors Let a and b be real numbers....Ch. 13.3 - Prob. 56ECh. 13.3 - Prob. 57ECh. 13.3 - Vectors with equal projections Given a fixed...Ch. 13.3 - Vectors with equal projections Given a fixed...Ch. 13.3 - Vectors with equal projections Given a fixed...Ch. 13.3 - Vectors with equal projections Given a fixed...Ch. 13.3 - Decomposing vectors For the following vectors u...Ch. 13.3 - Decomposing vectors For the following vectors u...Ch. 13.3 - Decomposing vectors For the following vectors u...Ch. 13.3 - Decomposing vectors For the following vectors u...Ch. 13.3 - An alternative line definition Given a fixed point...Ch. 13.3 - An alternative line definition Given a fixed point...Ch. 13.3 - Prob. 68ECh. 13.3 - An alternative line definition Given a fixed point...Ch. 13.3 - Orthogonal unit vectors in 3 Consider the vectors...Ch. 13.3 - Orthogonal unit vectors in 3 Consider the vectors...Ch. 13.3 - Orthogonal unit vectors in 3 Consider the vectors...Ch. 13.3 - Orthogonal unit vectors in 3 Consider the vectors...Ch. 13.3 - Flow through a circle Suppose water flows in a...Ch. 13.3 - Heat flux Let D be a solid heat-conducting cube...Ch. 13.3 - Hexagonal circle packing The German mathematician...Ch. 13.3 - Hexagonal sphere packing Imagine three unit...Ch. 13.3 - Properties of dot products Let u = u1, u2, u3, v =...Ch. 13.3 - Prob. 79ECh. 13.3 - Prob. 80ECh. 13.3 - Prob. 81ECh. 13.3 - Properties of dot products Let u = u1, u2, u3, v =...Ch. 13.3 - Direction angles and cosines Let v = a, b, c and...Ch. 13.3 - Prob. 84ECh. 13.3 - Prob. 85ECh. 13.3 - CauchySchwarz Inequality The definition u v = |u|...Ch. 13.3 - CauchySchwarz Inequality The definition u v = |u|...Ch. 13.3 - CauchySchwarz Inequality The definition u v = |u|...Ch. 13.3 - Diagonals of a parallelogram Consider the...Ch. 13.4 - Prob. 1QCCh. 13.4 - Explain why the vector 2u 3v points in the same...Ch. 13.4 - A good check on a product calculation is to verify...Ch. 13.4 - What is the magnitude of the cross product of two...Ch. 13.4 - Prob. 2ECh. 13.4 - Suppose u and v are nonzero vectors. What is the...Ch. 13.4 - Use a geometric argument to explain why u (u v) =...Ch. 13.4 - Compute |u v| if u and v are unit vectors and the...Ch. 13.4 - Compute |u v| if |u| = 3 and |v| = 4 and the...Ch. 13.4 - Prob. 7ECh. 13.4 - For any vector v in 3, explain why v v = 0.Ch. 13.4 - Explain how to use a determinant to compute u v.Ch. 13.4 - Explain how to find the torque produced by a force...Ch. 13.4 - Cross products from the definition Find the cross...Ch. 13.4 - Cross products from the definition Find the cross...Ch. 13.4 - Cross products from the definition Sketch the...Ch. 13.4 - Prob. 14ECh. 13.4 - Prob. 15ECh. 13.4 - Prob. 16ECh. 13.4 - Coordinate unit vectors Compute the following...Ch. 13.4 - Prob. 18ECh. 13.4 - Prob. 19ECh. 13.4 - Coordinate unit vectors Compute the following...Ch. 13.4 - Prob. 21ECh. 13.4 - Prob. 22ECh. 13.4 - Prob. 23ECh. 13.4 - Prob. 24ECh. 13.4 - Prob. 25ECh. 13.4 - Prob. 26ECh. 13.4 - Prob. 27ECh. 13.4 - Prob. 28ECh. 13.4 - Area of a parallelogram Find the area of the...Ch. 13.4 - Area of a parallelogram Find the area of the...Ch. 13.4 - Area of a parallelogram Find the area of the...Ch. 13.4 - Area of a parallelogram Find the area of the...Ch. 13.4 - Area of a triangle For the given points A, B, and...Ch. 13.4 - Areas of triangles Find the area of the following...Ch. 13.4 - Area of a triangle For the given points A, B, and...Ch. 13.4 - Area of a triangle For the given points A, B, and...Ch. 13.4 - Areas of triangles Find the area of the following...Ch. 13.4 - Areas of triangles Find the area of the following...Ch. 13.4 - Collinear points and cross products Explain why...Ch. 13.4 - Collinear points Use cross products to determine...Ch. 13.4 - Collinear points Use cross products to determine...Ch. 13.4 - Orthogonal vectors Find a vector orthogonal to the...Ch. 13.4 - Orthogonal vectors Find a vector orthogonal to the...Ch. 13.4 - Orthogonal vectors Find a vector orthogonal to the...Ch. 13.4 - Computing torque Answer the following questions...Ch. 13.4 - Computing torque Answer the following questions...Ch. 13.4 - Computing torque Answer the following questions...Ch. 13.4 - Computing torque Answer the following questions...Ch. 13.4 - Prob. 49ECh. 13.4 - Prob. 50ECh. 13.4 - Prob. 51ECh. 13.4 - Arm torque A horizontally outstretched arm...Ch. 13.4 - Force on a moving charge Answer the following...Ch. 13.4 - Prob. 54ECh. 13.4 - Prob. 55ECh. 13.4 - Force on a moving charge Answer the following...Ch. 13.4 - Prob. 57ECh. 13.4 - Finding an unknown Find the value of a such that...Ch. 13.4 - Prob. 59ECh. 13.4 - Prob. 60ECh. 13.4 - Prob. 61ECh. 13.4 - Express u, v, and w in terms of their components...Ch. 13.4 - Prob. 63ECh. 13.4 - Prob. 64ECh. 13.4 - Scalar triple product Another operation with...Ch. 13.4 - Prob. 66ECh. 13.4 - Prob. 67ECh. 13.4 - Three proofs Prove that u u = 0 in three ways. a....Ch. 13.4 - Associative property Prove in two ways that for...Ch. 13.4 - Prob. 70ECh. 13.4 - Prob. 71ECh. 13.4 - Prob. 72ECh. 13.4 - Identities Prove the following identities. Assume...Ch. 13.4 - Prob. 74ECh. 13.4 - Cross product equations Suppose u and v are known...Ch. 13.5 - Describe the line r = t k. for t . Describe the...Ch. 13.5 - In the equation of the line x, y, zx0, y0, z0x1 ...Ch. 13.5 - Find the distance between the point Q(1, 0, 3) and...Ch. 13.5 - Consider the equation of a plare in the form n P0P...Ch. 13.5 - Verify that in Example 6, the same equation for...Ch. 13.5 - Determine whether the planes 2x 3y + 6z = 12 and...Ch. 13.5 - Find a position vector that is parallel to the...Ch. 13.5 - Find the parametric equations of the line r =...Ch. 13.5 - Explain how to find a vector in the direction of...Ch. 13.5 - What is an equation of the line through the points...Ch. 13.5 - Determine whether the plane x + y + z = 9 and the...Ch. 13.5 - Determine whether the plane x + y + z = 9 and the...Ch. 13.5 - Give two pieces of information which, taken...Ch. 13.5 - Find a vector normal to the plane 2x 3y + 4z =...Ch. 13.5 - Where does the plane 2x 3y + 4z = 12 intersect...Ch. 13.5 - Give an equation of the plane with a normal vector...Ch. 13.5 - Equations of lines Find equations of the following...Ch. 13.5 - Equations of lines Find equations of the following...Ch. 13.5 - Equations of lines Find equations of the following...Ch. 13.5 - Equations of lines Find both the parametric and...Ch. 13.5 - Equations of lines Find equations of the following...Ch. 13.5 - Equations of lines Find both the parametric and...Ch. 13.5 - Equations of lines Find both the parametric and...Ch. 13.5 - Equations of lines Find equations of the following...Ch. 13.5 - Equations of lines Find equations of the following...Ch. 13.5 - Equations of lines Find equations of the following...Ch. 13.5 - Prob. 21ECh. 13.5 - Equations of lines Find equations of the following...Ch. 13.5 - Prob. 23ECh. 13.5 - Prob. 24ECh. 13.5 - Equations of lines Find both the parametric and...Ch. 13.5 - Equations of lines Find both the parametric and...Ch. 13.5 - Line segments Find an equation of the line segment...Ch. 13.5 - Line segments Find an equation of the line segment...Ch. 13.5 - Line segments Find an equation of the line segment...Ch. 13.5 - Line segments Find an equation of the line segment...Ch. 13.5 - Parallel, Intersecting, or skew lines Determine...Ch. 13.5 - Parallel, Intersecting, or skew lines Determine...Ch. 13.5 - Parallel, Intersecting, or skew lines Determine...Ch. 13.5 - Parallel, Intersecting, or skew lines Determine...Ch. 13.5 - Parallel, Intersecting, or skew lines Determine...Ch. 13.5 - Parallel, Intersecting, or skew lines Determine...Ch. 13.5 - Parallel, Intersecting, or skew lines Determine...Ch. 13.5 - Intersecting lines and colliding particles...Ch. 13.5 - Distance from a point to a line Find the distance...Ch. 13.5 - Distance from a point to a line Find the distance...Ch. 13.5 - Billiards shot A cue ball in a billiards video...Ch. 13.5 - Prob. 42ECh. 13.5 - Equations of planes Find an equation of the...Ch. 13.5 - Equations of planes Find an equation of the...Ch. 13.5 - Equation of a plane Find an equation of the plane...Ch. 13.5 - Equation of a plane Find an equation of the plane...Ch. 13.5 - Equations of planes Find an equation of the...Ch. 13.5 - Equations of planes Find an equation of the...Ch. 13.5 - Equations of planes Find an equation of the...Ch. 13.5 - Equations of planes Find an equation of the...Ch. 13.5 - Equations of planes Find an equation of the...Ch. 13.5 - Equations of planes Find an equation of the...Ch. 13.5 - Equations of planes Find an equation of the...Ch. 13.5 - Equations of planes Find an equation of the...Ch. 13.5 - Prob. 55ECh. 13.5 - Prob. 56ECh. 13.5 - Equations of planes Find an equation of the...Ch. 13.5 - Prob. 58ECh. 13.5 - Parallel planes is the line x = t + 1, y = 2t + 3,...Ch. 13.5 - Do the lines x = t, y = 2t + 1, z = 3t + 4 and x =...Ch. 13.5 - Properties of planes Find the points at which the...Ch. 13.5 - Prob. 62ECh. 13.5 - Properties of planes Find the points at which the...Ch. 13.5 - Prob. 64ECh. 13.5 - Pairs of planes Determine whether the following...Ch. 13.5 - Pairs of planes Determine whether the following...Ch. 13.5 - Pairs of planes Determine whether the following...Ch. 13.5 - Pairs of planes Determine whether the following...Ch. 13.5 - Equations of planes For the following sets of...Ch. 13.5 - Equations of planes For the following sets of...Ch. 13.5 - Lines normal to planes Find an equation of the...Ch. 13.5 - Lines normal to planes Find an equation of the...Ch. 13.5 - Intersecting planes Find an equation of the line...Ch. 13.5 - Intersecting planes Find an equation of the line...Ch. 13.5 - Intersecting planes Find an equation of the line...Ch. 13.5 - Intersecting planes Find an equation of the line...Ch. 13.5 - Line-plane intersections Find the point (if it...Ch. 13.5 - Line-plane intersections Find the point (if it...Ch. 13.5 - Line-plane intersections Find the point (if it...Ch. 13.5 - Line-plane intersections Find the point (if it...Ch. 13.5 - Explain why or why not Determine whether the...Ch. 13.5 - Distance from a point to a plane Suppose P is a...Ch. 13.5 - Find the distance from the point Q (6, 2, 4) to...Ch. 13.5 - Find the distance from the point Q (1, 2, 4) to...Ch. 13.5 - Symmetric equations for a line If we solve fort in...Ch. 13.5 - Symmetric equations for a line If we solve fort in...Ch. 13.5 - Angle between planes The angle between two planes...Ch. 13.5 - Prob. 88ECh. 13.5 - Prob. 89ECh. 13.5 - Orthogonal plane Find an equation of the plane...Ch. 13.5 - Three intersecting planes Describe the set of all...Ch. 13.5 - Three intersecting planes Describe the set of all...Ch. 13.6 - To which coordinate axis in 3 is the cylinder z 2...Ch. 13.6 - Explain why the elliptic cylinder discussed in...Ch. 13.6 - Assume 0 c b a in the general equation of an...Ch. 13.6 - The elliptic paraboloid x=y23+z27 is a bowl-shaped...Ch. 13.6 - Which coordinate axis is the axis of the...Ch. 13.6 - Prob. 6QCCh. 13.6 - To which coordinate axes are the following...Ch. 13.6 - Describe the graph of x = z2 in 3.Ch. 13.6 - What is a trace of a surface?Ch. 13.6 - What is the name of the surface defined by the...Ch. 13.6 - What is the name of the surface defined by the...Ch. 13.6 - What is the name of the surface defined by the...Ch. 13.6 - Cylinders in 3 Consider the following cylinders in...Ch. 13.6 - Cylinders in 3 Consider the following cylinders in...Ch. 13.6 - Cylinders in 3 Consider the following cylinders in...Ch. 13.6 - Cylinders in 3 Consider the following cylinders in...Ch. 13.6 - Cylinders in 3 Consider the following cylinders in...Ch. 13.6 - Cylinders in 3 Consider the following cylinders in...Ch. 13.6 - Cylinders in 3 Consider the following cylinders in...Ch. 13.6 - Cylinders in 3 Consider the following cylinders in...Ch. 13.6 - Identifying quadric surfaces Identify the...Ch. 13.6 - Identifying quadric surfaces Identify the...Ch. 13.6 - Identifying quadric surfaces Identify the...Ch. 13.6 - Identifying quadric surfaces Identify the...Ch. 13.6 - Identifying quadric surfaces Identify the...Ch. 13.6 - Identifying quadric surfaces Identify the...Ch. 13.6 - Identifying surfaces Identify and briefly describe...Ch. 13.6 - Identifying surfaces Identify and briefly describe...Ch. 13.6 - Identifying surfaces Identify and briefly describe...Ch. 13.6 - Identifying surfaces Identify and briefly describe...Ch. 13.6 - Identifying surfaces Identify and briefly describe...Ch. 13.6 - Identifying surfaces Identify and briefly describe...Ch. 13.6 - Identifying surfaces Identify the following...Ch. 13.6 - Identifying surfaces Identify the following...Ch. 13.6 - Quadric surfaces Consider the following equations...Ch. 13.6 - Quadric surfaces Consider the following equations...Ch. 13.6 - Quadric surfaces Consider the following equations...Ch. 13.6 - Quadric surfaces Consider the following equations...Ch. 13.6 - Quadric surfaces Consider the following equations...Ch. 13.6 - Quadric surfaces Consider the following equations...Ch. 13.6 - Quadric surfaces Consider the following equations...Ch. 13.6 - Quadric surfaces Consider the following equations...Ch. 13.6 - Quadric surfaces Consider the following equations...Ch. 13.6 - Prob. 38ECh. 13.6 - Quadric surfaces Consider the following equations...Ch. 13.6 - Quadric surfaces Consider the following equations...Ch. 13.6 - Quadric surfaces Consider the following equations...Ch. 13.6 - Prob. 42ECh. 13.6 - Quadric surfaces Consider the following equations...Ch. 13.6 - Prob. 44ECh. 13.6 - Quadric surfaces Consider the following equations...Ch. 13.6 - Quadric surfaces Consider the following equations...Ch. 13.6 - Prob. 47ECh. 13.6 - Prob. 48ECh. 13.6 - Quadric surfaces Consider the following equations...Ch. 13.6 - Quadric surfaces Consider the following equations...Ch. 13.6 - Quadric surfaces Consider the following equations...Ch. 13.6 - Prob. 52ECh. 13.6 - Prob. 53ECh. 13.6 - Identifying surfaces Identify and briefly describe...Ch. 13.6 - Identifying surfaces Identify and briefly describe...Ch. 13.6 - Identifying surfaces Identify and briefly describe...Ch. 13.6 - Identifying surfaces Identify and briefly describe...Ch. 13.6 - Identifying surfaces Identify and briefly describe...Ch. 13.6 - Prob. 59ECh. 13.6 - Matching graphs with equations Match equations af...Ch. 13.6 - Explorations and Challenges 61. Solids of...Ch. 13.6 - Prob. 62ECh. 13.6 - Prob. 63ECh. 13.6 - Light cones The idea of a light cone appears in...Ch. 13.6 - Prob. 65ECh. 13.6 - Hand tracking Researchers are developing hand...Ch. 13.6 - Designing a snow cone A surface, having the shape...Ch. 13.6 - Designing a glass The outer, lateral side of a...Ch. 13 - Explain why or why not Determine whether the...Ch. 13 - Prob. 2RECh. 13 - Prob. 3RECh. 13 - Prob. 4RECh. 13 - Prob. 5RECh. 13 - Working with vectors Let u = 2, 4, 5 and v = 6,...Ch. 13 - Working with vectors Let u = 2, 4, 5 and v = 6,...Ch. 13 - Prob. 8RECh. 13 - working with vectors Let u = 2,4,5 , v = 6,10,2...Ch. 13 - working with vectors Let u = 2,4,5 , v = 6,10,2...Ch. 13 - working with vectors Let u = 2,4,5 , v = 6,10,2...Ch. 13 - working with vectors Let u = 2,4,5 , v = 6,10,2...Ch. 13 - working with vectors Let u = 2,4,5 , v = 6,10,2...Ch. 13 - working with vectors Let u = 2,4,5 , v = 6,10,2...Ch. 13 - working with vectors Let u = 2,4,5 , v = 6,10,2...Ch. 13 - Scalar multiples Find scalars a, b, and c such...Ch. 13 - Velocity vectors Assume the positive x-axis points...Ch. 13 - Prob. 18RECh. 13 - Spheres and balls Use set notation to describe the...Ch. 13 - Spheres and balls Use set notation to describe the...Ch. 13 - Spheres and balls Use set notation to describe the...Ch. 13 - Identifying sets. Give a geometric description of...Ch. 13 - Identifying sets. Give a geometric description of...Ch. 13 - Identifying sets. Give a geometric description of...Ch. 13 - Identifying sets. Give a geometric description of...Ch. 13 - Prob. 26RECh. 13 - Prob. 27RECh. 13 - Cross winds A small plane is flying north in calm...Ch. 13 - Prob. 29RECh. 13 - Canoe in a current A woman in a canoe paddles cue...Ch. 13 - Sets of points Describe the set of points...Ch. 13 - Angles and projections a. Find the angle between u...Ch. 13 - Prob. 33RECh. 13 - Prob. 34RECh. 13 - Computing work Calculate the work done in the...Ch. 13 - Computing work Calculate the work done in the...Ch. 13 - Prob. 37RECh. 13 - Inclined plane A 1804b map stands on a hillside...Ch. 13 - Area of a parallelogram Find the area of the...Ch. 13 - Area of a triangle Find the area of the triangle...Ch. 13 - Vectors normal to a plane Find a unit vector...Ch. 13 - Angle in two ways Find the angle between 2, 0, 2...Ch. 13 - Prob. 43RECh. 13 - Suppose you apply a force of |F| = 50 N near the...Ch. 13 - Prob. 45RECh. 13 - Lines in space Find an equation of the following...Ch. 13 - Lines in space Find an equation of the following...Ch. 13 - Lines in space Find an equation of the following...Ch. 13 - Lines in space Find an equation of the following...Ch. 13 - Lines in space Find an equation of the following...Ch. 13 - Equations of planes Consider the plane passing...Ch. 13 - Intersecting planes Find an equation of the line...Ch. 13 - Intersecting planes Find an equation of the line...Ch. 13 - Equations of planes Find an equation of the...Ch. 13 - Prob. 55RECh. 13 - Prob. 56RECh. 13 - Equations of planes Find an equation of the...Ch. 13 - Distance from a point to a line Find the distance...Ch. 13 - Distance from a point to a plane Find the distance...Ch. 13 - Identifying surfaces Consider the surfaces defined...Ch. 13 - Identifying surfaces Consider the surfaces defined...Ch. 13 - Identifying surfaces Consider the surfaces defined...Ch. 13 - Identifying surfaces Consider the surfaces defined...Ch. 13 - Identifying surfaces Consider the surfaces defined...Ch. 13 - Identifying surfaces Consider the surfaces defined...Ch. 13 - Identifying surfaces Consider the surfaces defined...Ch. 13 - Identifying surfaces Consider the surfaces defined...Ch. 13 - Identifying surfaces Consider the surfaces defined...Ch. 13 - Identifying surfaces Consider the surfaces defined...Ch. 13 - Identifying surfaces Consider the surfaces defined...Ch. 13 - Identifying surfaces Consider the surfaces defined...Ch. 13 - Identifying surfaces Consider the surfaces defined...Ch. 13 - Prob. 73RECh. 13 - Identifying surfaces Consider the surfaces defined...Ch. 13 - Prob. 75RECh. 13 - Designing a water bottle The lateral surface of a...
Additional Math Textbook Solutions
Find more solutions based on key concepts
What is the domain and the range of y=secx ?
Precalculus (10th Edition)
The integrals in Exercises 1-34 converge. Evaluate the integrals without using tables.
1.
Thomas' Calculus: Early Transcendentals (14th Edition)
In Example 1, what is the average velocity between t=2 and t=3? Example 1 Average Velocity A rock is launched v...
Calculus, Single Variable: Early Transcendentals (3rd Edition)
A point P in the first quadrant lies on the graph of the function . Express the coordinates of P as functions o...
University Calculus: Early Transcendentals (3rd Edition)
The intercepts of the equation 9 x 2 +4y=36 are ______. (pp.18-19)
Precalculus Enhanced with Graphing Utilities (7th Edition)
Find T, N, and κ for the plane curves in Exercises 1–4.
3. r(t) = (2t + 3)i + (5 − t2)j
University Calculus: Early Transcendentals (4th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Similar questions
- Java Assignment: Mathematics is the very interesting subject and for the India it is also a point of pride because Mr. Brahmagupta gives the 0 to world. So, in this series want to be great mathematician like Brahmagupta. He is keep practicing for her goal achievement. Once He knew about the Vector dot Product So He asked his friend Sammer the problem. He gave her two vectors A and B length N. He asked him to reduce the dot output of these two vectors. Sammer has the option to change the order of the objects of these two carriers i.e., in any two objects I and j at any vector can change the shape of these objects. Since Sammer is new to the program, he has asked you to resolve the issue using C++ Programming language. Input: 1 4 142-5 3 -8 5 2 Output: -50arrow_forwardCCC '13 J1 - Next in line Canadian Computing Competition: 2013 Stage 1, Junior #1 You know a family with three children. Their ages form an arithmetic sequence: the difference in ages between the middle child and youngest child is the same as the difference in ages between the oldest child and the middle child. For example, their ages could be 5, 10 and 15, since both adjacent pairs have a difference of 5 years. Given the ages of the youngest and middle children, what is the age of the oldest child? Input Specification The input consists of two integers, each on a separate line. The first line is the age Y of the youngest child (0arrow_forwardIn mathematics, a prime number is a natural number greater than 1 that is not a product of two smaller natural numbers, i.e. is it has only two factors 1 and itself. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself.Note that the prime number series is: 2, 3, 4, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, …a. Write a Java method named isPrime that takes a natural number as a parameter and returns the if the given number is prime or not using the following header: Public static boolean isPrime(int num) b. Write a Java class called PrimeNumbers that: o Reads from the user a natural value n (should be less than or equal 200). o Prints a list of the prime numbers from 2 to n and their number and values. o The program has to work EXACTLY as given in the following sample run.arrow_forwardCorrect answer will be upvoted else Multiple Downvoted. Don't submit random answer. Computer science. Sasha likes exploring diverse mathematical articles, for instance, wizardry squares. However, Sasha comprehends that enchanted squares have as of now been examined by many individuals, so he sees no feeling of concentrating on them further. All things considered, he designed his own kind of square — a superb square. A square of size n×n is called prime if the accompanying three conditions are held all the while: all numbers on the square are non-negative integers not surpassing 105; there are no indivisible numbers in the square; amounts of integers in each line and every segment are indivisible numbers. Sasha has an integer n. He requests you to view as any great square from size n×n. Sasha is certain beyond a shadow of a doubt such squares exist, so help him! Input The principal line contains a solitary integer t (1≤t≤10) — the number of experiments. Every one…arrow_forwardIn mathematics, a prime number is a natural number greater than 1 that is not a product of two smaller natural numbers, i.e. is it has only two factors 1 and itself. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 x 1, involve 5 itself. Note that the prime number series is: 2, 3, 4, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, .. a. Write a Java method named isPrime that takes a natural number as a parameter and returns the if the given number is prime or not using the following header: Public static boolean isPrime (int num) b. Write a Java class called PrimeNumbers that: Reads from the user a natural value n (should be less than or equal 200). Prints a list of the prime numbers from 2 to n and their number and values. The program has to work EXACTLY as given in the following sample run. Hints: You should create a single dimension array to store the prime…arrow_forwardA magic square is an n by n matrix in which each of the integers 1, 2, 3...n appears exactly once and all column sums, row sums, and diagonal sums are equal. For example, the following is a 5 by 5 magic square in which all rows, columns and diagonals sum to 65. 17 24 1 8. 15 23 7 14 16 4 6. 13 20 22 10 12 19 21 3 11 18 25 9 The following is a procedure for constructing an n by n magic square for any ODD integer n. Place 1 in the middle of the top row. Then.m after integer k has been placed, move up one row and one column to the right to place the next integer k+1 unless one of the following occurs: If a move takes you above the top row in the jth column, move to the bottom of the jth column and place k+1 there. If the move takes you outside to the right of the square in the ith row place k+1 in the ith row in the left side. If the move takes you to an already filled square or if you move out of the square at the upper right hand corner place k+1 immediately below k. Write a C++ program…arrow_forwardQ3: Interplanetary Spaceflight Milan Tusk is the richest person in the universe. After devoting decades of his life to further our space exploration technologies, he’s finally ready to retire. Being a space enthusiast, the first thing he wants to do is visit n planets p1, p2, …, pn, in this order. He’s currently on planet p0. Milan knows that the distance between planets pi and pi + 1 (for 0 ≤ i < n) is d[i]light years. His spaceship uses 1 tonne of fossil fuels per light year. He starts with a full tank and can fill up his tank at any of the n planets (but he must not run out in between two planets). There’s a huge cost to set up the spaceship for refuelling. Due to financial constraints (he’s not THAT rich), he can fill up his tank at most ktimes. In order to save money and make his spaceship lighter, Milan is looking for the smallest possible fuel tank that enables him to complete his space travel and reach planet pn. What is the smallest tank capacity that enables him to do so?…arrow_forwardCan you help me with this code I only need help with two of the parts. I have attached my code in the photo. question that i need help with: the Eight Puzzle consists of a 3 x 3 board of sliding tiles with a single empty space. For each configuration, the only possible moves are to swap the empty tile with one of its neighboring tiles. The goal state for the puzzle consists of tiles 1-3 in the top row, tiles 4-6 in the middle row, and tiles 7 and 8 in the bottom row, with the empty space in the lower-right corner.you will develop two solvers for a generalized version of the Eight Puzzle, in which the board can have any number of rows and columns. A natural representation for this puzzle is a two-dimensional list of integer values between 0 and r · c -1 (inclusive), where r and c are the number of rows and columns in the board, respectively. In this problem, we will adhere to the convention that the 0-tile represents the empty space.tasks: In the TilePuzzle class, write a method…arrow_forwardpython3xs = np.linspace(0,5,100)plane1 = np.array([ 2. , 2.40393306, 2.8072224 , 3.20922595, 3.60930489, 4.00682534, 4.40115993, 4.79168942, 5.17780427, 5.5589062 , 5.93440972, 6.3037436 , 6.66635235, 7.02169765, 7.36925969, 7.70853849, 8.03905523, 8.36035341, 8.67200004, 8.97358676, 9.26473085, 9.54507622, 9.81429434, 10.07208503, 10.31817726, 10.55232985, 10.77433205, 10.98400411, 11.1811977 , 11.36579635, 11.53771568, 11.69690365, 11.84334071, 11.97703979, 12.09804633, 12.20643815, 12.3023252 , 12.38584936, 12.45718401, 12.51653364, 12.56413329, 12.60024796, 12.62517195, 12.6392281 , 12.64276695, 12.63616588, 12.61982812, 12.59418173, 12.55967851, 12.51679284, 12.4660205 , 12.40787736, 12.34289809, 12.27163481, 12.19465564, 12.11254329, 12.02589357, 11.93531385, 11.84142153, 11.74484244, 11.64620928, 11.54615999, 11.4453361 , 11.34438114, 11.24393896, 11.14465211, 11.04716019,…arrow_forwardPerfect numbers are numbers that are equal to the sum of their positive divisors except itself. The smallest perfect number is 6. The positive divisors of 6: The sum of the divisors of 1, 2, 3 and 6 except itself: 1 + 2 + 3 = 6 and 6 is a perfect number. Likewise, the positive divisors of 28: 1, 2, 4, 7, 14, 28 is the sum of the divisors except itself: 1 + 2 + 4 + 7 + 14 = 28 and 28 is a perfect number. So, write a MATLAB function that checks if a given number is a perfect number.arrow_forward6. The Jaccard coefficient between two sets {a, b, c, d, e, f, g} and {a, b, g, h, i, j} is: Group of answer choices 0.2 0.3 0.4 0.5arrow_forwardPlayer A and player B invented a game in which a person who sorts playing cards is a winner. The cards with red color should come before those with black color, and cards with small numbers should come before those with big numbers. The cards with images should be in this order: Jack, Queen and King. The game allows player to start by small number of cards, then increase step by step, e.g, 2,3,4, ....n. Design an efficient algorithm that helps a player A to win the game by sorting n number of cards faster than player B. Note that n number of cards which is very large can be obtained by repeating cards with the same number and same color, e.g, card 3 with color red can be repeated m times while marrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
Recommended textbooks for you
- Database System ConceptsComputer ScienceISBN:9780078022159Author:Abraham Silberschatz Professor, Henry F. Korth, S. SudarshanPublisher:McGraw-Hill EducationStarting Out with Python (4th Edition)Computer ScienceISBN:9780134444321Author:Tony GaddisPublisher:PEARSONDigital Fundamentals (11th Edition)Computer ScienceISBN:9780132737968Author:Thomas L. FloydPublisher:PEARSON
- C How to Program (8th Edition)Computer ScienceISBN:9780133976892Author:Paul J. Deitel, Harvey DeitelPublisher:PEARSONDatabase Systems: Design, Implementation, & Manag...Computer ScienceISBN:9781337627900Author:Carlos Coronel, Steven MorrisPublisher:Cengage LearningProgrammable Logic ControllersComputer ScienceISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill Education
![Text book image](https://www.bartleby.com/isbn_cover_images/9780078022159/9780078022159_smallCoverImage.jpg)
Database System Concepts
Computer Science
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:McGraw-Hill Education
![Text book image](https://www.bartleby.com/isbn_cover_images/9780134444321/9780134444321_smallCoverImage.gif)
Starting Out with Python (4th Edition)
Computer Science
ISBN:9780134444321
Author:Tony Gaddis
Publisher:PEARSON
![Text book image](https://www.bartleby.com/isbn_cover_images/9780132737968/9780132737968_smallCoverImage.gif)
Digital Fundamentals (11th Edition)
Computer Science
ISBN:9780132737968
Author:Thomas L. Floyd
Publisher:PEARSON
![Text book image](https://www.bartleby.com/isbn_cover_images/9780133976892/9780133976892_smallCoverImage.gif)
C How to Program (8th Edition)
Computer Science
ISBN:9780133976892
Author:Paul J. Deitel, Harvey Deitel
Publisher:PEARSON
![Text book image](https://www.bartleby.com/isbn_cover_images/9781337627900/9781337627900_smallCoverImage.gif)
Database Systems: Design, Implementation, & Manag...
Computer Science
ISBN:9781337627900
Author:Carlos Coronel, Steven Morris
Publisher:Cengage Learning
![Text book image](https://www.bartleby.com/isbn_cover_images/9780073373843/9780073373843_smallCoverImage.gif)
Programmable Logic Controllers
Computer Science
ISBN:9780073373843
Author:Frank D. Petruzella
Publisher:McGraw-Hill Education
08 - Conic Sections - Hyperbolas, Part 1 (Graphing, Asymptotes, Hyperbola Equation, Focus); Author: Math and Science;https://www.youtube.com/watch?v=Ryj0DcdGPXo;License: Standard YouTube License, CC-BY