Given f(x) =Vx + 8 and g(x) = 8x - 12, find (f • g)(x).

Q: How do you find the intersection of two lines in space? A line and a plane? Two planes? Give example...

A: Explanation:

Q: n Exercises 39–41, find the distance from the point to the plane. 39. (2, -3, 4), x + 2y + 2z = 13 4...

A: Given, (2, -3, 4), x + 2y + 2z = 13.

Q: dy/dx of pi

A: pi is a constant.It has value 3.14 approx.

Q: 15. Previous Answers + 0/1 points TanApCalcBr10 2.1.032. Find the domain of the function. (Enter you...

A: Find the domain of the given function

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the...

A: First graph the situation  

Q: Is the attached question true or false? Please explain.

A: To show the below property is true or false:

Q: Show that the point P(3, 1, 2) is equidistant from the points A(2, -1, 3) and B(4, 3, 1).

A: Let the distance between P(3, 1, 2) and A(2, -1, 3) be d1 and the distance between P(3, 1, 2) and B(...

Q: describe the given set with a single equation or with a pair of equations.The set of points in space...

A: Let the points are given by (x,y,z) 

Q: Find the points in which the line x = 1 + 2t, y =-1 - t, z = 3t meets the three coordinate planes.

A: Given line is  x = 1 + 2t, y =-1 - t, z = 3tWhen the line meets xy plane then z=0So, 3t=0Or, t=0

Q: Exercises 17–20 give equations for ellipses. Put each equation in standard form. Then sketch the ell...

A: Note: We’ll answer the 17th question since we answer only one question at a time. Please submit a ne...

Q: Exercise. The Earth travels in an orbit around the Sun that can be approximated by a circle. The dis...

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If y...

Q: Find the distance from the point (4, 3, 0) to the a. x-axis b. y-axis c. z-axis

A: To determine the distance of the point from,Part (a) x-axisPart (b) y-axisPart (c) z-axis

Q: What geometric or physical interpretations do cross products have? Give examples.

A: Geometric or physical interpretations:The magnitude of the cross product of two vectors is the area ...

Q: Find a 2 * 2 determinant formula for the area of the triangle in the xy-plane with vertices at (0, 0...

A: Given, vertices of the triangle are

Q: Find the point on the sphere x2 + (y - 3)2 + (z + 5)2 = 4 nearest a. the xy-plane. b. the point (0, ...

A: Consider the given equation of the sphere.

Q: in the following Exercises 9–16, find B and t for these space curves. 9. r(t) = (3 sin t)i + (3 cos ...

A: As per our norms we can solve one question at a time, so I am solving question 9 and please post the...

Q: Find the point on the curve y = ex where the curvature is greatest.

A: Given: Find the point on the curve y = ex where the curvature is greatest.

Q: If vectorAB =-7i + 3j + 8k and A is the point (-2, -3, 6), find B.

A: Given : AB =-7i + 3j + 8k and A=(-2, -3, 6)

Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral)  y1...

A: Given, functions are

Q: Find the limit of the equation.

A: Given limit

Q: What is a curve’s binormal vector? Give an example. How is this vector related to the curve’s torsio...

A: The binormal vector of the curve in space is a vector which is orthogonal to both unit tangent and u...

Q: What is a hyperbola? What are the Cartesian equations for hy-perbolas centered at the origin with fo...

A: Problem 1:Recall the following fact.

Q: What points in the xy-plane satisfy the equations and inequalities in Exercises 11–12? Draw a figure...

A: Since you have submitted two questions, we\'ll answer the first question. For the second question pl...

Q: Can I get help step by step with this problem please?

A: Multiply numerator and denominator by conjugate of the numerator. Apply (a+b)(a-b)= a^2 - b^2 formul...

Q: The wind passing over a boat’s sail exerted a 1000-lb magnitude force F as shown here. How much work...

A: The wind passing over a boat’s sail exerted a 1000-lb magnitude force F 

Q: Find the one-sided limit (if it exists). (If an answer does not exist, enter DNE.) 6x2 + x – 1 lim x...

A: Given, limit function is

Q: Show that for every real number k the plane x - 2y + z + 3 + k(2x - y - z + 1) = 0 contains the line...

A: Show that for every real number k the plane x - 2y + z + 3 + k (2x - y - z + 1) = 0 contains the lin...

Q: Which of the following are always true, and which are not always true? Give reasons for your answers...

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and s...

Q: The planes 3x + 6z = 1 and 2x + 2y - z = 3 intersect in a line. a. Show that the planes are orthogon...

A: Given,

Q: Use the component form to generate an equation for the plane through P1(4, 1, 5) normal to n1 = i - ...

A: Recall the following fact.

Q: In Exercises 19 and 20, find projv u. 19. v = 2i + j - k u = i + j - 5k 20. u = i - 2j v = i + j + k

A: Exercise 19:

Q: In Exercises 33–34, find the distance from the point to the line. 33. (2, 1, 3); x = 2 + 2t, y = 1 +...

A: Since we only answer up to 1 question, we’ll answer the first question. Please resubmit the question...

Q: What are the vector and parametric equations for ideal projectile motion? How do you find a projecti...

A: The vector equation and the Parametric Equation for ideal projectile motion :

Q: evaluate the definite integral from 0 to (1/3) of pi*tan(pi*x)dx

A: Given expression is,

Q: In Exercises 37 and 38, find an equation for the plane through points P, Q, and R. 37. P(1, -1, 2), ...

A: Given, the points P(1, -1, 2), Q(2, 1, 3), R(-1, 2, -1)The vector

Q: What points in the xy-plane satisfy the equations and inequalities in Exercises 11–12? Draw a figure...

A: Since you have submitted two questions, we'll answer the first question. For the second question ple...

Q: Can I get help step by step with this problem please?

A: We have given

Q: #19

A: Consider the function.

Q: Find a formula for the distance from the point P(x, y, z) to the a. xy-plane . b. yz-plane c. zx-pla...

A: a) xy plane is given by z=0 We have to find distance of (x,y,z) from z=0 

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the...

A: We need to find the volume V of the solid obtained by rotating the region bounded by the given curve...

Q: Find the limit of the equation.

A: Limit x-> pi/4 means x is approaching pi/4 .Plug x=pi/4 in the expression.

Q: Find the point of intersection of the lines x = t, y = -t + 2, z = t + 1, and x = 2s + 2, y = s + 3,...

A: Given lines are  x = t, y = -t + 2, z = t + 1, and x = 2s + 2, y = s + 3, z = 5s + 6Set the x and y ...

Q: Show that the line in which the planes x + 2y - 2z = 5 and 5x - 2y - z = 0 intersect is parallel to ...

A: Find the vectors normal to the planes x + 2y - 2z = 5 and 5x - 2y - z = 0.

Q: Find a formula for the distance from the point P(x, y, z) to the a. x-axis.    b. y-axis    c. z-axi...

A: The formula for distance between two points (x, y, z) and (a, b, c) is

Q: The vertices of an ellipse of eccentricity 0.5 lie at the points (0, +-2). Where do the foci lie?

A: The vertices of an ellipse of eccentricity is 0.5 lies on (0,+-2). Find the foci

Q: In Exercises 25–26, express each vector as a product of its length and direction. 25. 5k 26. 3/5i+4/...

A: We’ll answer the 25th question since we answer only one question at a time. Please submit a new ques...

Q: Exercises 17–20 give equations for ellipses. Put each equation in stan-dard form. Then sketch the el...

A: Note: We’ll answer the 17th question since we answer only one question at a time. Please submit a ne...

Q: Determine the infinite limit:    (See image below).   The answer key says that we will take the ln(a...

A: Given limit is 

Q: Describe the interval(s) on which the function is continuous. (Enter your answer using interval nota...

A: Consider the provided function,f(x) = (x+8)/(square root x)The rational function is continuous every...

Q: Marcos traveled for 2 hours and 17 minutes on Interstate 17 as he drove (without stopping) a distanc...

A: Given:Marcos travelled a distance of 155 miles in 2 hours and 17 minutes.