Classify each curve as simple, simple closed, closed, or none of these. а. b. с.

Q: Find the exact length ot the curve

A: We have to find arc length of a curve  in a given interval .Curve is defined below:

Q: r = 3sin(Ɵ) Draw the curve, explaining it down to the smallest detail.

A: Given equation is r=3sinθ We have to draw the curve of r=3sinθ. First of all convert the given polar…

Q: For the point P(2 segment PQ

A: Given points are: P21,-9 and Q26,-4 Then the distance between the points P and Q is given by:…

Q: If a unit circle C is traced by R(t), R(0) = (0, 1) and (0) = (2,0), then the circle

A:

Q: 15 6, В

A: Given, if the line AB is tangent to the circle and the radius of the circle is 5.Then we have to…

Q: (4) Find the circle a(x² +y³)+b(x+y) = 1, which best fits the following data. (0, –1), (–1,0),…

A: Given that a(x2+y2)+b(x+y)=1 satisfy the given data (0,-1),(-1,0),(1,-1),(1,1)  that is it gives…

Q: The tangent lines from a point to a circle are congruent. True or Fale? O True O False

A:

Q: Consider the following equation of a circle. 49 + (у — 1)? . 16 - |

A: Given: x-762+y-12=4916

Q: Find the length of the curve

A:

Q: Draw an arrow indicating the direction of motion, and determinethe interval of t-values…

A:

Q: a. Family of circles whose center is on the line y = 3x

A:

Q: Find the center and radius of each circle. 1. x2+y2 25 2. (x- 1)2+ (y+ 1)2 = 49 3. (x+ 2)2 + y2 = 36…

A: The general equation of a circle is (x-h)2+(y-k)2=r2,  Where h= x-coordinate of the center of circle…

Q: For each curve in Figure 31, state whether it is symmetric with respect to the y-axis, the origin,…

A: To state whether it is symmetric with respect to the y-axis, the origin, both, or neither.

Q: It is a line that intersects the circle at exactly two points

A:

Q: Suppose the professor wants the scores to be curved in a way that results in the following: Top 10%…

A: Given: Top 10% of scores receive an A Bottom 10% of scores receive an F Scores between the 70th and…

Q: The family of circles that pass through the origin and have their center on the r-axis.

A:

Q: Find an equation of the circle that has center C(3, -2) and is tangent to the line y = 5.

A: We have, the center of the circle as C3,-2. Also line y=5 is tangent to the circle. As we know that,…

Q: Draw the following curves by extracting their points and then identifying their symmetries 4

A: Solution is given below:

Q: Which of the lines in Figure  are tangent to the curve?

A: Given, A curve with lines A,B,C,D from geometry we can define tangent as a tangent line on a plain…

Q: Find the midpoint of the following line segment

A: Using Midpoint formula,

Q: Determine if AB is tangent to the circle. 12 6.

A: In the question it is asked to proof that line segment AB is tangent to the given circle.

Q: Determine if line AB is tangent to the circle.

A: Given data: The given radius is r=7.5. The given length of the tangent is AB=8. The length of the…

Q: Find the distance between A and B given in the following graph. B

A: In a right triangle the lengths of the sides are related to each other by the Pythagoras theorem. If…

Q: 3.2 5.5 6. A

A:

Q: Find the following for each pair of points:(a) The distance between the points(b) The midpoint of…

A: The given points are (4,-4) and (4,8) a) By using distance formula, D=(x2-x1)2+(y2-y1)2 Take (x1,…

Q: Show that the point is on the unit circle. V7 4' 4

A: The unit circle is a circle with its center at the origin of the coordinate plane and with a radius…

Q: Which line is tanget to the curve g + v = 50? 4

A:

Q: Which line would be tangent to the circle shown? Ay %24

A: A tangent to a circle is a straight line which touches the circle at only one point. This point is…

Q: A secant line from a point to a circle touches the circle in exactly one point. True or False? O…

A:

Q: Find the angle of intersection of the following curve. xy = 6 and x'y = 12

A: As we know that the expression for angle of intersection of two curves is:…

Q: Consider the circle with two intersecting chords. D x+2 x-1 x+5 Solve for x. 1.

A:

Q: Find a parabolic curve to the following data. 1 3 4 5 y:1090 1220 1390 1625 1915

A:

Q: Find the distance from point A to point B.

A: The schematic diagram below represents the relative location of the points A, B, and C.

Q: Verify that the point lies on the graph of the unit circle. V3

A:

Q: and graph the curve. 1

A: the center of the circle is at (1,0) with radius equal to 1. P1 being the variable point  on the…

Q: Determine if line AB is tangent to the circle. 1) 2) 6.6 16 12 A 11 13 3) 4) 12 16 11.4 20 19 15.2 B

A: Answer

Q: What is the equation of the circle that passes through points (2, 3), (6, 1), (4, –3)? x? – y? – 6x…

A:

Q: A secant line from a point to a circle touches the circle in two points. True or False? O True O…

A:

Q: Find the distance between the following pairs of points. (0,12) ,(5,0)

A: 0, 12  &  5, 0

Q: At what points will the line y =x intersect the unit circle x2 +y2 =1 ?

A: We have to find the points where line y=x is intersecting the unit circle: x2+y2=1 To find the…

Q: Which of the following could be the contour map of a cone?

A: Explained below

Q: Find the length of the curve r

A:

Q: Find the exact length or the curve 2.

A: The given curve C is as shown on the white board. Length, L is given by the standard formula shown…

Q: 10.5 A 10 14.5 B

A: The figure is given by To determine : Whether line AB is tangent to the circle or not.

Q: Find the lines of symmetry, if any, for each of the following figures. a. b.

A: The line of symmetry divides the shape into two equal parts which are a mirror image of each other.…

Q: Graph each spiral of Archimedes r = Θ (use both positive and nonpositive values)

A:

Q: Find the sector Area for both of these circles

A: To find  The sector area of the given circles .

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.