4. (a) What is the composition of a 90 degree rotation about the origin, followed by a 90 degree rotation about (1,0)? (b) What is the composition of a 90 degree rotation about the origin, followed by the reflection across the line x=y?

Q: -38, find parametric equations for the given curve. 3x 34. Segment joining (-3,0) and (0, 4)

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Q: (1 point) Suppose that C is the curve defined by the polar equation r = 2 +4 cos 0 (called a…

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Q: 1) Find the parametric equations of the line that is tangent to circle x² + y2 = 25 %3D at point (3,…

A: Given: Equation of circle: x2+y2=25 and tangent at point 3, -4

Q: 4. A carnival ride is drawn on a coordinate plane so that the first car is located at the point (30,…

A: Coordinate point is (30,0) Rotation is 270 degrees.

Q: In math land, there is a clock. The hour hand of this clock is 1 ft long. However, the clock is…

A:

Q: 4. Given an equation of a conic in polar formr= f(0), substituting (0 – a) results in a…

A: Given an equation of the conic in the polar form r = f(θ), Substituting θ - α results in a…

Q: Describe the graph of the equation. r = 10 cos ti + 3 sin t j – k O Itis an ellipse in the z = -1…

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Q: 10) (section 10.7) Find parametric equations for a circle centered at ( 5,6) with a radius of 4 and…

A: Given:

Q: Graph the line and conic section. r = 1/(1 + 2 cos u)

A: To graph r  = 11 + 2 cos u.

Q: ed 3. For a conic defined byr = the directrix is (horizontal/vertical) with equation 1 + esin 0'

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Q: A 43-degree counterclockwise rotation about the origin sends the point P(5,12) to the point P'(x,y).…

A: A 43-degree counterclockwise rotation about the origin sends the point P(5,12) to the point P'(x,y).…

Q: 9. The coordinates of point P on the (-). What unit circle are are the coordinates of Q if Q is a…

A: Given: The coordinates of point P on the unit circle are -34, 74 To determine: Coordinates of Q if…

Q: The point (3, 4) is plotted on the coordinate plane below.   What are the coordinates of the…

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Q: Example 7 Sketch the curves (a) r 1 (b) @ = 4. %3D in polar coordinates.

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Q: 2. Find the symmetric and parametric equations of the line containing the point A(1,2, 1) and x-2…

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Q: 30. Show that the circle with its center at (5,) in Figure 20 has polar equation r = sin 0 + cos 0…

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Q: Is the given statement true or false? Justify your answer. 10 3-2 cos 0 is a = 13. Directrix of a…

A: The given polar equation is r=103-2cosθ. Rewrite it as follows.

Q: If you have two points and conic angles theta 1 and theta 2 have a difference of 180 degrees, how do…

A:

Q: Consider a particle traveling clockwise on the elliptical path                              x2/ 100…

A: Given: x2100+y225=1  or  x2102+y252=1 Leaving point of the particle from the orbit (−8,3)

Q: 8) (Section 10.7) Eliminate the parameter and find the correspond rectangular equation for the set…

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Q: The knuckleball is one of the most exotic pitches in baseball. Batters describe the ball as…

A: The left/right position of the ball when thrown is given by the following function:…

Q: 2. \ Evaluate •V4-2² dydx + dydx 2x-r2 using polar coordinates.

A: We have to evaluate the integral using polar coordinates.

Q: Find the differential equation of the family of ellipses with center at the origin a and the major…

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Q: Give each rule for counterclockwise rotation about the origin 90°: (x,y)

A: To rotate a figure each point of figure rotate in given direction.

Q: In math land, there is a clock. The hour hand of this clock is 1 ft long. However, the clock is…

A:

Q: 4 4. a) Identify the conic section given by the polar equation and also determine 1-cos e its…

A: We convert the equation into rectangular form first This is a parabola.

Q: EXAMPLE 3 Find parametric equations for the tangent line to the helix with parametric equations X =…

A: The vector equation of the curve isrt=⟨5cost,2sint,t⟩Therefore r't=⟨−5sint,2cost,1⟩The parameter…

Q: 6. Find the image equation of the line -2x +y + 3 = 0 under the rotation about C = (1, 1) at an…

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Q: Describe the graph of the equation. r = 7 cos ti – 18 sin t j+ k O An ellipse in the planex = 1,…

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Q: Sketch a graph of the helix r(t) = (- cos(2πt), 4 sin(2πt), 3t), listing the rotation direction,…

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Q: Give each rule for counterclockwise rotation about the origin 270°: (x,y)

A: Given Rule for counterclockwise rotation about the origin 270°: (x,y)

Q: slime mold grows in a spiral pattern with polar radius . If the mold grows by continuing the spiral…

A: We have to find the Cartesian location of the endpoint at given angular velocity.

Q: 1) reflection are equivalent to a rotation. True or False: Three consecutive reflections across…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: the Image tion of theT line 2x ty -1=0 under the rotation about wんat is equati the point (i,!) angle…

A: What is the image equation of the line 2x+y-1=0 under the rotation about the point (1,1) at an angle…

Q: coordinates of A(-11.5, 9), B(14, 8), and C(6, -7). What are the coordinates of its image after a…

A: Given data:     The first point is: A=(x1,y1)=(-11.5,9). The second point is: B=(x2,y2)=(14,8). The…

Q: What is the image equation of the line 2x+y-1=O under the rotation about the point (1, -1) at an…

A:

Q: 10. What will be the coordinates of point T after a 180* rotation about the origin?

A: Given coordinates of RSTU R (2,5) S (7,7) T (6,4) U (1,2)

Q: Graph XY with endpoints X( 3, 1) and Y(4, - 5) and its image after the composition. Rotation: 270°…

A: Given: X-3, 1 and Y4,-5 To find the graph of rotation is 270° about the origin and reflection point…

Q: The center of a windmill is (0, 0) and it has 5 blades, each 1 meter in length. A point P is at the…

A: We will find relation between θ and position of point P . Then find values from graph

Q: 9. What will be the coordinates of point Nafter a 270 counterclockwise rotation about the origin?

A: When rotating a point 270° counterclockwise about the origin our point N(x,y) becomes N'(y,-x). This…

Q: Chapter 13, Section 13.7, Question 005 Find an equation for the tangent plane and parametric…

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Q: Consider the conic below a2 + 4xy+4y² – 2/5x + V5y = 0 and determine what is asked. 1)…

A: If we have a rotated conic with the general equation: Ax2 + Bxy + Cx2 + Dx + Ey + F = 0, then, we…

Q: Describe the graph of the equation. r = 6 cos ti - 10 sin tj + k major axis of length 6 parallel to…

A: The graph of the given parametric curve is:

Q: 6. Find the image equation of the line –2x + y + 3 = 0 under the rotation about C = (1, 1) at an…

A:

Q: 1) Find the parametric equations of the line that is tangent to circle x² + y² = 25 at point (3, -4)

A: Given, Equation of circle: x2 +y2=25 at a point (3,-4). now, parametric equation of the line is…

Q: Chapter 12, Section 12.1, Question 010 Describe the graph of the equation. r = 4 sin 6t i– 4 cos 6t…

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Q: If I have a pair of parametric equations  x=20cos(t) and y=10sin(t)  How can I increase the speed…

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Q: 9.45.) (a) Use the figure to show that x =r cos ø, y = r sin ø and x' = r cos( ø – 0),y' = r sin (4…

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