13. Find the image of CD with C(0, 4) and D(3, 4) under a rotation of 90° about the origin.

Q: Q17:- In polar coordinates prove that** 第。

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Q: Chapter 12, Section 12.3, Question 006 Find the arc length of the parametric curve. x = 6 cos t, y =…

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Q: 12/2 Use polar coordinates to evaluate dydx. 3 0. (x² + y²)²

A: To convert cartesian coordinates to polar coordinates , put x=rcosθ, y=rsinθ , dydx=rdrdθ So,…

Q: 12. What will be the coordinates of point A after a 90 clockwise rotation about the origin?

A: Given coordinates of A A ( 2, -3 ) for 90 degree clockwise rotation  (x,y)→(y,-x)

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

A:

Q: Determine the appropriate rotation formulas to use so that the new equation contains no xy-term.

A: Definition used -                                Ax2+Bxy+Cy2+Dx+Ey+F=0 , B≠0…

Q: If there is a 60° angle from the positive x-axis to the positive x′-axis, explain how to obtain the…

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Q: What do I do after substituting the expressions for x and y from the rotation formulas into the…

A: The rotation formulas for co-ordinates are if the coordinate is (x,y) then rotate the axis into 90°…

Q: 3. Deduce from the orbit equation (1 + e)ro 1 + e cos 0 that a planet is closest to its sun when 0 =…

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Q: Write a polar equation for the conic with the given characteristics. e = 1.6; directrix: y = 4 6.4…

A: Given :  Eccentricity,   e=1.6       and  Directrix,         y=4

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

A: To graph r  = 11 + 2 cos u.

Q: The polar equation 9 cos 0 + 2 sin 0 = X + 1 9x + 2y 1 9y + 2x = 1 9x + 2y = x² + y² || || 1 - r in…

A: To find  the cartesian form of the given polar equation.

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

A: The resulting image is perpendicular to the given line.

Q: Suppose that A and B are rotations of 180° about the points a and b,respectively. What is A followed…

A: Let Let A be the rotation of 180 degree about point a. Then a is midpoint of P and f(P). It follows…

Q: 7) What will be the coordinates of K' after a +90 degree rotation about the origin? Use parentheses.…

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Q: 3. Locate the CENTER of the rotation that was used to rotate AABC onto AA'B'C'. SHOW WORK on the…

A: This can be done by geometric construction and analytical method.

Q: Evaluate the polar coordinate E| 4r2 cos 0 rdrd0.

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Q: Plot the points with polar coordinates 4, and 3, using the pencil. 4 2n 3 4 0. 4. 9. 11n 9. 5T 4 4…

A: Topic:- Geometry

Q: 1. Change ſ, Lz xy dydx to polar form. 4-x2

A: We will answer the first question as we don't answer multiple question at a time. Please resubmit…

Q: Graph the image of the figure using the transfor and its image. 1) rotation 180° about the origin…

A: In the question it is asked to calculate the image of the given graph by taking a rotation of 180°,…

Q: What are the polar equations of the lines parallel to the liner cos (θ − π/3)= 1?

A: rcosθ-π3=1

Q: 11n Plot the points with polar coordinates 3, TT and using the pencil. 4 5n TE 6. 2 4 11n 6 6 5n 4.…

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Q: What is the minimum angle of rotation (in degrees) that will carry the six-sided star onto itself: I…

A: It is a 6 sided star that means it will redivided into 3 parts:⇒ we divide 360°( full rotation ) by…

Q: = Replace the polar equation 8r cos 0 + 9r sin 0 Cartesian equation. OA) 8x +9y = 1 B) 8y + 9x = 1…

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

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Q: Plot the polar point. (25. 푸) 4 2 3 4 2 4 4. 2. klN 3. 3.

A: To plot the given point

Q: Find the polar coovdinates rectanguar coordinak es the point whose (x,y)= LI,}) are

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Q: Find the exact length of the polar curve described by: T= 3e-8 on the Interval TSOS 9n.

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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: (2. Plot the points with polar coordinates 2, and -3, 2 using the pencil. 6. 3 3n 4 5n 6. 4. 7n 6.…

A: topic - plotting of points in polar coordinate system

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: Compute the length of the polar curve 702 for 0 s 0 < 4.

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Q: aluate the dnd to polar

A: Given that, ∫0a∫02a-x2xx2+y2dxdy Take x=rcosθ, y=rsinθ where 0≤θ≤2π.

Q: Determine the angle of rotation necessary to transform the equation in x and y into an equation in X…

A: Determine the angle of rotation necessary to transform the equation in x and y into an equation in X…

Q: Find polar coordinates for each of the seven points plotted in Figure 17. (Choose r > 0 and 0 in [0,…

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Q: If the parametric curve starts at (5, 10) when t = 0 and ends at (3, 8) at t = 1, then find a, b, c,…

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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: 2. Use polar coordinates to evaluate 2 1. √4+7++5² dy dz. Jo

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Q: What is the rotation that translates AWXY to ΔW 'ΧΎ'?

A: W'X' Side of W'X'Y' triangle is Perpendicular to WX side of WXY Triangle.

Q: What solid of rotation is created here if the axis of rotation is the x-axis? -2

A: to find:- type of solid generated after rotation about the x-axis.

Q: The rotation about the origin at an angle e=180° is defined by (ху)-(ху) (ху)-(ух) O (x.y)->(x,-y)…

A: The rotation about the origin at an angle 180° is defined by :-

Q: find the volu me of the o bócct Caused by the rotation oftne bouncled ared be twen y= aQ ,y=X…

A: Integrals and derivatives are considered as the inverses of each other. For example if we have a…

Q: Find the length of the curve: r = /1+ cos(20),0ses 2n

A: The length of the curve is given by the formula ∫abr2+drdθ2dθ  ,       where a≤θ≤b

Q: (B) if y = -x sketch in polar

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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: Sketch the curve r= cos 2θ

A: Symmetric test for polar coordinates r=f(θ): If f(θ)=f(-θ) then graph is symmetric about polar…

Q: Write a polar equation of the formr cos(0 – 0) = ro for the line x - V3y = 2.

A: We have to solve given problem: