While playing at the Nawaka Sevens, four of the rugby players are observed to be located at the corners such that it makes a perfect square with sides of length d. The coach has brought about a new technique to train players and it is observed that all the players move counterclockwise at the same speed towards the next rugby player, as shown in the Figure 1 below. Find the polar equation of a rugby player’s path as it spirals towards the centre of the square

Q: The propellers for a toy boat are manufactured by stamping out a rose with n petals and then bending…

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Q: Find a polar equation that has the same graph as the equation in x and y.(x - 1)2 + y2 = 1

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Q: Consider the conic section given by the polar equation 4 1-sin 0 r=

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Q: Sketch the graph of r² = 4cos2θ in polar coordinates.

A: To Sketch the graph of r² = 4cos2θ in polar coordinates.

Q: 4. Write down the name of the conic given by the polar curve r = 15 / (3 + 2 sine). Determine the…

A: We have to draw graph of given curve.

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: Use the identity cos 2θ = cos2 θ − sin2 θ to find a polar equation of the hyperbola x2 − y2 = 1.

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Q: Graph the line and conic section. r = 8/(1 - sin u)

A: We can convert this into rectangular form. Then,…

Q: Sketch the following polar rectangle. 2x = {(r,0): 4sr5,

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Q: Find a polar equation that has the same graph as the equation in x and y.y2 - x2 = 4

A: y2-x2=4

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: Identify the conic section and graph the polar equation: r = 2/(1 - cos θ)

A: The given polar equation is r=21-cosθ Here, the given equation can be ellipse, parabola and…

Q: Find a polar equation that has the same graph as the equation in x and y.x2 + y2 = 16

A: The polar coordinates of a point are given by x=rcosθ,y=rsinθ. For a circle with equation x2+y2=R2…

Q: Under what conditions can you find the length of a curver = ƒ(θ), a ≤ θ ≤ b, in the polar coordinate…

A: step 1 :           Conditions to find the length of the curver = f(θ) , ∝ ≤ θ ≤ B* The curve r =f(θ)…

Q: Find the analogous polar equation for horizontal lines in the xy-plane.

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Q: Write the name of the conics giver by poloar curve r=6/(2+sin(t)) a) Determine the vertices in the…

A: We need to write the name of the conics given by the polar curve r=6/(2+sin(t)). Also, we need to…

Q: Work out the product of 2cos60° x 3cos30° in polar and rectangular form.

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Q: Sketch the graph of the polar equation using symmetry, zeros, maximum r-values, and any other…

A: make a table value to graph the function

Q: 4. Write down the name of the conic given by the polar curve r = 15/( 2 sine). Determine the…

A: Given the polar curve is r=153+2sinθ

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: State the polar Equation of a Conic Section.

A: Polar equations of conic sections:  If the directrix is a distance d away, then the polar form of a…

Q: Write a polar equation of the form r sin(0-00) = ro for the line 3 x + y 1. 2mark dentify and draw…

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Q: ) Identify the conic section given by the polar equation r =

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Q: Graph the line and conic section. r = 8/(4 + cos u)

A: Graph the line and conic section. r = 8/(4 + cos u)

Q: compute the length of the polar curve.  The cardioid r = 1 − cos θ in Figure 16

A: compute the length of the polar curve.  The cardioid r = 1 − cos θ

Q: Sketch the graph of the polar equation.r2 = 4 cos 2θ (lemniscate)

A: The polar equation is,r2=4 cos 2θ

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: Find the distance between P1(1, –91°) and P2(3, 335°) on the polar plane.

A: We know that, Distance between two Cartesian coordinates is,  Distance , D=x2-x22+(y2-y1)2 We know…

Q: Consider the polar equation of a conic. Determine the eccentricity. -5 r = 1 + cos(0) e =

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Q: convert the given polar equation to a Cartesian equation. Write in the standard form of a conic if…

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Q: Consider the rose curve with polar equation r = cos(20), whose graph is shown below. 0.5 -0.8-0.4서…

A: An integral assigns numbers to functions in a way that describes displacement, area, volume, and…

Q: Find a polar equation that has the same x² - y² = 7 as graph

A: topic:- geometry

Q: compute the length of the polar curve. r = cos2 θ

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Q: If the original 2-D shape and the reflected image combine to form a new 2-D shape, what is the angle…

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Q: The propellers for a toy boat are manufactured by stamping out a rose with n petals and then bending…

A:

Q: Replace the Cartesian equations with equivalent polar equations and discusss its symmetries x2 + xy…

A: Given an equation in Cartesian form. We need to convert it into equivalent polar form and discuss…

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

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Q: Match the point in polar coordinates with either A, B, C, or D on the graph. 1)

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Q: Find a polar equation that has the same graph as the equation in x and y.y = 6x

A: Given y=6x To find a polar equation that has the same graph as the equation in x and y. The polar…

Q: Sketch the graph of the polar equation.r = 2θ, θ ≥ 0 (spiral)

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Q: 11. Find the rectangu lar coordin ates of a point whose polar coordinates are (4, 180).

A: Here we convert the rectangular coordinates into polar coordinates.

Q: What is the polar equation of a circle of radius a centered at the origin? Use this equation to…

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Q: Sketch a graph of r=(12)/2+4cos(theta). Use the graph to write a Cartesian equation for the conic

A: Consider the given: r=122+4cosθ

Q: Sketch the graph of the polar equation.r = 2θ, θ ≥ 0

A: The given polar curve is: r=2θ; θ≥0 Now, as θ changes r changes 2 times of it. That is:  θ      r 0…

Q: 4. (a) What is the composition of a 90 degree rotation about the origin, followed by a 90 degree…

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.