Scientists and engineers often use polar equations to model the motion of satellites in earth orbit. Let's consider a satellite whose orbit is modeled by the equation

Q: Write Parametric Equations to Represent a Curve for the given curve for the given definitio:

A: In question number 32, we are asked to form only parametric equations, that means equation of x and…

Q: Suppose a baseball is thrown at 30 ft/s at a 60degree angle to the  horizontal from a height of 4 ft…

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Q: Explain how to convert from a rectangular equation to a polar equation.

A: In order to convert rectangular equation to polar equation, substitute x=rcosθ  and  y=rsinθ in the…

Q: In two or more complete sentences, explain how to find the time it takes for a rocket following the…

A: We will find the time taken by the rocket to hits the ground as shown below

Q: Graph the pair of parametric equations with the aid of a graphing calculator. (Hint: don't forget to…

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Q: find a set of parametric equations to represent the graph of the rectangular equation using and…

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Q: Determine the 3 rectangular equations of the tangent lines at the indicated points (black dots)on…

A: the given polar equation is ; r=2cos(3θ)

Q: Find two different parametric equations for rectangular equation. y= 2x2-8.

A: Given that, y=2x2-8

Q: Convert the equation r = 4 sec (0) from polar coordinates to rectangular coordinates. (Express…

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Q: * ifr = 8 sece then the cartesian equation is

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Q: The path of a projectile that is launched h feet above the ground with an initial velocity of v0…

A: x=100 cos 40t=76.6t and y=6+100 sin 40t-16t2=6+64.3t-16t2 describe the position of the ball as a…

Q: Explain parametric equations.

A: Query- Explain parametric equations. Answer- Parametric equation, a type of equation that employs an…

Q: Which equation in rectangular coordinates has the same graph as the equation r in polar sin 0-cos 0…

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Q: Construct parametric equations describing the graph of the line passing through the following…

A: Topic = Coordinate geometry

Q: Sketch the graph of r = -2 sin 0. %3D What is the rectangular equation for this graph?

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Q: In two or more complete sentences, explain how to find the time it takes for a rocket following the…

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Q: What are ( in polar coordinates ) the zeroes of the equation r = 8 sin ( θ ) + 8 ?

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Q: If you are given parametric equations of a curve, what is the formula for finding its arclength?…

A: To write the arc length formula for the given types of curves.

Q: parabolic antenna follows the equation y^2 + 4x 0. Which of the following is the coordinates of its…

A: Topic = Parabola

Q: What equations relate polar coordinates to Cartesian coordinates?

A: We have to write the equation which relate the polar coordinates to the Cartesian coordinates. We…

Q: Graph the rectangular equation (x+3)^2+y^2=9 and then choose one point to start with rectangular…

A: We need to graph the rectangular equation: x+32+y2=9 We know that, x-h2+y-k2=r2 is the equation of…

Q: Write an equation of the line tangent to this curve at point A r = −8 sin(θ)  polar coordinate…

A: Given query is to find the equation of the tangent line

Q: Convert (x + 2)² + y² = 4 to polar form. Drag and drop an answer to each box to correctly complete…

A: Let's find.

Q: -2-j3 3+j4 (final answer should be in polar form)

A: We need to evaluate complex number,  -2 - j33 + j4 First we need to multiply and divide by complex…

Q: Graph polar equation r2 = 16 sin 2θ. Be sure to test for symmetry.

A: Given polar equation is r2=16sin2θ To test for symmetry of given polar equation and graph the polar…

Q: if you have a parametric equation grapher, graph the equations over the given intervals x = 3 cos t…

A: Given a parametric equation

Q: Convert the polar equation r sin (θ - π/4) = 2 to a rectangular equation. Then determine the graph’s…

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Q: Find the equation in polar coordinates of the line through the origin with slope

A: The line passing through origin and slope 13

Q: Scientists and engineers often use polar equations to model the motion of satellites in earth orbit.…

A: Given that r=220004-cosθ. Here 4-cosθ is maximum when cosθ=-1.

Q: 5. Solve the equation z = 2 – 51. Use radians and leave your answer in polar form. Round numbers to…

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Q: What equations relate polar coordinates to Cartesian coordinates? Why might you want to change from…

A: Equations relate polar coordinates to Cartesian coordinates are, x=rcosθ & y=rsinθ

Q: : The position of a particle is given by the parametric equations x = sin t and y = cos t where t…

A: If the particle moves twice as fast around the circle then we multiply the parameter by 2

Q: Find parametric equations for the given curve. Line through (1, -2) with slope 3

A: we know that equation of line which passes through pointx1,y1 and slope is m given by y-y1=mx-x1…

Q: 8. First graph the polar curve r= sin(20) on 0<60<2n and plot the point on the curve that…

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Q: Find parametric equations for the line of slope 2 that passes through the point 13, 52 .

A: Equation of line in the parametric form form when it is passes through point x1,y1 and slope 'r' is…

Q: if you have a parametric equation grapher, graph the equations over the given intervals x = 2 cos t…

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Q: 2) Eliminate the parameters and write as a Cartesian equation. Then graph your result, including the…

A: Given equation is : x=sin12θ     .........1y=cos12θ    ...............2

Q: A very tall light standard is swaying in an east-west direction in a strong wind. An observer notes…

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Q: Convert the equation of the curve x^2−y^2=1 to polar coordinates. Your answer should be in the form…

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Q: Test for symmetry and then graph polar equation r = 2 + 3 sin 2θ.

A: r=2+3sin2θ Replace r, θ with -r, -θ, we get -r=2+3sin2-θ⇒-r=2-3sin2θ⇒r=-2+3sin2θ Which is not same…

Q: Select two different sets of parametric equations for the rectangular equation. 7 y =

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Q: 5 Graph r=5-5 sin0, r=7-6cos 0, and r=2+4cos0 on the same axis system. (polar)

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Q: [Question 7] Find the Cartesian coordinates of the point whose polar coordinates are (- 3,31/2): 212

A: we know that relationship between Cartesian coordinate (x, y)  and polar coordinate (r, θ) are x = r…

Q: 4. Change to an equiv- 1+2 sin 0 alent rectangular equation.

A: