6. Consider the polar equation: r = 2-3 sin 0 (a) Graph the curve. (b) Write integral(s) representing the area in the first quad- rant which is inside the circle r = 6 and outside the above curve. (c) Write an integral representing the length of this curve. You do not need to calculate this integral.

Q: ye(2y*) dy

A: Given the integral I=∫ye2y2dy     ....(1)

Q: A curve with polar equation r = 42 6 sin(0) + 31 cos(0) y = has Cartesian equation:

A: cartesian equation is y=7−631x​Explanation:Step 1:given that r=6sinθ+31cosθ42​using cross…

Q: (10) Let r(t) = (e'cos 2t, et sin 2t, e2t) %3D a) The curve lies on a quadric surface. Give the…

A: Let y(t) = ( et cos 2t , et sin 2t , e2t ) . Then, we have to identify the quadric surface and it's…

Q: (10) Let r(t) = (e'cos 2t, e sin 2t, e2t) a) The curve lies on a quadric surface. Give the equation…

A: Given parametric equation is  rt=etcos2t,etsin2t,e2t           (i) Let us consider…

Q: Consider the polar curve given by the equation r(0) = 1 - sin(30). It is an example of what is…

A: Graph:

Q: 6. Consider the curves: r = 2+ cos 20 and r = 2+ sin 20, a) Sketch a graph of both curves on the…

A:

Q: Eliminate the parameter for the given parametric equations to write an equation in the form of y=…

A: Given x=ln t and y=et

Q: When graphing the polar equation r =3 cos(20) as Ø approaches from 0, the radius changes from ◆ to

A:

Q: Graph the curves having the following polar equations. (a) r² = sin(20). Explain how the curve…

A: (a) Given equation in polar coordinate is Noted that curve is symmetrical about the line ,also…

Q: 2. On February 10, 1990, high tide in Boston occurred at midnight. The water level at high tide was…

A: Given 1. High tide at midnight t=0. 2. Water level at high tide = 9.9 feet. 3. Low tide at 12 noon…

Q: 1 Sketch the curve r=-+sin0 cos 0 ,0 < 0<2n in the polar plane.

A: Any point on the Cartesian coordinate system is represented as x, y. Any point on the polar…