Question

In: Math

If a circle C with radius 1 rolls along the outside of the circle x2 +...

If a circle C with radius 1 rolls along the outside of the circle x2 + y2 = 36, a fixed point P on C traces out a curve called an epicycloid, with parametric equations x = 7 cos(t) − cos(7t), y = 7 sin(t) − sin(7t). Graph the epicycloid.

Find the area it encloses.

Solutions

Expert Solution

From Green's Theorem, the area of a region enclosed by a curve

[Trignometric formula used

]


Related Solutions

an object is moving along a circle of radius 400.0m with a speed of 20.0m/s. the...
an object is moving along a circle of radius 400.0m with a speed of 20.0m/s. the centripetal force acting on the object is 500.0N a) find the mass of the object b) find the work done by the centripetal force c) what is the angular velocity of the object
Write a C++ program that prompts the user for the radius of a circle and then...
Write a C++ program that prompts the user for the radius of a circle and then calls inline function circleArea to calculate the area of that circle. It should do it repeatedly until the user enters -1. Use the constant value 3.14159 for π Sample: Enter the radius of your circle (-1 to end): 1 Area of circle with radius 1 is 3.14159 Enter the radius of your circle (-1 to end): 2 Area of circle with radius 2 is...
Let C be the boundary of the quarter circle with radius 1, oriented counterclockwise (Figure 1)....
Let C be the boundary of the quarter circle with radius 1, oriented counterclockwise (Figure 1). Evaluate H C(ex + y2) dx + (ey + x2) dy
If C is the part of the circle (x2)2+(y2)2=1(x2)2+(y2)2=1 in the first quadrant, find the following...
If C is the part of the circle (x2)2+(y2)2=1(x2)2+(y2)2=1 in the first quadrant, find the following line integral with respect to arc length. ∫C(8x−6y)ds
1) A circle of radius r has area A = π r2. If a random circle...
1) A circle of radius r has area A = π r2. If a random circle has a radius that is evenly distributed in the interval (0, 1), what are the mean and variance of the area of ​​the circle? choose the correct answer A) 1/3 and 1/12 B) Pi/3 and 1/12 C) Pi/3 and 1/5 D) Pi/3 and (4/45)*Pi^2
1. If the radius r of a circle is measured to be r  0.325 +\-...
1. If the radius r of a circle is measured to be r  0.325 +\- 0.001 m, then calculate the area of the circle A =3.14 r^2, as well as the uncertainty in the area. 2. Explain the difference between precision and accuracy. 3. Do systematic errors affect precision or accuracy? Do random errors affect precision or accuracy?
Parametrize the osculating circle to the parabola y = x2 at x = -1
Parametrize the osculating circle to the parabola y = x2 at x = -1
Write c code program for the following Write a function, circle, which takes the radius of...
Write c code program for the following Write a function, circle, which takes the radius of a circle from the main function and assign the area of the circle to the variable, area, and the perimeter of the circle to the variable, perimeter. Hint: The function should have three variables as input. Since the contents of the variables are to be modified by a function, it is necessary to use pointers. Please type out the full usable program. Thank you.
A circle of radius r has area A = πr2. If a random circle has a...
A circle of radius r has area A = πr2. If a random circle has a radius that is uniformly distributed on the interval (0, 1), what are the mean and variance of the area of the circle? Change the distribution of the radius to an exponential distribution with paramter β = 2. Also find the probability that the area of the circle exceeds 3, if it is known that the area exceeds 2.
1) A circle with a radius of 0.3 meters is placed in the x-y plane in...
1) A circle with a radius of 0.3 meters is placed in the x-y plane in a magnetic field directed in the -z direction. It is wound once and its resistance is 6 Ohms. The initial magnetic field is 0.8 Tesla. The magnetic field is then changed in 0.6 s and the average induced current is 0.04 amps running counter-clockwise. First, find the final magnetic field to needed to induce this average current. Then, the magnetic field (still in the...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT