Find the volume of the solid generated when the region enclo…
Find the volume of the solid generated when the region enclosed by y=6, y=x, x=1, and x=4{“version”:”1.1″,”math”:”y=6, y=x, x=1, and x=4″} is revolved about the x-axis. Note: Leave your answer in terms of π{“version”:”1.1″,”math”:”π”}.
Read DetailsConsider the following set of parametric equations: x (…
Consider the following set of parametric equations: x ( t ) = 4 t y ( t ) = 8 t + 5 {“version”:”1.1″,”math”:”\begin{align*} x(t) &= 4\sqrt{t} \\ y(t) &= 8t+5 \end{align*}”} Part A — 5 points Find the derivative dydx{“version”:”1.1″,”math”:”dydx”} in terms of t{“version”:”1.1″,”math”:”t”} using parametric differentiation methods. Write your answer in the first answer box. Part B — 5 points Eliminate the parameter t{“version”:”1.1″,”math”:”t”} to obtain an equation for y{“version”:”1.1″,”math”:”y”} in terms of x{“version”:”1.1″,”math”:”x”}. Write your answer in the second answer box. Note: This part does not utilize the result from Part A. Part C — 5 points Using the original parametric equations as a reference, convert your answer from Part B from a function of t{“version”:”1.1″,”math”:”t”} to a function of x{“version”:”1.1″,”math”:”x”}. Take a standard derivative of this and write your answer in the third answer box.
Read DetailsConsider the function f(x) = x13{“version”:”1.1″,”math”:”f(x…
Consider the function f(x) = x13{“version”:”1.1″,”math”:”f(x) = x13″} between y=0 and y=1{“version”:”1.1″,”math”:”y=0 and y=1″}. Find the surface area generated by revolving this arc about the y-axis. Note: Leave your answer in terms of π{“version”:”1.1″,”math”:”π”}.
Read DetailsPart A — 4 points Write a polar equation of the parabola wh…
Part A — 4 points Write a polar equation of the parabola whose focus is at the pole and vertex at 10,0{“version”:”1.1″,”math”:”10,0″}. Part B — 4 points Is the polar point 403,π3{“version”:”1.1″,”math”:”403,π3″} on the parabola?
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