Show that y=cos(t)y=cos(t) is a solution to (dydt)2=1−y2(dydt)2=1−y2. Enter your answers below in terms of the independent variable tt in the order in which the terms were given. Be sure you can justify your answer.

Find the arc length parameter along the given curve from the point where tequals=0 by evaluating the integral s(t)equals=integral from 0 to t startabsolutevalue bold v left parenthesis tau right parenthesis endabsolutevalue d tau∫0tv(τ) dτ. then find the length of the indicated portion of the curve r(t)equals=1010cosine tcost iplus+1010sine tsint jplus+88t k, where 0less than or equals≤tless than or equals≤startfraction pi over 3 endfraction π 3.

Determine the volume of a cylinder bucket if the diameter is 8.5 in. and the height is 11.5 in.

1) what is the measure of the exterior angle, ∠uvw ? 2) in triangle man, what is the measure of the exterior angle at n (in degrees)?