Both a and y denote functions of t that are related by the equation y = 8x + 3. Use this equation and the given information that da/ dt = -8 to find dy/dt when x = -6. Answer:Suppose that a: : t) and y : y(t) are both functions oft. If y2+my3:B:9, and (y/tit = 1 when a: = 1 and y = 4, what is (gs/(1t? aim/(it: g; Suppose that x = x(t) and y = y(t) are both functions of t. If x' + xy = -3, and dx/ dt = 4 when x = 3 and y = -4, what is dy/ dt? dy/dt =(1 point) If the radius of a sphere is increasing at a constant rate of 3 cm/ sec, then the volume is increasing at a rate of y" Cling/SEC when the radius is 3 cm. Hint: E = E - a, and the volume ofa sphere is V 2 gm; The volume V of a right circular cylinder of radius r and height h is V = mr h. (a) How is av dt related to do if h is constant and r varies with time? (Enter dr as dr/dt.) dV dt (b) How is dy related to dh if r is constant and h varies with time? (Enter of dV dh as dh/dt.) dt (c) How is du related to dh and if both h and r vary with time? dV dt