Good evening, can you help with those questions

1.

Find the derivative of y with respect to s. y = sec (3s3 + 4) dy = dsA balloon is rising vertically above a level, straight road at a constant rate of 4 ft/sec. Just s(t) is increasing by ft/ sec. when the balloon is 48 it above the ground, a bicycle moving at a constant rate of 15 ft/sec (Simplify your answer.) passes under it. How fast is the distance s(t) between the bicycle and balloon increasing 3 seconds later? 37(t ) s( t )On a morning of a day when the sun will pass directly overhead, the shadow of a 92-ft building on level ground is 69 ft long. At the moment in question, the angle 0 the sun makes with the ground is increasing at the rate of 0.26"/min. At what rate is the shadow decreasing? Remember to use radians in your calculations. Express your answer in inches per minute. The shadow is decreasing at inches per minute (Round to one decimal place as needed.)(a) Find the slope of the curve y = x - 9x at the given point P(2, - 10) by finding the limiting value of the slope of the secants through P. (b) Find an equation of the tangent line to the curve at P(2, - 10) (a) The slope of the curve at P(2, - 10) isFind (a) the slope of the curve at the given point P. and (b) an equation of the tangent line at P. y = 1x, P(4,2) a. The slope of the curve at the given point is (Simplify your answer.)For the given function f(x) and values of L, c, and & > 0 find the largest open interval about c on which the inequality |f(x) - LI holds. Then determine the largest value for 6 > 0 such that 0 0 such that 0 [(x) = L| 0, find L = lim f(x) X-C Then determine the largest value for 6 > 0 such that 0