The figure shows a 10-foot ladder leaning against a wall. (a) Use the Pythagorean theorem to find an equation relating x and y. (b) Suppose that the foot of the ladder is being pulled along the ground at the rate of 3 feet per second. How fast is the top end of the ladder sliding down the wall at the time when the foot of the ladder is 7 feet from the 10 dy at the time when dt dx wall? That is, what is =3 and x = 7? dt 2+y = 100. (a) The equation is dy dt (b) =(Type an exact answer, using radicals as needed.)

A kite glides horizontally at an altitude of 20 m while we unspool the string. Consequently, the angle made between the string and the horizon diminishes. We would like to determine the rate at which this angle decreases once 40 m of string has been unspooled, given that, at that instant, the kite's horizontal velocity is 1 m/s. To solve this problem, let be the angle in radians made between the string and the horizontal, the kite's horizontal position in meters since being attached to the ground, and t the time in seconds. We further suppose that the string is straight and taut. (a) Sketch a diagram of this question and use it to express as a function of a. 0 = tan (20/x) (b) What is the value of at the moment in question? Give the exact value. x = 20*sqrt(3) (c) What is the value of de dt rad -1/60 sec(1/sqrt(3))^2 m do at the same moment? Give the exact value, paying attention to the sign. dt rad/s

Let y(t) be the height (in meters) after time t (in seconds) of a rover that is landing on some other planet with the help of a parachute. Taking into account gravity and air resistance, physicists suggest that the air resistance is proportional to velocity. Further data suggests that the fall can be modeled by y"=-4-3y'. If the parachute is released at a height of 600m with an initial velocity of 0m/s, what is its height after t seconds? What is its terminal velocity? y(t) = The terminal velocity is m/s. m/s

On the moon, all free-fall distance functions are of the form s(t) = 0.8112, where t is in seconds and s is in meters. An P object is dropped from a height of 350 meters above the moon. After 6 sec, consider parts (a) through (d) below. a) How far has the object fallen? b) How fast is it traveling? c) What is its acceleration? d) Explain the meaning of the second derivative of this free-fall function. FEE a) The object has fallen m. (Type an integer or decimal rounded to two decimal places as needed.)