Suppose that a = x(t) and y = y(t) are both functions of t. If y'+ xy - 3x =65, and dy/ dt = -1 when x = -5 and y = -5, what is da / dt? dx / dt =A kite 100 ft above the ground moves horizontally at a speed of 8 ft/s. At what rate is the angle between the string and the horizontal decreasing when 250 ft of string has been let out? Write your answer as a positive number since the word decreasing already means negative. Rate: 2 rad/s 175Air is being pumped into a spherical balloon so that its volume increases at a rate of 60 cm3 /s. How fast is the surface area of the balloon increasing when its radius is 18 cm? Recall that a ball of radius r has volume V = = wr and surface area S = 4mr2. Rate: 2.59 cm sA trough is 4ft long and its ends have the shape of isosceles triangles that are 3 ft across at the top and have a height of 3 ft. If the trough is being filled with water at a rate of 3 fts / min, how fast is the water level rising when the wate is 3 in deep? Be sure to convert inches to feet before you plug in. Rate: W/ N ft /minA potter forms a piece of clay into a right circular cylinder. As she rolls it, the height h of the cylinder increases and the radius r decreases. Assume that no clay is lost in the process. Suppose the height of the cylinder is increasing by 0.6 centimeters per second. What is the rate at which the radius is changing when the radius is 7 centimeters and the height is 12 centimeters? 0.055 cm (Include help (units) with your answer.) secA point P is moving along the curve whose equation is y - 4x . How fast is the distance between P and the point (3,0) changing at the instant when P is at (3, 12) if a is decreasing at the rate of 4 units/s at that instant