Hi everyone,

I need help for solve these problems.

41. The volume of a falling spherical raindrop grows at a rate which is proportional to the surface area of the drop. Show that the radius of the drop increases at a constant rate.

42. The temperature of the atmosphere decreases with altitude at a rate of 2^{o}C per kilometer at the top of a certain cliff. A hang-glider pilot finds that the outside temperature is rising at the rate of (10^{-4})^{o}C per second. How fast is the glider falling?

43. For temperatures in the range [-50, 150] (degrees Celsius), the pressure in a certain closed container of gas changes linearly with the temperature. Suppose that the 40^{o}increase in temperature causes the pressure to increase by 30 millibars. (A millibar is one-thousandth of the average atmospheric pressure at sea level.)

(a) What is the rate of change of pressure with respect to temperature?

(b) What change of temperature would cause the pressure to drop by 9 millibars?

44. Find the rate of change of the length of an edge of a cube with respect to its surface area.

45. The organismamoebus rectilineusalways maintains the shape of a right triangle whose area is 10^{-6}square millimeters. Find the rate of change of the perimeter at a moment when the organism is isosceles and one of the legs is growing at 10^{-4}millimeters per second.

I tried to solve it but i did not succeed it. Maybe you can help me?

Thank you!

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