1) A runner sprints around a circular track of radius 100 m at a constant speed of 7 m/s. The runner's friend is standing at a distance 200 m from the center of the track. How fast is the distance between the friends changing when the distance between them is 200 m ?
2) If two resistors with resistances R1 and R2 are connected in parallel, as in the figure below, then the total resistance R, measured in ohms (Ω). If R1 and R2 are
increasing at rates of 0.3 Ω/s and 0.2 Ω/s, respectively, how fast is R changing when R1 = 90 Ω and R2 = 120 Ω? (Round to 3 decimal places.)
3) y = sin^(-1) x
4) A water trough is 10 m long and a cross-section has the shape of an isosceles trapezoid that is 30 cm wide at the bottom, 80 cm wide at the top, and has height 50 cm. If the trough is being filled with water at the rate of 0.2m^3/min, how fast is the water level rising when the water is 30 cm deep?
5) prove that the function f(x ) = x^101 + x^51 + x + 1