01. As the altitude of a space shuttle increases, an astronaut's weight decreases until a state of weightlessness is achieved. The weight of a125 lbastronaut at an altitude ofxkilometers above the sea level is given by

w = 125 (

64006400 + x

)2, at what altitude is the astronaut's weight less than5 lb?

Explain your steps that you have used during the calculation to solve the problem.

02. Findcifc = sin x1 + cos x. Explain your steps that you have used during the calculation to solve the problem.

03. If a projectile is fired from ground level with an initial velocity ofvft/secand at an angle of, then the rangeRof the projectile is given by

R =

v2 16

sin cosfor0 < <

2 .Find the rate of change ofRwith respect to. Explain your steps that you have used during the calculation to solve the problem.

04. Evaluatecos35t sin 5t dt. Explain your steps that you have used during the calculation to solve the problem.

05.Findf(x)if(x) = ( 7x + x2 + 6)4. Explain your steps that you have used during the calculation to solve the problem.