To prepare astronauts for the experience of zero gravity (technically, microgravity) in space, NASA uses a specially designed jet. A pilot accelerates the plane upward to an altitude of approximately 9,000 meters and then reduces power. During the time of reduced power, the plane is in freefall and the astronauts experience microgravity. The altitude A(t), in meters, of the plane t seconds after power was reduced can be approximated by A(t) = −4.9t2 + 90t + 9,000. The graph is shown as follows. A coordinate plane is given with a plane flying along a curve. The horizontal axis is labeled "Time (seconds)". The vertical axis is labeled "Altitude (meters)". The curve starts at approximately (−5, 8400), goes up and right becoming less steep, passes

When a bus pass from Albuquerque to Los Alamos is priced at p dollars, a bus company takes in a monthly revenue of R(p) = 1.5p − 0.01p2 (in thousands of dollars). (a) Estimate R if the price rises from $50 to $53. (b) If p = 80, how will revenue be affected by a small increase in price? Explain using the Linear Approximation.

In winter, cold wind blows from North to South which brings dramatic decrease in temper- atures in Oregon. At t = 0 the temperature in Portland is 30° F and directly south of it, in Corvallis the temperature is 40° F. Joe Smith starts driving from Portland to Corvallis (at t = 0) with a temperature probe attached to the car antenna. The speed of his car is constant at 50 miles/hr throughout his journey and is exactly equal to the speed of the wind which is blowing southwards. The probe attached to the car antenna records an increase in temperature at the rate of 1º F/hr as the car moves southwards. Assuming linear temperature variation between Portland and Corvallis, find the temperature in Corvallis when Joe Smith arrives there. Assume distance between Portland and Corvallis is 100 miles Clearly indicate each term and its value in equations/laws you are using.

A ball is thrown vertically into the air has its height above ground given by  y(t)=112t−16t2 , where t is given in seconds and y is its height in feet. Find the maximum height of the ball.