Calculus Answers

Write the Taylor polynomial T5(x) for the function f(x)=cos(x) centered at x=0.
Answer: T5(x)=

The manager of a large apartment complex knows from experience that 80 units will be occupied if the rent is 324 dollars per month. A market survey suggests that, on the av- erage, one additional unit will remain vacant for each 6 dollar increase in rent. Similarly, one additional unit will be occupied for each 6 dollar decrease in rent. What rent should the manager charge to maximize revenue?

11. (1 pt) The manager of a large apartment complex knows from experience that 80 units will be occupied if the rent is 324 dollars per month. A market survey suggests that, on the av- erage, one additional unit will remain vacant for each 6 dollar increase in rent. Similarly, one additional unit will be occupied for each 6 dollar decrease in rent. What rent should the manager charge to maximize revenue?

the dot product of two perpendicular vectors is?????

Find the real numbers a and b such that the equation is true.
(a+6) + 2bi=6-5i

A hot-air balloon is 150 feet above the ground when a motorcycle passes directly beneath it (traveling in a straight line on a horizontal road). The motorcycle is traveling at 40 mph. If the balloon is rising vertically at a rate of 10 ft/sec, what is the rate of change of the distance between the balloon and the motorcycle ten seconds later? (Needed - mathematical model and derivative)

Assume that all barrels of wine have precisely cylindrical shape of
radius r and height h. The wine merchant prices each barrel by the length d of a dipstick that
can be inserted diagonally through a hole in the center of the top disc of the barrel and that
reaches the edge of the bottom. For a fixed length d, determine the ratio r/h that maximizes
the volume of the barrel.

a trough is 10 ft long and its ends have the shape of isosceles triangles that are 3 ft across the top and have a height of 1 ft. if the trough is being filled with water at a rate of 12 feet cubed per min. how fast is the water level rising when the water is 6 inches deep?

Find the derivative of the following:
y=(8-2x^2)(4-x)