Calculus Answers

A boy in a hot air balloon drops his cellular phone when the balloon is 150 ft above the ground and rising at the rate of 10 ft/s.

a.How long will it take the cellular phone to reach the ground?

b. With what speed will it strike the ground?

of 10 genes studied in yeast, 7 are found to form a network of metabolic interactions. If this set of 7 genes was chosen arbitrarily from the 10 that were studied, how many different sets would be possible? Show your calculation and the reasoning.a

A stone is thrown vertically upward from the ground with an initial velocity of 40 ft/sec. 

 What is the height of the ball when its velocity is one-half the initial velocity?

Determine the half-life of the radioactive substance

Three cars arrive simultaneously at a four way stop and all want to proceed straight through the intersection. How many ways are there for this to happen if they proceed on at a time. Show a diagram with your explanation.

A cone of radius r centimetres and height h centimetres iss lowered first at a rate of 1 cm/s into a tall cylinder of radius R that is partially filled with water. How fast is the water level rising at the instant the cone is completely submerged?

Sketch the graph of f(x)=|x| where x belongs to R, state it domain and range.

Let f: R->R be defined by f(x)=x²+2 where R is the set of real numbers

(i) find the domain and range of f

(ii) is f one-to-one or onto ?

A baseball player is running from the second base to the third base at 20ft/sec. At what rate is his

distance from the home plate changing when he is 30ft from the third base. The baseball diamond

is a square 90ft on aside.

9) Use your value of x to calculate a value for 𝑒𝑥 from the first four

terms.

X = 1