8000

Mathematics Calculus Level: Misc Level

Suppose that a motorboat is moving at 30 ft/sec when its motor suddenly quits,and that 5 seconds later the boat has slowed to 15 ft/sec.Assume that the resistance it encounters while coasting is proportional to its velocity.How far will the boat coast in all?




7997

Mathematics Calculus Level: Misc Level

Solve the initial value problem dy/dx = y3 ,y(0)=1

 

                                                   




7976

Mathematics Calculus Level: Misc Level

The total profit(,p,in dollars) for sales of ,x, machines is given by p(x)=-0.2x2+300x-200. Find the following;

a.The profit if 500 machines are sold.

b.How many machines must be sold for maximum profit?




7975

Mathematics Calculus Level: Misc Level

The monthly profit p (in dollars) that Jim makes on the sale of x mobile homes is determined by the formula p=x2+5x-50.Find the values of x for which Jim makes profit.




7974

Mathematics Calculus Level: Misc Level

Q 19;A company uses the cost function C (w)= 0.04 w2-6.0 w+ 275 to model the unit cost in dollars for producing w widgets. Find;

a.How many widgets the company needs to make to achieve minimum unit cost?

b.What is the minimum unit cost?




7973

Mathematics Calculus Level: Misc Level

A soccer ball is kicked straight up with an initial velocity of 32 ft.per second. Its height above the earth is given by s(t )= -16t+32t, where,s, is the height in ft. at any time,t,seconds.

a.What is the maximum height reached by the ball?

b.How long after it was thrown up the ball reaches its maximum height?




7972

Mathematics Calculus Level: Misc Level

Find the minimum or maximum value of y in each of the following functions;

a) y=33-x2

b) y= x2- 2x + 5


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