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?
Mathematics Calculus Level: Misc Level
Solve the initial value problem dy/dx = y3 ,y(0)=1
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?
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.
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?
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 )= -16t2 +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?
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
