Download I`RE-CALCULUS NAME QUADRATIC APPLICATIONS DATE 1. The

I’RE-CALCULUS
QUADRATIC APPLICATIONS
NAME
DATE
1. The sum of a number and its square is 56. Find the number
2. The sum of two numbers is 12. Find the two numbers if their product is to be a maximum.
3. Maximizing Revenue. The manufacturer of a gas clothes dryer has found that, when the unit price isp dollars,
the revenue R (in dollars) is: R(p) = —4p
2 + 400p
What unit price should be established for the dryer to maximize revenue?
What is the maximum revenue?
4. Demand Equation. The price p and the quantityx sold of a certain product obey the demand equation
p=—x+1OO;
0x600
a. Express the revenue as a function of x. (R
=
xp)
b. What is the revenue if 200 units are sold?
c. What quantity x maximizes revenue? What is the maximum revenue?
d. What price should the company charge to maximize revenue?
5. Enclosing a rectangular field. David has 400 yards available for fencing and wishes to enclose a rectangular
area.
a. Express the area A of the rectangle as a function of the width x of the rectangle.
b. For what value of x is the area largest?
c. What is the maximum area?
6. A farmer with 4000 meters of fencing wants to enclose a rectangular plot that borders on a river. If the farmer
does not fence the side along the river, what is the largest area that can be enclosed? (See the flaure)
4
:x
4000
7. Engineering. A suspension bridge has twin towers that extend 75 meters above the road surface and are 400
meters apart. The cables form a parabolic shape and are suspended from the tops of the towers. The cables touch
the road surface at the center of the bridge. Find the height of the cables 100 meters from the center.
8. A projectile is fired from a cliff 200 feet above the water and moves in the path of a parabola. The height of the
2
—32x
+ x + 200, where x is the horizontal distance.
projectile is given by: h(x)
2
.
.
=
a.
How far from the bridge is the projectile at a maximum height?
b.
Find the maximum height.
c.
How far from the base of the cliff will the projectile strike the water?
2x