Question 80407
1. The length of a rectangle is 1 cm longer than its width. If the diagonal of the rectangle is 4 cm, what are the dimension of the rectangle?
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Let the width be "x"; then the length is "x+1"
Use Pythagoras to find x:
x^2 + (x+1)^2 = 4^2
2x^2+2x+1=16
2x^2+2x-15=0
x=[-2+-sqrt(4-4*2*-15]/4
x=[-2+-sqrt124]/4
x=[-2+-2sqrt31]/4
x=[-1+-sqrt31]/2
Positive answer: x=[-1+sqrt31]/2=2.284 cm
x+1=3.284 cm
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2. The equation h(t)=-16t^2+112t gives the height of an arrow, shot upward from the ground with an initial velocity of 112ft/s where t is the time after the arrow leaves the ground. Find the time it takes for the arrow to reach a a height of 120 ft.
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120=-16t^2+112t
16t^2-112t+120=0
2t^2-14t+15=0
t=[14+-sqrt(196-4*2*15]/4
t=[14+-sqrt76]/4
t=[14+-2sqrt19]/4
t=[7+-sqrt19]/2
Positive answer:1.32 seconds for it to reach a height of 120 ft.
Another answer is 5.68 seconds which tells you when it is again at 120 ft
above the ground on it's way down to the ground.
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3. A ball is throw upward from th roof of a building 100 m tall with an inital velocity of 20 m/s. When will the ball reach a height of 80 m? 
This requires a different formula because the measurements are in meters.
But the procedure is the same.
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4. The demand equation for a certain type of printer is given by 
D=-200p+35,000
The supply equation is predicted to be 
S=-p^2+400p-20,000
Find the equilbrium price.
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Equilibrium occurs when supply equals demand
-200p+35000= -p^2+400p-20000
Rearrange and solve the quadratic equation for "p".
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Cheers,
Stan H.