Question 85605: The length of a rectangle is 1 cm longer than its width. If the diagonal of the rectangle is 4cm, what are the dimensions (the length and the width) of the rectangle?
The equation h=-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 height of 120ft?
A ball is thrown upward from the roof of a building 100m tall with an initial velocity of 20m/s. When will the ball reach a height of 80m?
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 equilibrium price?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The length of a rectangle is 1 cm longer than its width. If the diagonal of the rectangle is 4cm, what are the dimensions (the length and the width) of the rectangle?
:
This problem can easily be solved using the pythag theorem: a^2 + b^2 = c^2
Where: a = width; b = (a+1) (the length) and c = 4,
:
a^2 + (a+1)^2 = 4^2
a^2 + (a^2 + 2a + 1) = 16; FOILed (a+1)(a+1), squared 4
2a^2 + 2a + 1 - 16 = 0, combined like terms, subtracted 16 from both sides
2a^2 + 2a - 15 = 0; a quadratic eq, needs be solved using the quadratic formula
:
a = 2; b = 2; c = -15; to avoid confusion call our solution x
 ; remember minus a minus is a plus
 ; we are only concerned with the positive solution here.
x = 2.284; the width, Length = 3.284
:
Check solution on a calc: Enter: 2.284^2 + 3.284^2 = 16.00 (which is 4^2)
:
:
The equation h=-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 height of 120ft?
:
Substitute 120 for h and you have:
-16t^2 + 112t = 120
-16t^2 + 112t - 120 = 0; a quadratic equation
:
Use the quadratic formula, a=-16; b=112; c=-120; find t
I'll let you do the math here. Both solutions are positive, you want the
smaller value because it asks for the time it takes to reach 120 ft
The 2nd value will be when it is at 120 ft on the way down.
:
:
A ball is thrown upward from the roof of a building 100m tall with an initial velocity of 20m/s. When will the ball reach a height of 80m?
:
This is a similar problem, the equation will include the fact it is thrown from
100 m tall building:
-16x^2 + 20x + 100 = h
:
Substitute 80m for h:
-16x^2 + 20x + 100 = 80
-16x^2 + 20x + 100 - 80 = 0
-16x^2 + 20x + 20 = 0
Here again, you need to use the quadratic equation: a=-16; b=20; c=20
Do it just as we have been doing above, you should be getting the idea now
Let me know if you are having difficulty
:
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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 equilibrium price? This occurs when D = S, so we have:
:
-200p + 35000 = -p^2 + 400p - 20000
:
+p^2 - 200p - 400p + 35000 + 20000 = 0; arrange everything on the left
p^2 - 600p + 55000 = 0; another quadratic equation requiring the quad formula
:
a=1; b=-600; c=55000
We have two solutions
p = $112.92, one solution
and
p = $487.10, another solution
:
Substitute both in the original equations. It's interesting that both will
give you equilibrium however the higher value produces a negative value so
it probably is not valid.
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