SOLUTION: 1) A toy rocket is launched from ground level. its distance in feet from the ground in t seconds is given by. s(t)= -16t^2+208t Find the number of seconds required for the pr

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Question 472878: 1) A toy rocket is launched from ground level. its distance in feet from the ground in t seconds is given by.
s(t)= -16t^2+208t
Find the number of seconds required for the projectile to reach maximum height. What is the maximum height.
2) A washing machine can be filled in 8 minutes if both the hot and cold water taps are fully opened. Filling water with hot water alone takes 9 minutes longer than filling it with cold water alone. How long does it take to fill the washer with cold water?
Answer by ankor@dixie-net.com(22740) (Show Source):
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A toy rocket is launched from ground level. its distance in feet from the ground in t seconds is given by.
s(t)= -16t^2+208t
Find the number of seconds required for the projectile to reach maximum height.
:
Max height will be reached at the axis of symmetry, x = -b/(2a)
In this equation a=-16; b=208
t =
t =
t = +6.5 sec to reach max height
:
What is the maximum height.
Find the max height by replacing t with 6.5
h = -16(6.5^2) + 208(6.5)
h = -676 + 1352
h = +676 ft is max height
:
:
2) A washing machine can be filled in 8 minutes if both the hot and cold water taps are fully opened.
Filling water with hot water alone takes 9 minutes longer than filling it with cold water alone.
How long does it take to fill the washer with cold water?
:
Let x = time required to fill the washer with cold water
then
(x+9) = time required to fill it with hot water
let a full washer = 1
;
+ = 1
multiply eq by x(x+9) to clear the denominators, results
8(x+9) + 8x = x(x+9)
8x + 72 + 8x = x^2 + 9x
arrange as a quadratic equation
x^2 + 9x - 16x - 72 = 0
x^2 - 7x - 72 = 0
Use the quadratic formula to find x, a=1, b=-7, c= -72
only the positive solution will make sense here