Question 414069: Can you please help me find the formulas to this word problems?
An old pump requires 6h longer to empty a pool than does a new pump. With both pumps working, the pool can be emptied in 4 h. find the time required for the new pump, working alone, to empty the pool.
The height s, in feet, of a rocket, after t seconds is given by the formula s(t) = 192t – 16t2. Find the maximum height of the rocket.
A courtyard at the corner of two buildings is to be enclosed using 100 ft of redwood fencing. Find the dimensions of the courtyard that will maximize the area.
thank you very much
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! An old pump requires 6h longer to empty a pool than does a new pump. With both pumps working, the pool can be emptied in 4 h. find the time required for the new pump, working alone, to empty the pool.
Let x= hours it takes new pump to empty pool
then
x+6 = hours for old pump
.
4(1/x + 1/(x_6)) = 1
.
The height s, in feet, of a rocket, after t seconds is given by the formula s(t) = 192t – 16t2. Find the maximum height of the rocket.
s(t) = 192t – 16t^2
s(t) = –16t^2 + 192t
vertex is at maximum
t = -b/(2a) = -192/(-32) = 6
.
max height = –16(6)^2 + 192(6)
.
A courtyard at the corner of two buildings is to be enclosed using 100 ft of redwood fencing. Find the dimensions of the courtyard that will maximize the area.
Let x = width
and y = length
.
from perimeter info:
2(x+y) = 100 (equation 1)
from area info:
area = xy (equation 2)
.
solving equation 1 for y:
y = 50-x
plug into equation 2:
area =x(50-x)
area = -x^2+50x
.
vertex gives max:
max width = -b/(2a) = -50/(-2) = 25 feet
max length = 50-25 = 25 feet
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