Answer:
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Step-by-step explanation:
Answer:
y = 2x - 12
Step-by-step explanation:
To find the inverse of a function, you switch x and y and solve for y.
x = 1/2 y + 6 switch x and y
x - 6 = 1/2 y subtract 6 from both sides
2x - 12 = y multiply both sides by 2
Assume:
Size of sides = x m
Depth of the pool = y m
Therefore, surface area = x^2+4xy =10 m^2
Then, y = (10-x^2)/(4x)
Now,
Volume (V) = x^2*y = x^2*y =x^2(10-x^2)/4x = (10x-x^3)/4 = 1/4(10x-x^3)
For maximum volume, first derivative of volume function is equal to zero.
That is,
dV/dx =0 = 1/4(10-3x^2)
Then,
1/4(10-3x^2) = 0
10-3x^2 = 0
3x^2=10
x= sqrt (10/3) = 1.826 m
And
y= (10-1.826^2)/(4*1.826) = 0.913 m
Therefore,
V= 1.826^2*0.913 = 3.044 m^3
18=3+36x-50x-55
18=3-14x-55
18=-14x-52
70=-14x
x=-5
Since 10 cm is bigger than 1 mm, the scale drawing is bigger
