Step-by-step explanation:
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Given two numbers x and y such that:
x + y = 12 ... (1)
<span>two numbers will maximize the product g</span>
from equation (1)
y = 12 - x
Using this value of y, we represent xy as
xy = f(x)= x(12 - x)
f(x) = 12x - x^2
Differentiating the above function:
f'(x) = 12 - 2x
Maximum value of f(x) occurs at point for which f'(x) = 0.
Equating f'(x) to 0 we get:
12 - 2x = 0
2x = 12
> x = 12/2 = 6
Substituting this value of x in equation (2):
y = 12 - 6 = 6
Therefore, value of xy is maximum when:
x = 6 and y = 6
The maximum value of xy = 6*6 = 36
Answer:
162 passengers
Step-by-step explanation:
A roller coaster can take 162 passengers around the track in 9 minutes. The roller coaster operates at a constant rate.
Answer:
Step-by-step explanation:
Let height of a banner be 
, then we know that this is 
of the length 
of the banner; so we have
.
Now we can rearrange this equation to solve for the length of the banner given it's height:
So there we have it!
If the banner is 5 ft tall, then it's length will be:
