I suppose the answer is b. Graph the system to show all possible solutions
Answer:
- y = 81-x
- the domain of P(x) is [0, 81]
- P is maximized at (x, y) = (54, 27)
Step-by-step explanation:
<u>Given</u>
- x plus y equals 81
- x and y are non-negative
<u>Find</u>
- P equals x squared y is maximized
<u>Solution</u>
a. Solve x plus y equals 81 for y.
y equals 81 minus x
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b. Substitute the result from part a into the equation P equals x squared y for the variable that is to be maximized.
P equals x squared left parenthesis 81 minus x right parenthesis
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c. Find the domain of the function P found in part b.
left bracket 0 comma 81 right bracket
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d. Find dP/dx. Solve the equation dP/dx = 0.
P = 81x² -x³
dP/dx = 162x -3x² = 3x(54 -x) = 0
The zero product rule tells us the solutions to this equation are x=0 and x=54, the values of x that make the factors be zero. x=0 is an extraneous solution for this problem so ...
P is maximized at (x, y) = (54, 27).
Answer:


Step-by-step explanation:
← Equation 1

By simplifying the above equation we get,
(Simplifying the brackets)
(By subtracting
from
) ← Equation 2
Multiply Equation 1 by 5 and Equation 2 by 3 and add them together.
Equation 1 multiplied by 5 will give,

Equation 2 multiplied by 3 will give,

Add those together,
(After simplifying
values)
Therefor 
By substituting
to Equation 1 we get,


Therefor we can say,


Step-by-step explanation:
1.

2.

this may help you(:
The slope is 1/6. y= mx + b
m is always to slope.