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).
Dimensions of a rectangular solid:
a = 4 cm, b = 6 cm, c = 8 cm.
Surface Area = 2 * ( a b + b c + a c ) =
= 2 * ( 4 * 6 + 6 * 8 + 4 * 8 ) =
= 2 * ( 24 + 48 + 32 ) =
= 2 * 104 = 208 cm²
Answer: Its surface area is 208 cm².
Answer:
$18.96
Step-by-step explanation:
Multiply 24 by 0.15= 3.6
Multiply 24 by 0.06= 1.44
Add 3.6 and 1.44= 5.04
Subtract 5.04 from 24= $18.96
Well there is 13 possibilities so it would be 10/13
