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:
20%
Step-by-step explanation:
Earlier snow depth = 2 feet
Later snow depth = 1.6 feet
Change
2 - 1.6
0.4 feet
Percentage change
(0.4 / 2) * 100
20%
Any time you move up or down, it affects the y coordinate and going up is positive so 5 units up is y + 5.
Moving left or right affects the x coordinate and moving left is negative so x - 3
(x - 3, y + 5)
So the answer is Option C).
Tom started with 20 newspapers on the morning and returned with 8 newspaper.
<h3>Equation</h3>
Equation is an expression used to show the relationship between two or more variables and numbers
Let x represent the amount of newspaper Tom started with.
He Delivered 10 newspapers on Flinders Street, hence:
He Delivered 6 newspapers on Collins Street, hence:
He Picked up 20 newspapers from the newsagent and Delivered 15 newspapers on Lonsdale Street, hence:
- = x - 16 + 20 - 15 = x - 11
He returned home there were eight newspapers in his bag. Hence:
x - 11 = 8
x = 20
Tom started with 20 newspapers on the morning and returned with 8 newspaper.
Find out more on equation at: brainly.com/question/2972832
Line segment AB is 4 units
Line segment CD is
Line segment MN is 6 units
Line segment PQ is 7 units
The line segment of greatest length is PQ
