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Diano4ka-milaya [45]
3 years ago
13

Complete parts a through f below to find nonnegative numbers x and y that satisfy the given requirements. Give the optimum value

of P. x plus y equals 81 and Pequalsx squared y is maximized a. Solve x plus y equals 81 for y. yequals 81 minus x b. Substitute the result from part a into the equation Pequalsx squared y for the variable that is to be maximized. Pequals x squared left parenthesis 81 minus x right parenthesis c. Find the domain of the function P found in part b. left bracket 0 comma 81 right bracket ​(Simplify your answer. Type your answer in interval​ notation.) d. Find StartFraction dP Over dx EndFraction . Solve the equation StartFraction dP Over dx EndFraction equals0. StartFraction dP Over dx EndFraction equals nothing
Mathematics
1 answer:
MArishka [77]3 years ago
7 0

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

__

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

__

c. Find the domain of the function P found in part b.

  left bracket 0 comma 81 right bracket

__

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).

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Answer:

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Step-by-step explanation:

Slope - Intercept Form = y = mx + b

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(Should have been the answer)

BUT,

George's Solving:

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George's Mistake would be her miscalculation during her 2nd step. Where instead of distributing 2 to (x + 20), she has changed it to -x + 20, when in reality, it should have been 2x + 40.

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Can someone please answer this question please answer it correctly please show work
Zina [86]

Answer:

34) A

35) C

36) D

Step-by-step explanation:

34) The perimeter of a triangle is equal to the sum of the lengths of its sides

Sides: (6.2p + 4.5q) + (3.4p - 0.7r) + (2.9r - 4.1q)

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36)

<h3>(-\frac{4}{7}) / (-\frac{3}{4}) * (-2\frac{1}{3})</h3>

Convert to improper fractions

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Divide by finding the reciprocal

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