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dusya [7]
3 years ago
10

The range of the following relation R:

Mathematics
1 answer:
NemiM [27]3 years ago
3 0

Answer:

{- 5, - 4, 2 }

Step-by-step explanation:

the range is the corresponding values of y ( output) from the given set in ascending order without repeats


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Simplify, write without exponents.
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The angles of a triangle are 80°, 2x + 2°, and 5x°.
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The sum of interior of all angles in a triangle = 180
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Although still a sophomore at college, John O'Hagan's son Billy-Sean has already created several commercial video games and is c
Scilla [17]

Answer:

<em>27 feet for the south wall and 18 feet for the east/west walls</em>

Maximum area= 486\ ft^2

Step-by-step explanation:

<u>Optimization</u>

This is a simple case where an objective function must be minimized or maximized, given some restrictions coming in the form of equations.

The first derivative method will be used to find the values of the parameters that control the objective function and the maximum value of that function.

The office space for Billy-Sean will have the form of a rectangle of dimensions x and y, being x the number of feet for the south wall and y the number of feet for the west wall. The total cost of the space is

C=8x+12y

The budget to build the office space is $432, thus

8x+12y=432

Solving for y

\displaystyle y=\frac{432-8x}{12}

The area of the office space is

A=xy

Replacing the value found above

\displaystyle A=x\cdot \frac{432-8x}{12}

Operating

\displaystyle A= \frac{432x-8x^2}{12}

This is the objective function and must be maximized. Taking its first derivative and equating to 0:

\displaystyle A'= \frac{432-16x}{12}=0

Operating

432-16x=0

Solving

x=432/16=27

x=27\ feet

Calculating y

\displaystyle y=\frac{432-8\cdot 27}{12}

y=18\ feet

Compute the second derivative to ensure it's a maximum

\displaystyle A'= \frac{-16x}{12}

Since it's negative for x positive, the values found are a maximum for the area of the office space, which area is

A=xy=27\ ft\cdot 18\ ft\\\\\boxed{A=486\ ft^2}

5 0
3 years ago
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