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CaHeK987 [17]
2 years ago
6

Which is a correct interpretation of the slope of the line in this graph?

Mathematics
1 answer:
Vilka [71]2 years ago
7 0

Answer:

Option C. the volume of water in the tank is decreasing by 0.4L per hour

Step-by-step explanation:

step 1

Find the slope

we know that

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

we have

A(2,8)\ B(7,6)

Substitute the values

m=\frac{6-8}{7-2}

m=\frac{-2}{5}=-0.40\frac{liters}{hour}

The slope is negative

so

is decreasing

That means------> the volume of water in the tank is decreasing by 0.4L per hour

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Alenkinab [10]

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c

Step-by-step explanation:

3/4

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What percent of 33.5 is 21
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Take the number "of" divided by the other number then multiply it by 100% to get the percentage.
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Ramone pays $6 for lunch and $2 for juice each day.
VMariaS [17]

Answer:

D

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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>

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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

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Compute the second derivative to ensure it's a maximum

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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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