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Vedmedyk [2.9K]
3 years ago
6

The gray area is the sidewalk. The area of the sidewalk is ___________ square units. A) 48 B) 56 C) 72 D) 84

Mathematics
1 answer:
tamaranim1 [39]3 years ago
3 0
A i did this problem before with another user
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Suppose a rectangular pasture is to be constructed using 1 2 linear mile of fencing. The pasture will have one divider parallel
timama [110]

Answer:

\displaystyle A=\frac{1}{192}

Step-by-step explanation:

<u>Maximization With Derivatives</u>

Given a function of one variable A(x), we can find the maximum or minimum value of A by using the derivatives criterion. If A'(x)=0, then A has a probable maximum or minimum value.

We need to find a function for the area of the pasture. Let's assume the dimensions of the pasture are x and y, and one divider goes parallel to the sides named y, and two dividers go parallel to x.

The two divisions parallel to x have lengths y, thus the fencing will take 4x. The three dividers parallel to y have lengths x, thus the fencing will take 3y.

The amount of fence needed to enclose the external and the internal divisions is

P=4x+3y

We know the total fencing is 1/2 miles long, thus

\displaystyle 4x+3y=\frac{1}{2}

Solving for x

\displaystyle x=\frac{\frac{1}{2}-3y}{4}

The total area of the pasture is

A=x.y

Substituting x

\displaystyle A=\frac{\frac{1}{2}-3y}{4}.y

\displaystyle A=\frac{\frac{1}{2}y-3y^2}{4}

Differentiating with respect to y

\displaystyle A'=\frac{\frac{1}{2}-6y}{4}

Equate to 0

\displaystyle \frac{\frac{1}{2}-6y}{4}=0

Solving for y

\displaystyle y=\frac{1}{12}

And also

\displaystyle x=\frac{\frac{1}{2}-3\cdot \frac{1}{12}}{4}=\frac{1}{16}

Compute the second derivative

\displaystyle A''=-\frac{3}{2}.

Since it's always negative, the point is a maximum

Thus, the maximum area is

\displaystyle A=\frac{1}{12}\cdot \frac{1}{16}=\frac{1}{192}

6 0
3 years ago
A cone has volume 12 cubic inches. Its height is 4 inches. What is its radius?
Gekata [30.6K]

the radius of this cone is 2.9

6 0
2 years ago
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2 3/4÷2/5 will mark brainleyst
olga55 [171]

Answer:

6 7/8

Step-by-step explanation:

Result in decimals: 6.875

In pic

(Hope this helps can I pls have brainlist (crown) ☺️)

6 0
3 years ago
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What is 5 divided by 206 ?
Reika [66]
\frac{5}{206} cannot be simplified any further :

5=5x1
206=2*103
6 0
3 years ago
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Forgot how to do it, help please.
masya89 [10]
.................................:........:.................
8 0
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