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love history [14]
3 years ago
8

A livestock pen is built in the shape of a rectangle that is 2 times as long as it is wide. The perimeter is 30 feet. If the mat

erial used to build the pen is $ 1.75 per foot for the longer sides and $ 2.25 per foot for the shorter sides (the shorter sides have gates, which increase the cost per foot), find the cost to build the pen.
Mathematics
1 answer:
shutvik [7]3 years ago
7 0

Answer:

$57.5 is the total cost to build the pen.

Step-by-step explanation:

We are given the following in the question:

A livestock pen is built in the shape of a rectangle.

The length of rectangle is two times the width.

Let l be the length of rectangle and w be the width of rectangle. Thus, we can write

l = 2w

Perimeter = 30 feet

\text{Perimeter of rectangle} = 30\\2\times (l\times w) = 30

Putting values,

2(2w + w) = 30\\6w = 30\\w = 5\\l = 2w = 10

The length of rectangle is 10 feet and width of rectangle is 5 feet.

If the material used to build the pen is $ 1.75 per foot for the longer sides and $ 2.25 per foot for the shorter sides

Cost of building =

=2\times(\text{Cost of length}\times \text{Length} + \text{Cost of width}\times \text{Width})\\=2\times(1.75\times 10 + 2.25\times 5)\\=57.5

Thus, $57.5 is the total cost to build the pen.

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16. Suppose Eva has 12 3/4 pounds of flour. The day's baking will require triple that amount.
egoroff_w [7]

Answer:

Option D

Step-by-step explanation:

Given the following question:

12 \frac{3}{4} \times3

In order to find the answer, we have to convert the mixed number and then multiply by three, since how Eva needs triple the amount for today's baking.

12 \frac{3}{4} \times3
12\frac{3}{4} =4\times12=48+3=51=\frac{51}{4}
3=\frac{3}{1}
\frac{51}{4} \times\frac{3}{1}
51\times3=153
4\times1=4
=\frac{153}{4}

<u>Convert the improper fraction back into a mixed number:</u>

\frac{153}{4}
\frac{153}{4} =153\div4=38\frac{1}{4}
=38\frac{1}{4}

Which means Eva needs "38 1/4 pounds of flour" or option D for today's baking.

3 0
2 years ago
Can you plz help me with this problem I’ve been stuck on it for a long time
Tpy6a [65]

I think the answer is B

6 0
3 years ago
Read 2 more answers
You have a wire that is 20 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The o
Aleksandr [31]

Answer:

Therefore the circumference of the circle is =\frac{20\pi}{4+\pi}

Step-by-step explanation:

Let the side of the square be s

and the radius of the circle be r

The perimeter of the square is = 4s

The circumference of the circle is =2πr

Given that the length of the wire is 20 cm.

According to the problem,

4s + 2πr =20

⇒2s+πr =10

\Rightarrow s=\frac{10-\pi r}{2}

The area of the circle is = πr²

The area of the square is = s²

A represent the total area of the square and circle.

A=πr²+s²

Putting the value of s

A=\pi r^2+ (\frac{10-\pi r}{2})^2

\Rightarrow A= \pi r^2+(\frac{10}{2})^2-2.\frac{10}{2}.\frac{\pi r}{2}+ (\frac{\pi r}{2})^2

\Rightarrow A=\pi r^2 +25-5 \pi r +\frac{\pi^2r^2}{4}

\Rightarrow A=\pi r^2\frac{4+\pi}{4} -5\pi r +25

For maximum or minimum \frac{dA}{dr}=0

Differentiating with respect to r

\frac{dA}{dr}= \frac{2\pi r(4+\pi)}{4} -5\pi

Again differentiating with respect to r

\frac{d^2A}{dr^2}=\frac{2\pi (4+\pi)}{4}    > 0

For maximum or minimum

\frac{dA}{dr}=0

\Rightarrow \frac{2\pi r(4+\pi)}{4} -5\pi=0

\Rightarrow r = \frac{10\pi }{\pi(4+\pi)}

\Rightarrow r=\frac{10}{4+\pi}

\frac{d^2A}{dr^2}|_{ r=\frac{10}{4+\pi}}=\frac{2\pi (4+\pi)}{4}>0

Therefore at r=\frac{10}{4+\pi}  , A is minimum.

Therefore the circumference of the circle is

=2 \pi \frac{10}{4+\pi}

=\frac{20\pi}{4+\pi}

4 0
3 years ago
Sarah and her friends pick 3 3/4 pints of blueberries after they ate some of the blueberries only 2 1/3 pints remain how many pi
scoundrel [369]

3 3/4  - 2 1/3

get a common denominator of 12

3 3/4 * 3/3 = 3 9/12

2 1/3 * 4/4 = 2 4/12

3 9/12 - 2 4/12=

1 5/12

Answer: they ate 1 5/12 pints

7 0
3 years ago
The circle below is centered at (3, 1) and has a radius of 2. What is its<br> equation?
MissTica

Answer:

( x-3) ^2 + ( y-1) ^2 = 4

Step-by-step explanation:

The equation for a circle is given by

( x-h)^2 + ( y-k) ^2 = r^2  where (h,k) is the center and r is the radius

( x-3) ^2 + ( y-1) ^2 = 2^2

( x-3) ^2 + ( y-1) ^2 = 4

5 0
2 years ago
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