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Rus_ich [418]
3 years ago
8

A farmer plans to enclose two adjacent rectangular pens against a barn wall (see figure).

Mathematics
1 answer:
Licemer1 [7]3 years ago
3 0

Answer: Let's assume that the pig pens need to be fenced in the way shown in the diagram above.

Then, the perimeter is given by

4

x

+

3

y

=

160

.

4

x

=

160

−

3

y

x

=

40

−

3

4

y

The area of a rectangle is given by

A

=

L

×

W

, however here we have two rectangles put together, so the total area will be given by

A

=

2

×

L

×

W

.

A

=

2

(

40

−

3

4

y

)

y

A

=

80

y

−

3

2

y

2

Now, let's differentiate this function, with respect to y, to find any critical points on the graph.

A

'

(

y

)

=

80

−

3

y

Setting to 0:

0

=

80

−

3

y

−

80

=

−

3

y

80

3

=

y

x

=

40

−

3

4

×

80

3

x

=

40

−

20

x

=

20

Hence, the dimensions that will give the maximum area are

20

by

26

2

3

feet.

A graphical check of the initial function shows that the vertex is at

(

26

2

3

,

1066

2

3

)

, which represents one of the dimensions that will give the maximum area and the maximum area, respectively.

Hopefully this helps!

Step-by-step explanation: hope this helps

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Answer:

4) Alternate angles

Step-by-step explanation:

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7 0
2 years ago
In a standard deck of 52 playing cards, what is the complement (not below 8)?
Damm [24]

Answer 2/13

Step-by-step explanation:

There are 52 cards in a standard deck: 13 ordinal cards (Ace -10, jack, Queen, King)and 4 of them

- one to each sute (hearts, diamonds, clubs, spades ) and so we have 4x13=52

There are 8 card that fit the question (4 each of access and kings).

so if you in a random draw the odds of drawing one of those 8 card out of the total number of 52 is 8/52

which we simplify

8/2=2/13

8 0
2 years ago
Molly opened a savings account with a one‐time deposit of $100 that will be left in the account for at least 5 years. The saving
Anettt [7]

The amount of interest Molly will earn after 5 years on a deposit of \$100 compounded annually over 5 years is \$27.63

First, we need to find the future value of her investment, then we subtract the original deposit from it to get the amount of interest she will get at the end of 5 years.

The future value of an investment that is compounded annually is given by

A=P(1+r)^t

where

A=\text{Amount of money in Molly's account after 5 years}\\P=\text{Molly's initial deposit into her account}=\$500\\r=\text{The annual interest rate as a decimal}=0.05\\t=\text{The time the money is invested (in years)}=5

Substituting the available values into the formula and solving

A=100(1+0.05)^5=100(1.05)^5 \approx \$ 127.63

The interest Molly will earn after 5 years is

A-P=\$127.63-\$100=\$27.63

Therefore, the amount of interest Molly will earn after 5 years on a deposit of \$100 compounded annually over 5 years is \$27.63

Learn more about compound interest here: brainly.com/question/21270833

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What is the distance between each data point and the regression line called?
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Using the regression formula with a slope = 2000 and intercept = 15000, what would the predicted income be for someone who has 16 years of education.
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LUCKY_DIMON [66]

Answer: Ray B

Step-by-step explanation:

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