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yuradex [85]
2 years ago
15

A rancher plans to make 4 identical and adjacent rectangular pens against a barn (see figure below), each with an area of 100 m^

2. What are the dimensions of each pen that minimize the amount of fence that must be used?​

Mathematics
1 answer:
Tasya [4]2 years ago
7 0

Answer:

10 by 10 meters

Step-by-step explanation:

In calculus terms, you can use the formula for the perimeter which is 2l + 2w, and the area l × w.

Then since the area is 100

l × w = 100. So w = 100/l

Then substitute this into the perimeter formula.

w = 100/l → 2l + 2(w) = 2l + 2(100/l) = 2l + 200/l.

Then take the derivative d/dx [take the derivative of a quantity with respect to x], by using a simpler method known as the power rule:

d/dx[x^n] = nx^n-1

so p = 2l + 200/l becomes p' = 2 - 200/l^2

Since the derivative of a constant is 0, to solve for l, set p' to 0

0 = 2 - 200/l^2 → -200/l^2 = -2 → 200/l^2 = 2 → 2l^2 = 200 → l^2 = 100 → l = √100, l = 10.

Now that we know the length is 10, We can substitute the length in the original equation to find the width.

l = 10 → w = 100/l → w = 100/10, w = 10.

Therefore the perimeter of each rectangular pen is 40, with a length of 10 and width of 10.

If you want to do this algebraicly, there are more steps involved

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2 years ago
Linear model function
sveticcg [70]

Using equations of linear model function, the number of hours Jeremy wants to skate is calculated as 3.

<h3>How to Write the Equation of a Linear Model Function?</h3>

The equation that can represent a linear model function is, y = mx + b, where m is the unit rate and b is the initial value.

Equation for Rink A:

Unit rate (m) = (35 - 19)/(5 - 1) = 16/4 = 4

Substitute (x, y) = (1, 19) and m = 4 into y = mx + b to find b:

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b = 15

Substitute m = 4 and b = 15 into y = mx + b:

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Equation for Rink B:

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Substitute (x, y) = (1, 15) and m = 6 into y = mx + b to find b:

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Substitute m = 6 and b = 9 into y = mx + b:

y = 6x + 9 [equation for Rink B]

To find how many hours (x) both would cost the same (y), make both equation equal to each other

4x + 15 = 6x + 9

4x - 6x = -15 + 9

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The hours Jeremy wants to skate is 3.

Learn more about linear model function on:

brainly.com/question/15602982

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sladkih [1.3K]

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x = $70 + $70 * 5/100

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She will have $73.5 in 1 year

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Point K is on line segment JL. Given KL = 6 and JK = 14, determine the length<br> JL.
mestny [16]
JL= 20

JK+KL= JL
14+6= 20
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3 years ago
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