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2 years ago

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Mathematics

1 answer:

nata0808 [166]2 years ago

5 0

Answer:

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Step-by-step explanation:

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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:

Maximization With Derivatives

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

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

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2 years ago

What is 423.408 rounded to the neatest hundredth

xeze [42]

The hundredth is the second decimal place. You know the rounding rules are where you look at the previous place and if it's 5 or above the number place your rounding to goes up. So the answer is 423.41

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2 years ago

Read 2 more answers

Explain why the product of a nonzero rational number and an irrational number is irrational

spayn [35]

Answer:

If you multiply any irrational number by the rational number zero, the result will be zero, which is rational. Any other situation, however, of a rational times an irrational will be irrational.

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2 years ago

3 Select the correct answer. What are the solutions to this equation? 16x² + 9 = 25

Charra [1.4K]

Answer:

Step-by-step explanation:

16x^2 + 9 = 25

16x^2 = 16

x^2 = 1

x = 1, -1

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2 years ago

Write 7*7*b*b*b in exponential form

ycow [4]

Answer:

7²b³

Step-by-step explanation:

An exponent signifies repeated multiplication. Here, the factor 7 is repeated twice, and the factor b is repeated 3 times. These will get exponents of 2 and 3, respectively:

7²b³

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2 years ago