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3 years ago

The function f(x) varies inversely with x and f(x) = 4 when x = 12.

Mathematics

2 answers:

goldfiish [28.3K]3 years ago

4 0

Seriously know the answer, its 16, not 1. Just did it.

Alex777 [14]3 years ago

4 0

<h3>Answer: C. 16.</h3>

Step-by-step explanation:

We are given inverse relation between f(x) and x.

The function f(x) varies inversely with x.

Inverse relation could be written as

f(x) = $\frac{k}{x}$ .

We also given f(x) = 4 when x = 12.

Plugging f(x) = 4 and x=12 in the above inverse relation to get the value of constant k.

$4=\frac{k}{12}$ .

On cross multiplying, we get

12× 4 = $12 \times \frac{k}{12}$

48 = k

Now, we need to find f(x) for x=3.

Plugging k=48 and x=3 in inverse relation, we get

$f(x) = \frac{48}{3} = 16$ .

<h3>Therefore, f(x)=16 when x=3.</h3>

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3 years ago

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olga55 [171]

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3 years ago

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A farmer is constructing a rectangular pen with one additional fence across its width. Find the maximum area that can be enclose

konstantin123 [22]

The maximum area of the pen is the highest area the pen can have

The maximum area is 16200 square yards

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$\mathbf{P = 360}$

Because it has one additional fence, the perimeter is calculated as:

$\mathbf{2x + y = 360}$

Make y the subject

$\mathbf{y = 360 - 2x}$

The area is calculated as:

$\mathbf{A = xy}$

Substitute $\mathbf{y = 360 - 2x}$

$\mathbf{A = x(360 -2x)}$

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$\mathbf{A = 360x -2x^2}$

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$\mathbf{A' = 360 -4x}$

Set to 0

$\mathbf{360 -4x = 0}$

Rewrite as:

$\mathbf{4x = 360}$

Divide both sides by 4

$\mathbf{x = 90}$

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$\mathbf{A = 360 \times 90 - 2 \times 90^2}$

$\mathbf{A = 16200}$

Hence, the maximum area is 16200 square yards

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Artyom0805 [142]

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