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2 years ago

14

If f(x) = 6x – 4, what is f(x) when x = 8? 0.16

2 answers:

kykrilka [37]2 years ago

7 0

$f(8)=6\cdot8-4=48-4=44$

vodka [1.7K]2 years ago

4 0

Answer:

substitute x therefore 6*8=48

48-4=44

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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:

<u>Maximization With Derivatives</u>

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

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

6 0

3 years ago

Mixed numbers greater than 6 but less than 7 use an interval of 1/6 between each pair of numbers

GaryK [48]

Answer:

$[6\frac{1}{6},6\frac{1}{3},6\frac{1}{2},6\frac{2}{3},6\frac{5}{6}]$

Step-by-step explanation:

we have the compound inequality

$6 < x < 7$

where

x is a mixed number

so

The solution for the compound inequality are the numbers

$[6\frac{1}{6},6\frac{2}{6},6\frac{3}{6},6\frac{4}{6},6\frac{5}{6}]$

Simplify the numbers

$[6\frac{1}{6},6\frac{1}{3},6\frac{1}{2},6\frac{2}{3},6\frac{5}{6}]$

5 0

3 years ago

Tom received an allowance of $300 for his upcoming trip to Canada. He knows that he will spend $15 each day on food. Which equat

WARRIOR [948]

Answer:

m=15d-300

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

F(x) = (x + 2)/(x2 - 16)

serg [7]

(-2,8) This is a answer:)

3 0

3 years ago

Which numbers represent the lower quartile, the median, and the upper quartile of the following set of numbers?

kotegsom [21]

Answer:

Lower quartile: 85; median: 97; upper quartile 115.5

Step-by-step explanation:

4 0

3 years ago