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2 years ago

Make x the subject: a(x-b) = x

Mathematics

1 answer:

umka21 [38]2 years ago

5 0

Answer:

x = $\frac{ab}{a-1}$

Step-by-step explanation:

Given

a(x - b) = x ← distribute parenthesis on left side

ax - ab = x ( subtract x from both sides )

ax - x - ab = 0 ( add ab to both sides )

ax - x = ab ← factor out x from each term on the left side

x(a - 1) = ab ← divide both sides by a - 1

x = $\frac{ab}{a-1}$

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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

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

6 0

3 years ago

Help plzzzzzzzzz????? asapp

Fiesta28 [93]

The two angles are a linear pair.
(Explanations down below!)

Linear pair angles must add up to 180 degrees. You can tell that the two angles add up to 180 degrees because they form a straight line (which is 180 degrees).

Complementary angles add up to 90 degrees. The two angles are not complementary because they do not form a 90 degree angle (right triangle, square in corner, like a L shape).

Vertical angles are opposite each other and are equal to one another. These angles are adjacent to each other and do not look similar.

6 0

3 years ago

715 miles in 11 hours how long would it take to drive 845 miles

emmasim [6.3K]

715 miles / 11 hours = 65 mph

845 miles / 65 mph = 13 hours

It would take 13 hours to drive 845 miles.

8 0

2 years ago

In the pictures down below Can anyone help? Fractions and percents

wariber [46]

1st Picture:
$3)- \frac{6}{7} +\frac {10}{11}
\\\\LCD:77
\\\\\frac{6}{7}* \frac{11}{11} + \frac{10}{11}*\frac{7}{7}= \frac{66}{77} + \frac{70}{77} = \frac{136}{77} = 1\frac{59}{77} 
 \\ \\ 4) 3\frac{6}{7}* 2 \frac{1}{10}= \frac{27}{7} * \frac{21}{10} = \frac{567}{70} =\frac{81}{10} = 8\frac{1}{10}
\\\\5)2\frac{1}{2}+3\frac{1}{3}
\\\\LCD: 6
\\\\ 2\frac{3}{6} + 3\frac{2}{6} =5\frac{5}{6}
\\\\6)5\frac{1}{8}*-6\frac{6}{11}=\frac{41}{8}* \frac{72}{11}=\frac{2952}{88}=\frac{369}{11}=33\frac{6}{11}$

2nd Picture:

$1)80 percent of 80 = .8*80 =64
\\\boxed{64}
\\\\2)95percent of 100=.95*100=95
\\\boxed{95}$

7 0

3 years ago

From the graph of the function, determine the domain and the range.

harina [27]

Answer:

Domain(-4,4) and Range:(-3,0)

Step-by-step explanation:

Because the graph goes through - 4 and 4

3 0

2 years ago