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Pavlova-9 [17]
3 years ago
10

Rearrange the equation so xxx is the independent variable.

Mathematics
2 answers:
Keith_Richards [23]3 years ago
8 0

Answer:

No, it's 5x - 26

Step-by-step explanation:

y + 6 = 5(x - 4)

y + 6 = 5x - 20

y = 5x - 26

mr_godi [17]3 years ago
5 0

Answer:

x = (y+26)/5

Step-by-step explanation:

Given the equation y+6=5(x-4), in order to rearrange the equation so x is the independent variable means making x the subject of the formula from the equation.

To do that, we first expand the bracket to have;

y+6 = 5x-20

Taking y+6 to the other side:

0 = 5x-20-y-6

Taking 5x to the other side we have:

-5x = -y-26

Multiplying through by minus

5x = y+26

Dividing both sides by 5

5x/5 = (y+26)/5

x = (y+26)/5

This equation gives the required function

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A regular pentagon with a perimeter of 18 centimeters is dilated by a scale factor of 32 to create a new pentagon?
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A piece of wire 30 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle.
antiseptic1488 [7]

Answer:

a) 0 m

b) 16.8 m

Step-by-step explanation:

A piece of wire, 30 m long, is cut in two sections: a and b. Then, the relation between a and b is:

a+b=30\\\\b=30-a

The section "a" is used to make a square and the section "b" is used to make a circle.

The section "a" will be the perimeter of the square, so the square side will be:

l=a/4

Then, the area of the square is:

A_s=l^2=(a/4)^2=a^2/16

The section "b" will be the perimeter of the circle. Then, the radius of the circle will be:

2\pi r=b=30-a\\\\r=\dfrac{30-a}{2\pi}

The area of the circle will be:

A_c=\pi r^2=\pi\left(\dfrac{30-a}{2\pi}\right)^2=\pi\left(\dfrac{900-60a+a^2}{4\pi^2}\right)=\dfrac{900-60a+a^2}{4\pi}

The total area enclosed in this two figures is:

A=A_s+A_c=\dfrac{a^2}{16}+\dfrac{900-60a+a^2}{4\pi}=\left(\dfrac{1}{16}+\dfrac{1}{4\pi}\right)a^2-\dfrac{60a}{4\pi}+\dfrac{900}{4\pi}

To calculate the extreme values of the total area, we derive and equal to 0:

\left(\dfrac{1}{16}+\dfrac{1}{4\pi}\right)a^2-\dfrac{60a}{4\pi}+\dfrac{900}{4\pi}\\\\\\\dfrac{dA}{da}=\left(\dfrac{1}{16}+\dfrac{1}{4\pi}\right)(2a)-\dfrac{60}{4\pi}+0=0\\\\\\\left(\dfrac{1}{8}+\dfrac{1}{2\pi}\right)a=\dfrac{15}{\pi}\\\\\\\dfrac{\pi+4}{8\pi}\cdot a=\dfrac{15}{\pi}\\\\\\\dfrac{\pi+4}{8}\cdot a=15\\\\\\a=15\cdot \dfrac{8}{\pi+4}\approx 16.8

We obtain one value for the extreme value, that is a=16.8.

We can derive again and calculate the value of the second derivative at a=16.8 in order to know if the extreme value is a minimum (the second derivative has a positive value) or is a maximum (the second derivative has a negative value):

\dfrac{d^2A}{da^2}=\left(\dfrac{1}{16}+\dfrac{1}{4\pi}\right)(2)-0=\dfrac{1}{8}+\dfrac{1}{2\pi}>0

As the second derivative is positive at a=16.8, this value is a minimum.

In order to find the maximum area, we analyze the function. It is a parabola, which decreases until a=16.8, and then increases.

Then, the maximum value has to be at a=0 or a=30, that are the extremes of the range of valid solutions.

When a=0 (and therefore, b=30), all the wire is used for the circle, so the total area is a circle, which surface is:

A=\pi r^2=\pi\left( \dfrac{30}{2\pi}\right)^2=\dfrac{900}{4\pi}\approx71.62

When a=30, all the wire is used for the square, so the total area is:

A=a^2/16=30^2/16=900/16=56.25

The maximum value happens for a=0.

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Answer:

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Step-by-step explanation:

"• 10 - 2 = 33 8 = 33 33 – 8 25 • 37-23=83 14 = 83 83 - 14 69 • 82-4= 43 78 = 43 78 – 43 35 • 55-7=32 48 = 32 16 Now on solving the above four answer further we will get, 69 – 25 = 44 35 – 16 = 19 Further on subtracting them, 44 – [ 19 = 35 Hence, the answer is 76 – 45 = 35

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