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3 years ago

Find what n equals 8(2n-2) = 4 - 4n (explanation please)

Mathematics

2 answers:

Gre4nikov [31]3 years ago

8 0

Answer:

Step-by-step explanation:

Here you go mate

PEMDAS

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

Step 1

8(2n−2)=4−4n Equation

Step 2

8(2n−2)=4−4n Remove parenthesis

16n-16=-4n+4

Step 3

20n−16=4 Add n to both sides

20n=20

Step 4

20n=20 Divide both sides by themselves

answer

n=1

slavikrds [6]3 years ago

6 0

Answer:

$\huge\boxed{n=1}$

Step-by-step explanation:

In order to find the value of n that satisfies this equation, we can perform a series of algebraic steps on it to solve for n.

$8(2n-2) = 4- 4n$
Distribute in the 8 on the left side:
$16n-16=4-4n$
Add 4n to both sides
$20n-16=4$
Add 16 to both sides
$20n = 20$
Divide both sides by 20
$n=1$

Therefore, n=1 is the value of n that satisfies this equation.

Hope this helped!

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gtnhenbr [62]

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3 years ago

How do you solve 3/5×4 1/6?

Helen [10]

$\frac{3}{5}$ × $4 \frac{1}{6}$

First, convert $4\frac{1}{6}$ to an improper fraction. Use this rule: $a \frac{b}{c}$ = $\frac{ac+b}{c}$ / Your problem should look like: $\frac{3}{5}$ × $\frac{4x6+1}{6}$
Second, simplify 4 × 6 to 24. / Your problem should look like: $\frac{3}{5}$ × $\frac{24+1}{6}$
Third, simplify 24 + 1 to 25. / Your problem should look like: $\frac{3}{5}$ × $\frac{25}{6}$
Fourth, apply this rule: $\frac{a}{b}$ × $\frac{c}{d}$ = $\frac{ac}{bd}$ / Your problem should look like: $\frac{3x25}{5x6}$
Fifth, simplify 3 × 25 to 75. / Your problem should look like: $\frac{75}{5x6}$
Sixth, simplify 5 × 6 to 30. / Your problem should look like: $\frac{75}{30}$
Seventh, simplify. / Your problem should look like: $\frac{5}{2}$
Eighth, convert to mixed fraction. / Your problem should look like: $2\frac{1}{2}$

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3 years ago

A metal cylinder can with an open top and closed bottom is to have volume 4 cubic feet. Approximate the dimensions that require

Aleksandr-060686 [28]

Answer:

$r\approx 1.084\ feet$

$h\approx 1.084\ feet$

$\displaystyle A=11.07\ ft^2$

Step-by-step explanation:

Optimizing With Derivatives

The procedure to optimize a function (find its maximum or minimum) consists in :

Produce a function which depends on only one variable
Compute the first derivative and set it equal to 0
Find the values for the variable, called critical points
Compute the second derivative
Evaluate the second derivative in the critical points. If it results positive, the critical point is a minimum, if it's negative, the critical point is a maximum

We know a cylinder has a volume of 4 $ft^3$ . The volume of a cylinder is given by

$\displaystyle V=\pi r^2h$

Equating it to 4

$\displaystyle \pi r^2h=4$

Let's solve for h

$\displaystyle h=\frac{4}{\pi r^2}$

A cylinder with an open-top has only one circle as the shape of the lid and has a lateral area computed as a rectangle of height h and base equal to the length of a circle. Thus, the total area of the material to make the cylinder is

$\displaystyle A=\pi r^2+2\pi rh$

Replacing the formula of h

$\displaystyle A=\pi r^2+2\pi r \left (\frac{4}{\pi r^2}\right )$

Simplifying

$\displaystyle A=\pi r^2+\frac{8}{r}$

We have the function of the area in terms of one variable. Now we compute the first derivative and equal it to zero

$\displaystyle A'=2\pi r-\frac{8}{r^2}=0$

Rearranging

$\displaystyle 2\pi r=\frac{8}{r^2}$

Solving for r

$\displaystyle r^3=\frac{4}{\pi }$

$\displaystyle r=\sqrt[3]{\frac{4}{\pi }}\approx 1.084\ feet$

Computing h

$\displaystyle h=\frac{4}{\pi \ r^2}\approx 1.084\ feet$

We can see the height and the radius are of the same size. We check if the critical point is a maximum or a minimum by computing the second derivative

$\displaystyle A''=2\pi+\frac{16}{r^3}$