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Trava [24]
2 years ago
8

^+^1+9/3^n^-^1+1" align="absmiddle" class="latex-formula">
how do i solve it?
Mathematics
1 answer:
abruzzese [7]2 years ago
4 0

Answer:

Hello,

Step-by-step explanation:

\dfrac{3^{n+1}+9}{3^{n-1}+1} \\\\=\dfrac{9*(3^{n-1}+1)}{3^{n-1}+1}\\\\=9\\

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(3a^2+b^4)^3/ 2a^3 b^3) ^2
mezya [45]

(Answer included in imagine)

3 0
2 years ago
[10 points] A manufacturer wants to design an open box having a square base and a surface area of 108 square inches. What dimens
MissTica

Answer:

  6 inches square by 3 inches high

Step-by-step explanation:

For a given surface area, the volume of an open-top box is maximized when it has the shape of half a cube. If the area were than of the whole cube, it would be 216 in² = 6×36 in².

That is, the bottom is 6 inches square, and the sides are 3 inches high.

_____

Let x and h represent the base edge length and box height, respectively. Then we have ...

  x² +4xh = 108 . . . . box surface area

Solving for height, we get ...

  h = (108 -x²)/(4x) = 27/x -x/4

The volume is the product of base area and height, so is ...

  V = x²h = x²(27/x -x/4) = 27x -x³/4

We want to maximize the volume, so we want to set its derivative to zero.

  dV/dx = 0 = 27 -(3/4)x²

  x² = (4/3)(27) = 36

  x = 6

  h = 108/x² = 3

The box is 6 inches square and 3 inches high.

_____

<em>Comment on maximum volume, minimum area</em>

In the general case of<em> an open-top box</em>, the volume is maximized when the cost of the bottom and the cost of each pair of opposite sides is the same. Here, the "cost" is simply the area, so the area of the bottom is 1/3 the total area, 36 in².

If the box has a <em>closed top</em>, then each pair of opposite sides will have the same cost for a maximum-volume box. If costs are uniform, the box is a cube.

7 0
3 years ago
If you are solving y 2+2y=48 by completing the square, the next line would be
snow_tiger [21]

For this case we have the following equation:

y ^ 2 + 2y = 48

By completing squares we have:

Step 1:

Add (\frac {b} {2}) ^ 2 on both sides:

y ^ 2 + 2y + 1 = 48 + 1

Step 2:

We rewrite the equation:

(y + 1) ^ 2 = 49

Step 3:

We solve the equation:

y = \pm \sqrt {49} -1\\y = \pm7-1

Solutions:

y = 6\\y = -8

Answer:

the next line would be:

y ^ 2 + 2y + 1 = 48 + 1


6 0
3 years ago
Read 2 more answers
Reduce a ratio 3/4in: 3/16 ft
Dmitrij [34]

Answer:

4in : 1ft

Step-by-step explanation:

We start with:

3/4 in = 3/16 ft

This means that the length of 3/4 inches is the same as the length of 3/16 feet.

To reduce this, we can start by dividing by 3 in both sides of the equation:

(3/4)/3 in = (3/16)/3 ft

1/4 in = 1/16 ft

Now we can multiply both sides by 16:

16/4 in = 16/16ft

4 in = 1ft

now we reduced the ratio to:

4in : 1ft

5 0
3 years ago
Help please :( I can’t seem to get the answer
igomit [66]

Answer:

6 i don't know what the unit is, but its 6 for time

Step-by-step explanation:

It is a two step problem

54=9t

divide both sides by 9 to get the value of t

6=t

I hope that helps you :)

4 0
3 years ago
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