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3 years ago

14

Find g. Write your answer as an integer or as a decimal rounded to the nearest tenth.

1 answer:

Soloha48 [4]3 years ago

6 0

Step-by-step explanation:

$\frac{EG}{ \sin(/EFG) } = \frac{EF}{ \sin(/EFG) } \\ \frac{7}{ \sin(36°) } = \frac{g}{ \sin(121°) } \\ g = 10.208$

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Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its surface area is 181.5 square cen

3241004551 [841]

Answer:

The base and height of the solid is 5.5cm

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Step-by-step explanation:

Given

$Surface\ Area = 181.5cm^2$

Required

Determine the dimensions that maximizes the volume

Let the base dimension be x and the height be h

The volume is calculated as:

$Volume =x^2 * h$

$Volume =x^2h$

181.5 =x^2h

The surface area (S) is calculated as this:

$S = 2(x^2 + xh + xh)$

$S = 2(x^2 + 2xh)$

$S = 2x^2 + 4xh$

Substitute 181.5 for S

$181.5 = 2x^2 + 4xh$

Make h the subject:

$4xh = 181.5 - 2x^2$

$h = \frac{181.5 - 2x^2}{4x}$

Substitute $h = \frac{181.5 - 2x^2}{4x}$ in $Volume =x^2h$

$V = x^2(\frac{181.5 - 2x^2}{4x})$

$V = x(\frac{181.5 - 2x^2}{4})$

$V = \frac{1}{4}(x)(181.5 - 2x^2)$

$V = \frac{181.5x}{4} - \frac{2x^3}{4}$

$V = \frac{181.5x}{4} - \frac{x^3}{2}$

To get the maximum, we differentiate V with respect to t and set the differentiation to 0

$dV = \frac{181.5}{4} - \frac{3x^2}{2}$

Set to 0

$0 = \frac{181.5}{4} - \frac{3x^2}{2}$

$\frac{3x^2}{2} = \frac{181.5}{4}$

Multiply through by 4

$4 * \frac{3x^2}{2} = \frac{181.5}{4} * 4$

$2*3x^2 = 181.5$

$6x^2 = 181.5$

$x^2 = \frac{181.5}{6}$

$x^2 = 30.25$

$x = \sqrt{30.25$

$x = 5.5$

Recall that:

$h = \frac{181.5 - 2x^2}{4x}$

$h = \frac{181.5 - 2 * 5.5^2}{4 * 5.5}$

$h = \frac{181.5 - 60.5}{22}$

$h = \frac{121}{22}$

$h = 5.5$

So, we have:

$h = 5.5$

$x = 5.5$

<em>Hence, the base and height of the solid is 5.5cm</em>

7 0

3 years ago

Please help!!!! Will give Brainliest!!!!!!!!!!!!!!!!!!

Ilya [14]

Answer:

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3 years ago

Juliette spends $6.12 at the store Morgan spends 3 times as much as Juliette Jonah spends $4.29 more than Morgan how much money

lions [1.4K]

6.12 x 3=18.36
18.36+4.29=22.65
convert to money = $22.65

7 0

3 years ago

Reniel saves 30% of every paycheck. His paycheck last week was $560. How much did Reniel save last week?

nadezda [96]

$560* (30/100)
= $168

Reniel saved $168 last week~

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3 years ago

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Simplify:-(x +9) -3(4x - 3)<br> -13x + 18<br> -13x<br> -11x + 18<br> -11x

DochEvi [55]

Answer:The answer is -13x

Step-by-step explanation:

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4 years ago

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