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nikdorinn [45]
4 years ago
15

PLEASE HELP MEEEEE!!!! I WILL GIVE YOU BRAINLIST AND POINTS

Mathematics
1 answer:
Sloan [31]4 years ago
3 0

When you multiply numbers with the same base and exponents, you just add the exponents together. In the case of the first question:

11^{2} * 11^{7} = 11^{9}

When dividing, subtract the exponents instead, and when there's an exponent outside the parentheses the way it is on the 3rd question, multiply them together.

Hope this helps! :)

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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

<em></em>

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>

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Answer:

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<OBA= 90degrees =tangent perpendicular

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