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3 years ago

11

Notes on how to multiply/divide with scientific notation

1 answer:

snow_tiger [21]3 years ago

3 0

Answer:

Treat the numbers separately and powers separately.

Multiply the two results at the end.

Example:

(2×10⁵) ÷ (4×10²)

(2 ÷ 4) × (10⁵ ÷ 10²)

0.5 × 10³

5.0 × 10²

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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>

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3 years ago

Chen paid $36 for some books after a 25% discount was applied. What was the original price of the books?

Goryan [66]

The answer is $48 for the book

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3 years ago

Find two consecutive odd intefers whose product is 63

nikdorinn [45]

Two consecutive odd integers are known as back-to-back odd whole numbers; one right after the other.
For example; 1 and 3, 3 and 5, 5 and 7, and so on. Let’s work up to which two consecutive odd integers make a product of 63.
1 x 3 = 3; no
3 x 5 = 15; no
5 x 7 = 35; no
7 x 9 = 63; yes

From the work shown above, we can see that the two consecutive odd integers “7” and “9” make a product of 63.

I hope this helps!

4 0

4 years ago

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For f(x)=x^2, sketch the graph of g(x)=f(2x+6)

N76 [4]

Answer:

See image

Step-by-step explanation:

g(x) is a transformed version of f(x), its 6 units to the left with a verticle strech of a factor of 2

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3 years ago

Morgan scored 41 points in 3 games. How many points would you expect him to make in an 11 game season.

tino4ka555 [31]

Morgan will score 451 points in 11 games.

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3 years ago

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