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2 years ago

10

Which of the following shows the simplified function of csc x sin(pi/2 -x)?

1 answer:

alex41 [277]2 years ago

6 0

Answer:

cot x

Step-by-step explanation:

using the identities

csc x = $\frac{1}{sinx}$

sin( $\frac{\pi }{2}$ - x) = cos x

then

csc x × sin ( $\frac{\pi }{2}$ - x)

= $\frac{1}{sinx}$ × cosx

= $\frac{cosx}{sinx}$

= cot x

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strojnjashka [21]

Answer:

The candle has a radius of 8 centimeters and 16 centimeters and uses an amount of approximately 1206.372 square centimeters.

Step-by-step explanation:

The volume ( $V$ ), in cubic centimeters, and surface area ( $A_{s}$ ), in square centimeters, formulas for the candle are described below:

$V = \pi\cdot r^{2}\cdot h$ (1)

$A_{s} = 2\pi\cdot r^{2} + 2\pi\cdot r \cdot h$ (2)

Where:

$r$ - Radius, in centimeters.

$h$ - Height, in centimeters.

By (1) we have an expression of the height in terms of the volume and the radius of the candle:

$h = \frac{V}{\pi\cdot r^{2}}$

By substitution in (2) we get the following formula:

$A_{s} = 2\pi \cdot r^{2} + 2\pi\cdot r\cdot \left(\frac{V}{\pi\cdot r^{2}} \right)$

$A_{s} = 2\pi \cdot r^{2} +\frac{2\cdot V}{r}$

Then, we derive the formulas for the First and Second Derivative Tests:

First Derivative Test

$4\pi\cdot r -\frac{2\cdot V}{r^{2}} = 0$

$4\pi\cdot r^{3} - 2\cdot V = 0$

$2\pi\cdot r^{3} = V$

$r = \sqrt[3]{\frac{V}{2\pi} }$

There is just one result, since volume is a positive variable.

Second Derivative Test

$A_{s}'' = 4\pi + \frac{4\cdot V}{r^{3}}$

If $\left(r = \sqrt[3]{\frac{V}{2\pi}}\right)$ :

$A_{s} = 4\pi + \frac{4\cdot V}{\frac{V}{2\pi} }$

$A_{s} = 12\pi$ (which means that the critical value leads to a minimum)

If we know that $V = 3217\,cm^{3}$ , then the dimensions for the minimum amount of plastic are:

$r = \sqrt[3]{\frac{V}{2\pi} }$

$r = \sqrt[3]{\frac{3217\,cm^{3}}{2\pi}}$

$r = 8\,cm$

$h = \frac{V}{\pi\cdot r^{2}}$

$h = \frac{3217\,cm^{3}}{\pi\cdot (8\,cm)^{2}}$

$h = 16\,cm$

And the amount of plastic needed to cover the outside of the candle for packaging is:

$A_{s} = 2\pi\cdot r^{2} + 2\pi\cdot r \cdot h$

$A_{s} = 2\pi\cdot (8\,cm)^{2} + 2\pi\cdot (8\,cm)\cdot (16\,cm)$

$A_{s} \approx 1206.372\,cm^{2}$

The candle has a radius of 8 centimeters and 16 centimeters and uses an amount of approximately 1206.372 square centimeters.

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3 years ago

A camera has a listed price of $522.98 before tax. If the sales tax rate is 8.25%, find the total cost of the camera with sales

svetoff [14.1K]

Answer:

4,314.6

Step-by-step explanation:

522.98 multiplied by 8.25 is 4,314.585 which rounded to the nearest cent is 4,314.6

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Duncan shares 20 percent of all of his sales commissions with his personal assistant. If Duncan earns x dollars in commissions a

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Answer:

it b

Step-by-step explanation:

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2 years ago

Solve the equation. <br><br> 3.9 + x = − 8

AnnZ [28]

Answer:

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Step-by-step explanation:

-8 - 3.9 = -11.9

-11.9+ 3.9 = -8

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I... don’t know? How many hours is he working a year? How many days is he working?

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