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4 years ago

9

Mr. Gomez earned $320 for working an eight-hour shift at the lumber yard. What is his hourly wage?

1 answer:

Ksivusya [100]4 years ago

8 0

In this question, we're trying to find Mr. Gomez hourly wage.

This is how much he gets paid per hour.

We know that he earned $320 while working an 8 hour shift.

To find his hourly wage, divide 320 by 8:

320 ÷ 8 = 40

Answer:

Mr. Gomez hourly wage was $40

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True [87]

Answer:

∠ 1 = 20°, ∠ 2 = 160°

Step-by-step explanation:

∠ 1 and ∠ 2 are adjacent angles and are supplementary, that is sum to 180°

x - 12 + 5x = 180 , that is

6x - 12 = 180 ( add 12 to both sides )

6x = 192 ( divide both sides by 6 )

x = 32

Thus

∠ 1 = x - 12 = 32 - 12 = 20°

∠ 2 = 5x = 5 × 32 = 160°

5 0

3 years ago

The total surface area of a closed cylinder is

Degger [83]

The maximum volume of the cylinder is 27147.355 at the maximum point $r = \frac{50}{\sqrt{3} }$ .

<h3>How do you find the maximum volume of the cylinder?</h3>

The formula for the volume of the cylinder v = $\pi$ $r^{2}$ h, To find the maximum volume of the cylinder we apply the condition of maxima $\frac{\mathrm{d} v}{\mathrm{d} r}$ = 0.

Let r cm be the radius and h cm be the height of the closed cylinder.

Then, Total surface area of the cylinder = $2\pi r(r+h)$

$5000$ = $2\pi r^{2} +2\pi rh$

$h$ = $\frac{5000-2\pi r^{2} }{2\pi rh}$ .............(1)

Volume of the cylinder v = $\pi r^{2} h$

Substitute the value of $h$ in the above equation

$\Rightarrow$ = $\pi r^{2}$ × $\left [ \frac{5000-2\pi r^{2}}{2\pi r} \right ]$

$\Rightarrow$ = $\frac{r}{2}$ × $(5000-2\pi r^{2} )$

$\Rightarrow$ v = $2500r-\pi r^{3}$ ..............(2)

Now, for the maximum volume of the cylinder $\frac{\mathrm{d} v}{\mathrm{d} r}$ = 0

$\Rightarrow$ $\frac{\mathrm{d} (2500r-\pi r^{3})}{\mathrm{d} r} = 0$

$\Rightarrow$ $3\pi r^{2} = 2500$

$\Rightarrow$ $r^{2} = \frac{2500}{3\pi }$

$\Rightarrow$ $r = \frac{50}{\sqrt{3\pi } }$

Volume is maximum for $r = \frac{50}{\sqrt{3\pi } }$

Then, v = $2500r-\pi r^{3}$

$\Rightarrow$ = $2500 \frac{50}{\sqrt{3\pi } } -\pi (\frac{50}{\sqrt{3\pi } } )^{3}$

$\Rightarrow$ = $\frac{125000}{\sqrt{3\pi } } - \frac{125000}{3\sqrt{3\pi } }$

$\Rightarrow$ = $\frac{125000}{\sqrt{3\pi } }$ × $\frac{2}{3}$

$\Rightarrow$ = $\frac{250000}{3\sqrt{3\pi } }$

$\Rightarrow$ v = 27147.355

Hence, The maximum volume of the cylinder is 27147.355 at the maximum point $r = \frac{50}{\sqrt{3} }$ .

To learn more about total surface area and volume of the cylinder from the given link

brainly.com/question/16095729

#SPJ4

3 0

2 years ago

What is the answer to -4p-7=5p+11 ? pls show work

Klio2033 [76]

<span>-4p-7=5p+11
-4p - 5p = 11 + 7
-9p = 18
p = -2</span>

4 0

4 years ago

Read 2 more answers

Which of the following describes the translation of the graph of y = x 2 to

VLD [36.1K]

Answer:

reflect over the x-axis and shift down 3

Step-by-step explanation:

The leading coefficient of -1 means the graph is reflected over the x-axis. The addition of -3 to the function means each graphed point is shifted down 3 units from the original.

The graph of y = -x^2 -3 is the result of the transformation ...

reflect over the x-axis and shift down 3

7 0

4 years ago

Cheryl is making a mixed fruit drink for a party. She mixes 8 pints each of apple juice and cranberry juice.

Natali5045456 [20]

Answer:

256 fluid onces

Step-by-step explanation:

Hope this helps!!!

6 0

3 years ago