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3 years ago

Please helpppp???????????

Mathematics

1 answer:

Temka [501]3 years ago

4 0

Step-by-step explanation:

I think 360-175 iam not sure

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HELP PLEASE!<br> Solve for m.<br><br> 3.6m = 14.4

Alekssandra [29.7K]

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3 years ago

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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

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2 years ago

What dose (-1/4) * (1/3)=

Nataly [62]

Answer:

7/12

Step-by-step explanation:

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3 years ago

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Simplify 4^9/4^3<br> can someone help me with this?

zaharov [31]

Answer:

4096

Step-by-step explanation:

Need to know how you got it? Comment on this answer.

4 0

3 years ago

Please help me if you are good at math!

iren2701 [21]

Answers:
y = 5(0.05) = 95% rate of decay
f(t) = 95(1.05) = 5% rate of growth
g(t) = 95(0.95) = 5% rate of decay
y = 5(1.95) = 95% rate of growth

Explanations:
y=5(0.05) has a 95% rate of decay because the number 5 is going down by 95%

f(t) = 95(1.05) has a 5% rate of growth because the number 95 is going up by 5%

g(t) = 95(0.95) has a 5% rate of decay because the number 95 is going down by 5%

y = 5(1.95) has a 95% rate of growth because the number 5 is going up by 95%

Hope this helped!

3 0

3 years ago

Please helpppp???????????​

Please helpppp???????????