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3 years ago

6

For which polygon is the sum of the interior angles equal to 720 degrees?

1 answer:

Goshia [24]3 years ago

4 0

The answer to this is Hexagon.

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The surface area of a right circular cone of radius r and height h is S = πr√ r 2 + h 2 , and its volume is V = 1 3 πr2h. What i

kirill115 [55]

Answer:

Required largest volume is 0.407114 unit.

Step-by-step explanation:

Given surface area of a right circular cone of radious r and height h is,

$S=\pi r\sqrt{r^2+h^2}$

and volume,

$V=\frac{1}{3}\pi r^2 h$

To find the largest volume if the surface area is S=8 (say), then applying Lagranges multipliers,

$f(r,h)=\frac{1}{3}\pi r^2 h$

subject to,

$g(r,h)=\pi r\sqrt{r^2+h^2}=8\hfill (1)$

We know for maximum volume $r\neq 0$ . So let $\lambda$ be the Lagranges multipliers be such that,

$f_r=\lambda g_r$

$\implies \frac{2}{3}\pi r h=\lambda (\pi \sqrt{r^2+h^2}+\frac{\pi r^2}{\sqrt{r^2+h^2}})$

$\implies \frac{2}{3}r h= \lambda (\sqrt{r^2+h^2}+\frac{ r^2}{\sqrt{r^2+h^2}})\hfill (2)$

And,

$f_h=\lambda g_h$

$\implies \frac{1}{3}\pi r^2=\lambda \frac{\pi rh}{\sqrt{r^2+h^2}}$

$\implies \lambda=\frac{r\sqrt{r^2+h^2}}{3h}\hfill (3)$

Substitute (3) in (2) we get,

$\frac{2}{3}rh=\frac{r\sqrt{R^2+h^2}}{3h}(\sqrt{R^2+h^2+}+\frac{r^2}{\sqrt{r^2+h^2}})$

$\implies \frac{2}{3}rh=\frac{r}{3h}(2r^2+h^2)$

$\implies h^2=2r^2$

Substitute this value in (1) we get,

$\pi r\sqrt{h^2+r^2}=8$

$\implies \pi r \sqrt{2r^2+r^2}=8$

$\implies r=\sqrt{\frac{8}{\pi\sqrt{3}}}\equiv 1.21252$

Then,

$h=\sqrt{2}(1.21252)\equiv 1.71476$

Hence largest volume,

$V=\frac{1}{3}\times \pi \times\frac{\pi}{8\sqrt{3}}\times 1.71476=0.407114$

3 0

3 years ago

Y=x+2<br> and then you have x=-3 <br><br><br> You also have to use transitive property

tresset_1 [31]

If y = x+2 and x = -3 then we can say that y = -3+2 after replacing the 'x' with -3

From here, we just add -3 and 2 to get -1 which is why y = -3+2 turns into y = -1

So together x = -3 and y = -1

They pair up to form (x,y) = (-3,-1)

8 0

3 years ago

PLEASE HELP!!!! <br>I WILL BE REPORTING ANSWERS THAT HAVE NOTHING TO DO WITH THE TOPIC

frez [133]

Answer:

its a little too small

Step-by-step explanation:

3 0

3 years ago

Equation Y equals 7X can be used to find the price of different amounts of honey

Fantom [35]

Answer:

x=y/7

Step-by-step explanation:

So, the variable x is the number of jars of honey.

y is the total price of the honey.

So, x=y/7

or,

y=7x

5 0

3 years ago

Three Questions 1) What does 5 7/8 - 2 3/8 equal? and 2)What does 5 7/12 -4 1/12 equal?3) What does 3 5/10 - 1 3/10 equal?

stiks02 [169]

1) 28/8=3 1/2
2) 18/12=1 1/2
3) 22/10=2 1/5

7 0

3 years ago