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2 years ago

6

Five eighths of x is 2 1/2. what is x?

1 answer:

Nitella [24]2 years ago

6 0

4

Step-by-step explanation:

8/5(put 8 as numerator becuz we need to find all x from 5/8) x 2 1/2＝4

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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

2 years ago

Will do brainly for this

Tcecarenko [31]

Answer:

180 Degrees

Step-by-step explanation:

I had the same question and it worked/correct.

6 0

3 years ago

To start planning the rooms' floor plans, you draw them each to scale on large sheets of paper. You are going to use the scale 1

Gre4nikov [31]

480 is the answer I just took the test

8 0

3 years ago

Select the decimal that is equivalent to 101/500

s344n2d4d5 [400]

The answer should be .202. If the question is looking for rounding, it might want .2 instead, but only if it tells you to round. Just divide 101 by 500 in a calculator and that's your answer.

Hopefully this helps! Let me know if you have any more questions.

4 0

2 years ago

Read 2 more answers

James is twice as old as Hannah. Four years from now, the sum of their ages will be 41. How old are they now?

NemiM [27]

James is 24.5 and Hannah is 12.5.

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2 years ago