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gizmo_the_mogwai [7]

3 years ago

5

Someone help pls need help on this one

1 answer:

garri49 [273]3 years ago

5 0

Answer:

$\dfrac{2}{3x^5y}$

Step-by-step explanation:

A negative exponent in the numerator is the same as a positive exponent in the denominator, and vice versa.

... a^-b = 1/a^b . . . . . for any value of b, positive or negative

The exponent of a product is the sum of the exponents:

... (a^b)(a^c) = a^(b+c)

___

Applying these rules, you have

... = 2/(3x^4·x·y) = 2/(3x^(4+1)·y) = 2/(3x^5·y)

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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

5. Based on its table of values, which graph has the greatest slope?

lions [1.4K]

D they all have the same slope.

8 0

3 years ago

How do you write 40.545 in word form

DiKsa [7]

Answer:

forty point five hundred forty-five

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

16,055 is divided by 16?

serious [3.7K]

Your answer will be 1,000.3125

hope i helped!! :)

3 0

3 years ago

Read 2 more answers

The ending bank statement balance at November 30 is $7,070. The bank statement shows a service charge of $95, electronic funds

maks197457 [2]

Answer:

The adjusted book balance at November 30 is $7285.

Step-by-step explanation:

The Adjusted book balance at November 30 =

Ending bank statement balance + Deposits in transit - outstanding checks

7,070+2,050-1,835 = 7285

8 0

3 years ago