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bogdanovich [222]

3 years ago

10

Suppose a circle is divided into congruent slices. Match each number of slices with the

1 answer:

Stells [14]3 years ago

8 0

26 skate and with wunno when ask what about the gc and the park to park in

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2log(x-3)+1=5<br><br> can someone explain how to solve for x?

Brums [2.3K]

$\bf 2log(x-3)+1=5\iff 2log_{10}(x-3)+1=5\\\\\\ 2log_{10}(x-3)=4
\\\\\\
log_{10}(x-3)=\cfrac{4}{2}\implies log_{10}(x-3)=2\\\\
-----------------------------\\\\
{{ a}}^{log_{{ a}}x}=x\impliedby \textit{using this cancellation rule}\\\\
-----------------------------\\\\
10^{\cfrac{}{}log_{10}(x-3)}=10^2\implies x-3=10^2\implies x=100+3$

5 0

3 years ago

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,

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

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3 years ago

A large garden has a set of underground sprinklers. Suppose the center of the garden is located at the origin of a grid with int

Klio2033 [76]

Answer:

D

Step-by-step explanation:

Got it right edge2021

4 0

3 years ago

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viktelen [127]

Answer:

peepeepoopoo

Step-by-step explanation:

ur mom

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3 years ago

Simplfy : (8(x-1)^2)/ (6(x^2-1))

Lemur [1.5K]

Hope it cleared your doubt.

3 0

3 years ago