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3 years ago

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Geometry help!! Will give Brainliest! What are the coordinates of Point A? (photo attached)

1 answer:

Nimfa-mama [501]3 years ago

8 0

last (-5,2,-4) yepp well

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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,

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

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3 years ago

What is a possible value for the missing term of the geometric sequence ?

lesantik [10]

50 * 3 = 150 and 150 * 3 = 450

So the answer is b 150

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3 years ago

A class is made up of 10 boys and 5 girls. Half of the boys wear glasses. A student is selected at random from this class. What

saveliy_v [14]

Answer:

1/3

Step-by-step explanation:

Of the 15 students in the class, 5 are boys with glasses. The probability of selecting one at random is 5/15 = 1/3.

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3 years ago

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How to factor z^12 - 64 (question 17.)

aivan3 [116]

(z^6 - 8)(z^6 + 8) is the answer. If you verify this by multiplying, you will see that: (z^6 - 8)(z^6 + 8) = z^(6+6) + 8z^6 - 8z^6 - 64 = z^12 + 0 - 64 = z^12 - 64 Hope this helps, Brian

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3 years ago

A postcard collector has 1,230 postcards if she display them on pages that hold 6 cards each how many pages does she need

Lady bird [3.3K]

205 pages of cards :))

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3 years ago

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