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3 years ago

Th Write an explicit formula for ans then term of the sequence 40,50,60, ....

Mathematics

1 answer:

kenny6666 [7]3 years ago

6 0

<h3>Answer: $a_n = 10n+30$ </h3>

n starts at 1, and n is a positive whole number (1,2,3,...)

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Explanation:

The sequence is arithmetic with first term 40 and common difference 10. Meaning we add 10 to each term to get the next one.

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a1 = 40 = first term

d = 10 = common difference

$a_n = a_1 + d(n-1)\\\\a_n = 40 + 10(n-1)\\\\a_n = 40 + 10n-10\\\\a_n = 10n + 30\\\\$

is the general nth term of this arithmetic sequence

Plug in n = 1 and you should get $a_1 = 40$

Plug in n = 2 and you should get $a_2 = 50$

and so on

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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:

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Step-by-step explanation:

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

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

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

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

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

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

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,

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

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

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Substitute this value in (1) we get,

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Answer:

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Step-by-step explanation:

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