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2 years ago

Write the sum using summation notation, assuming the suggested pattern continues.

Mathematics

1 answer:

Lina20 [59]2 years ago

4 0

ANSWER

$\sum _{n = 1} ^{18} (6n - 15)$

EXPLANATION

The given series

$- 9 - 3 + 3 + 9 + ... + 81$

This is an arithmetic series with a common difference of

$d = - 3 - - 9 = 6$

The first term of the series is:

$a_1 = - 9$

The general term is given by:

$a_n =a_1 + d(n - 1)$

$a_n = - 9+ 6(n - 1)$

$a_n = - 9+ 6n - 6$

$a_n =6n - 15$

The last term is 81

We can use this to determine the number of terms in the series.

$81=6n - 15$

$81 + 15=6n$

$6n = 96$

$n = \frac{96}{6} = 16$

The summation notation is:

$\sum _{n = 1} ^{18} (6n - 15)$

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Answer:

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Step-by-step explanation:

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2 years ago

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Olin [163]

I'm guessing the second derivative is for y with respect to x, i.e.

$\dfrac{\mathrm d^2y}{\mathrm dx^2}$

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$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm d\theta}\dfrac{\mathrm d\theta}{\mathrm dx}=\dfrac{\frac{\mathrm dy}{\mathrm d\theta}}{\frac{\mathrm dx}{\mathrm d\theta}}$

We have

$y=b\sin\theta\implies\dfrac{\mathrm dy}{\mathrm d\theta}=b\cos\theta$

$x=a\cos\theta\implies\dfrac{\mathrm dx}{\mathrm d\theta}=-a\sin\theta$

and so

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{b\cos\theta}{-a\sin\theta}=-\dfrac ba\cot\theta$

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$\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm df}{\mathrm dx}$

By the chain rule,

$\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm df}{\mathrm d\theta}\dfrac{\mathrm d\theta}{\mathrm dx}=\dfrac{\frac{\mathrm df}{\mathrm d\theta}}{\frac{\mathrm dx}{\mathrm d\theta}}$

We have

$f=-\dfrac ba\cot\theta\implies\dfrac{\mathrm df}{\mathrm d\theta}=\dfrac ba\csc^2\theta$

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2 years ago

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Answer:

Step-by-step explanation:

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3 years ago

Without using a calculator, choose the statement that best describes the value of

castortr0y [4]

Answer:

Step-by-step explanation:

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2 years ago

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ExtremeBDS [4]

Answer:

The value of Mode is 2.43

Step-by-step explanation:

To find the mode of the given data first we have to arrange it in a increasing order then find out mean and median of the given data
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so the median is equal to 3.65
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