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podryga [215]
2 years ago
8

Whats the ninth term of 25 20 15 10 5

Mathematics
1 answer:
Kaylis [27]2 years ago
3 0

Given:

The sequence is 25, 20, 15, 10, 5.

To find:

The ninth term of the given sequence.

Solution:

We have,

25, 20, 15, 10, 5

It is an AP because the difference between two consecutive terms are same.

Here,

First term (a) = 25

Common difference (d) = 20-25

                                       = -5

The nth terms of an AP is

a_n=a+(n-1)d

Where, a is the first term and d is the common difference.

Putting a=25, n=9 and d=-5 to get the 9th term.

a_9=25+(9-1)(-5)

a_9=25+(8)(-5)

a_9=25-40

a_9=-15

Therefore, the ninth term of the given sequence is -15.

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What is the image of (0, 1) after a reflection over the line y = x?
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2 years ago
Given that cot θ = 1/√5, what is the value of (sec²θ - cosec²θ)/(sec²θ + cosec²θ) ?
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Step-by-step explanation:

\mathsf{Given :\;\dfrac{{sec}^2\theta - co{sec}^2\theta}{{sec}^2\theta + co{sec}^2\theta}}

\bigstar\;\;\textsf{We know that : \large\boxed{\mathsf{{sec}\theta = \dfrac{1}{cos\theta}}}}

\bigstar\;\;\textsf{We know that : \large\boxed{\mathsf{co{sec}\theta = \dfrac{1}{sin\theta}}}}

\mathsf{\implies \dfrac{\dfrac{1}{cos^2\theta} - \dfrac{1}{sin^2\theta}}{\dfrac{1}{cos^2\theta} + \dfrac{1}{sin^2\theta}}}

\mathsf{\implies \dfrac{\dfrac{sin^2\theta - cos^2\theta}{sin^2\theta.cos^2\theta}}{\dfrac{sin^2\theta + cos^2\theta}{sin^2\theta.cos^2\theta}}}

\mathsf{\implies \dfrac{sin^2\theta - cos^2\theta}{sin^2\theta + cos^2\theta}}

Taking sin²θ common in both numerator & denominator, We get :

\mathsf{\implies \dfrac{sin^2\theta\left(1 - \dfrac{cos^2\theta}{sin^2\theta}\right)}{sin^2\theta\left(1 + \dfrac{cos^2\theta}{sin^2\theta}\right)}}

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\mathsf{\implies \dfrac{1 -cot^2\theta}{1 + cot^2\theta}}

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\mathsf{\implies \dfrac{1 - \left(\dfrac{1}{\sqrt{5}}\right)^2}{1 + \left(\dfrac{1}{\sqrt{5}}\right)^2}}

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\mathsf{\implies \dfrac{5 - 1}{5 + 1}}

\mathsf{\implies \dfrac{4}{6}}

\mathsf{\implies \dfrac{2}{3}}

<u>Hence</u><u>,</u><u> option</u><u> </u><u>(</u><u>a)</u><u> </u><u>2</u><u>/</u><u>3</u><u> </u><u>is </u><u>your</u><u> </u><u>correct</u><u> </u><u>answer</u><u>.</u>

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iVinArrow [24]

Answer:

87.92

Step-by-step explanation:

you have to multiply 3.14 by 2 which will give you 6.28, then you multiply 6.28 by 14 which gives you 87.92. hope this helps

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