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3 years ago

15

What is the twentieth term of the arithmetic sequence described by the equation an= 3n - 10?

1 answer:

sergij07 [2.7K]3 years ago

8 0

Answer:

The twentieth term is 50.

Step-by-step explanation:

The equation that describes the arithmetic sequence describes it's "general term", which means that all the numbers in that sequence must follow that equation. For instance, if we want to find the first term of the sequence we must make a = 1 and we have:

a1 = 3*1 - 10

a1 = -7

Therefore to find the twentieth term we need to make n equal to 20. This is done below:

a20 = 3*20 - 10

a20 = 60 - 10

a20 = 50

The twentieth term is 50.

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2 years ago

Find the standard form of the equation for the conic section represented by x^2 + 10x + 6y = 47.

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Answer:

The standard form of the equation for the conic section represented by $x^2\:+\:10x\:+\:6y\:=\:47$ is:

$4\left(-\frac{3}{2}\right)\left(y-12\right)=\left(x-\left(-5\right)\right)^2$

Step-by-step explanation:

We know that:

$4p\left(y-k\right)=\left(x-h\right)^2$ is the standard equation for an up-down facing Parabola with vertex at (h, k), and focal length |p|.

Given the equation

$x^2\:+\:10x\:+\:6y\:=\:47$

Rewriting the equation in the standard form

$4\left(-\frac{3}{2}\right)\left(y-12\right)=\left(x-\left(-5\right)\right)^2$

Thus,

The vertex (h, k) = (-5, 12)

Please also check the attached graph.

Therefore, the standard form of the equation for the conic section represented by $x^2\:+\:10x\:+\:6y\:=\:47$ is:

$4\left(-\frac{3}{2}\right)\left(y-12\right)=\left(x-\left(-5\right)\right)^2$

where

vertex (h, k) = (-5, 12)

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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2 years ago

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