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3 years ago

X^2+4x-1/(x+2)^2=0 solve for x

1 answer:

5 0

x^2+4x-1/(x+2)^2=0
x^2 + 4x - 1 = 0

$\frac{x^2+10x-7}{x^2+10x+25} =0\\x^2+10x-7=0\\x= \frac{-b\pm\sqrt{b^2-4ac}}{2a}$ ;
where a = 1, b = 4 and c = -1

$x=\frac{-4\pm\sqrt{4^2-(4\times1\times(-1)}}{2\times1}\\=\frac{-4\pm\sqrt{16+4}}{2}=\frac{-4\pm\sqrt{20}}{2}\\=\frac{-4\pm\sqrt{4\times5}}{2}=\frac{-4\pm2\sqrt{5}}{2}=-2\pm\sqrt{5}\\=-2+\sqrt{5}
 \ or \ -2-\sqrt{5}\\x=0.24 \ or \ x = -4.24$

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What is the sum of the first 51 consecutive odd positive integers?

Angelina_Jolie [31]

We call:

$a_{n}$ as the set of the first 51 consecutive odd positive integers, so:

 $a_{n} = \{1, 3, 5, 7, 9...\}$

Where:
$a_{1} = 1$
$a_{2} = 3$
$a_{3} = 5$
$a_{4} = 7$
$a_{5} = 9$
and so on.

In mathematics, a sequence of numbers, such that the difference between two consecutive terms is constant, is called Arithmetic Progression, so:

3-1 = 2
5-3 = 2
7-5 = 2
9-7 = 2 and so on.

Then, the common difference is 2, thus:

 $a_{n} = \{ a_{1} , a_{1} + d, a_{1} + d + d,..., a_{1} + (n-2)d+d\}$

Then:

 $a_{n} = a_{1} + (n-1)d$

So, we need to find the sum of the members of the finite series, which is called arithmetic series:

There is a formula for arithmetic series, namely:

 $S_{k} = ( \frac{a_{1} + a_{k}}{2} ).k$

Therefore, we need to find:
 $a_{k} = a_{51}$

Given that $a_{1} = 1$ , then:

$a_{n} = a_{1} + (n-1)d = 1 + (n-1)(2) = 2n-1$

Thus:
$a_{k} = a_{51} = 2(51)-1 = 101$

Lastly:

$S_{51} = ( \frac{1 + 101}{2} ).51 = 2601$

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3 years ago

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elena-14-01-66 [18.8K]

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3 years ago

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4 years ago

On his way to a local Hunting and Gathering Convention, Caveperson Stony Grok picks up a rock, drops it into a lake and watches

olganol [36]

Answer:

I guess that "Ura nok seblu" means that all rocks sink in water.

Step-by-step explanation:

A conjecture is an idea, opinion, theory or hypothesis, that is based on partial or incomplete information or evidence. Conjectures are generally speculations since there is not enough proof or evidence to support them.

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3 years ago

<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%7D%7B10.1%7D%20%20%3D%203.5" id="TexFormula1" title=" \frac{x}{10.1} = 3.5" al

dsp73

Answer:

x=35.35

Step-by-step explanation:

If you multiply $\frac{x}{10.1} .1$ by 10.1 that will cancel out the 10.1s, then since you multiplies one side of the equation by something you have to multiply the other too. So 3.5*10.1 = 35.35. Then since the 10.1s canceled out this leaves us with x=35.35. Let me know if you need any more help.

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3 years ago