What value of x makes this equation true?

Mathematics

1 answer:

Softa [21]2 years ago

3 0

Well you gotta find out what x means

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Help 12-14 please !!!

In-s [12.5K]

I would suggest asking your teacher for help that seems like a lot... :(

8 0

2 years ago

Integral of x"2+4/x"2+4x+3

dolphi86 [110]

I'm guessing you mean

$\displaystyle \int\frac{x^2+4}{x^2+4x+3}\,\mathrm dx$

First, compute the quotient:

$\displaystyle \frac{x^2+4}{x^2+4x+3} = 1 + \frac{4x-1}{x^2+4x+3}$

Split up the remainder term into partial fractions. Notice that

x ² + 4x + 3 = (x + 3) (x + 1)

Then

$\displaystyle \frac{4x-1}{x^2+4x+3} = \frac a{x+3} + \frac b{x+1} \\\\ \implies 4x - 1 = a(x+1) + b(x+3) = (a+b)x + a+3b \\\\ \implies a+b=4 \text{ and }a+3b = -1 \\\\ \implies a=\frac{13}2\text{ and }b=-\frac52$

So the integral becomes

$\displaystyle \int \left(1 + \frac{13}{2(x+3)} - \frac{5}{2(x+1)}\right) \,\mathrm dx = \boxed{x + \frac{13}2\ln|x+3| - \frac52 \ln|x+1| + C}$

We can simplify the result somewhat:

$\displaystyle x + \frac{13}2\ln|x+3| - \frac52 \ln|x+1| + C \\\\ = x + \frac12 \left(13\ln|x+3| - 5\ln|x+1|\right) + C \\\\ = x + \frac12 \left(\ln\left|(x+3)^{13}\right| - \ln\left|(x+1)^5\right|\right) + C \\\\ = x + \frac12 \ln\left|\frac{(x+3)^{13}}{(x+1)^5}\right| + C \\\\ = \boxed{x + \ln\sqrt{\left|\frac{(x+3)^{13}}{(x+1)^5}\right|} + C}$

3 0

2 years ago

If R is the total resistance for a parallel circuit with two resistors of resistances of r1 and r2 then 1/r=1/r1+1/r2 find the r

Allushta [10]

A little Algebra, and we're home free!

We are given R = 20 and r2 = 75. We need to find r1.

The formula is 1/R = 1/r1 + 1/r2. Plug-in:
1/20 = 1/r1 + 1/75
1/20 - 1/75 = 1/r1
0.0366 = 1/r1
r1 = 1/0.03666
r1 = 27.272

Our answer is r1 = 27 ohms.

6 0

3 years ago

Read 2 more answers

what is the leading term of the following polynomial? f(x)=5x4-3x3+9x2+6x-7 A.5x4. B.-3x4. C.9x2. D.6x

mixas84 [53]

Answer:

A = 5x^4

Step-by-step explanation:

3 0

3 years ago

What is the slope of the line passing through the points (–1, 3) and (4, –7)?

WINSTONCH [101]