All categories

3 years ago

Factor over the complex numbers: 36x2 + 9.

Mathematics

1 answer:

ludmilkaskok [199]3 years ago

4 0

$36x^2+9=(6x)^2-(-9)=(6x)^2-(-3^2)\\\\=(6x)^2-(3i)^2=(6x-3i)(6x+3i)\\\\\text{Used:}\\a^2-b^2=(a-b)(a+b)\\\\i^2=-1$

You might be interested in

Integrate dx/3sinx+4cosx

german

$\displaystyle\int\frac{\mathrm dx}{3\sin x+4\cos x}$

A standard approach would be the tangent half-angle substitution:

$t=\tan\dfrac x2\implies\mathrm dt=\dfrac12\sec^2\dfrac x2\,\mathrm dx$

Then

$\sin x=2\sin\dfrac x2\cos\dfrac x2\implies\sin x=\dfrac{2t}{1+t^2}$

$\cos x=\cos^2\dfrac x2-\sin^2\dfrac x2\implies\cos x=\dfrac{1-t^2}{1+t^2}$

from which we get

$\mathrm dx=\dfrac2{1+t^2}\,\mathrm dt$

So the integral becomes

$\displaystyle\int\frac{\frac2{1+t^2}}{\frac{6t}{1+t^2}+\frac{4(1-t^2)}{1+t^2}}\,\mathrm dt=\int\frac{\mathrm dt}{3t+2(1-t^2)}=-\int\frac{\mathrm dt}{2t^2-3t-2}$

Rewrite the denominator as

$2t^2-3t-2=(2t+1)(t-2)$

and expand the integrand into its partial fractions:

$\dfrac1{2t^2-3t-2}=\dfrac15\left(\dfrac1{t-2}-\dfrac2{2t+1}\right)$

We have

$\displaystyle-\frac15\int\frac1{t-2}-\frac2{2t+1}\,\mathrm dt=-\frac15(\ln|t-2|-\ln|2t+1|)+C$

$=\dfrac15\ln\left|\dfrac{2t+1}{t-2}\right|+C$

$=\dfrac15\ln\left|\dfrac{2\tan\frac x2+1}{\tan\frac x2-2}\right|+C$

6 0

3 years ago

At a local school supply store, a highlighter costs $1.25, a ballpoint pen costs $0.80, and a spiral notebook costs $2.75. Expla

egoroff_w [7]

Since the communative property shows you can add or multipy in any order, this means you can add all three of these in a different order and still get the same answer.....For example, you can do $1.25 + $0.80 + $2.75 or you can switch it around and do it in another way

4 0

4 years ago

Peggy worked 20 2/3 hours over three days last week. She worked the same number of hours each day. How many hours did Peggy work

Butoxors [25]

[20 2/3]/3 can be rewritten as an improper fraction.

20 2/3 = 62/3. Now we divide 62/3 by 3, which is the same as multiplying by 1/3.

62/9 is the number of hours each day, or 6 8/9 hours. Almost 7 hours. And this makes sense, as 20 2/3 is almost 21 hours.

3 0

4 years ago

Read 2 more answers

Hans is on the swim team. Each week he swims a total of 4000 meters. How many kilometers does he swim each week?

FrozenT [24]

Answer:

4 kilometers

plz give brainliest

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers