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3 years ago

I don’t understand how to factor fractions :( can someone help me with this problem

Mathematics

1 answer:

anzhelika [568]3 years ago

6 0

Can you take a picture of the whole problem? i may be able to solve it then. Thanks!

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Differentiate with respect to X <br><img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B%20%5Cfrac%7Bcos2x%7D%7B1%20%2Bsin2x%20%7D%20

Mice21 [21]

Power and chain rule (where the power rule kicks in because $\sqrt x=x^{1/2}$ ):

$\left(\sqrt{\dfrac{\cos(2x)}{1+\sin(2x)}}\right)'=\dfrac1{2\sqrt{\frac{\cos(2x)}{1+\sin(2x)}}}\left(\dfrac{\cos(2x)}{1+\sin(2x)}\right)'$

Simplify the leading term as

$\dfrac1{2\sqrt{\frac{\cos(2x)}{1+\sin(2x)}}}=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}$

Quotient rule:

$\left(\dfrac{\cos(2x)}{1+\sin(2x)}\right)'=\dfrac{(1+\sin(2x))(\cos(2x))'-\cos(2x)(1+\sin(2x))'}{(1+\sin(2x))^2}$

Chain rule:

$(\cos(2x))'=-\sin(2x)(2x)'=-2\sin(2x)$

$(1+\sin(2x))'=\cos(2x)(2x)'=2\cos(2x)$

Put everything together and simplify:

$\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{(1+\sin(2x))(-2\sin(2x))-\cos(2x)(2\cos(2x))}{(1+\sin(2x))^2}$

$=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{-2\sin(2x)-2\sin^2(2x)-2\cos^2(2x)}{(1+\sin(2x))^2}$

$=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{-2\sin(2x)-2}{(1+\sin(2x))^2}$

$=-\dfrac{\sqrt{1+\sin(2x)}}{\sqrt{\cos(2x)}}\dfrac{\sin(2x)+1}{(1+\sin(2x))^2}$

$=-\dfrac{\sqrt{1+\sin(2x)}}{\sqrt{\cos(2x)}}\dfrac1{1+\sin(2x)}$

$=-\dfrac1{\sqrt{\cos(2x)}}\dfrac1{\sqrt{1+\sin(2x)}}$

$=\boxed{-\dfrac1{\sqrt{\cos(2x)(1+\sin(2x))}}}$

5 0

3 years ago

If a polynomial has one root in the form a+√b , it has a second root in the form of a_√b

Elina [12.6K]

Answer:

Step-by-step explanation:

a+√b

a-√b

3 0

2 years ago

It’s all in the picture number 5!!!pleaseee help‼️‼️‼️‼️‼️‼️ASAP‼️‼️

Mariulka [41]

We know that m<JKL = m<JKM + m<MKL

Let's substitute the values from the picture into our equation above.

10x - 11 = 43 + 8x - 20

Combine like terms.

10x - 11 = 8x + 23

Subtract 8x from both sides and add 11 to both sides.

2x = 34

Divide both sides by 2

x = 17

m<MKL = 8x - 20 = 8(17) - 20 = 136 - 20 = 116 degrees.

m<JKL = 10x - 11 = 10(17) - 11 = 170 - 11 = 159 degrees.

7 0

3 years ago

Can someone explain 15-20? I really need help and it's due tomorrow. Thank you in advance!

zubka84 [21]

15-20 is -5. If you put 15 on a number line and go back twenty spaces you land on -5 hope this helps.

7 0

3 years ago

Read 2 more answers

A + (B + C) = (A + B) + C <br> property

charle [14.2K]

Answer:

a+b

Step-by-step explanation:

math

8 0

2 years ago

Read 2 more answers