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3 years ago

3M

Mathematics

1 answer:

Amiraneli [1.4K]3 years ago

7 0

Liza did 60 push ups

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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

I need an answer quick. I am trying to finish this fast.

inessss [21]

Answer:

D, m<4 is 137°

Step-by-step explanation:

The answer would be D, because m<4 would be supplementary with the angle that's 43 degrees. Supplementary angles add up to 180, so this could be found through the following equation.

x + 43 = 180

x would represent <4

You would now subtract 43 from both sides.

x = 137

8 0

3 years ago

Read 2 more answers

Number of comments got maxed out so here's another post.

suter [353]

That’s cool. i need p01nts so imma comment

7 0

3 years ago

PLEASE HELP THIS IS MATH 171 the topic is partial fraction decomposition

mars1129 [50]

What do you mean? Where is the question?

8 0

2 years ago

Help with my algebra homework

Maru [420]

Let's solve your equation step-by-step.

2x /5 + 3 = x/10 - 1

Step 1: Simplify both sides of the equation.

2x /5 + 3 = x/10 - 1

2/5x + 3 = 1/10x - 1

Step 2: Subtract 1/10x from both sides.

2/5x + 3 - 1/10x = 1/10x - 1 - 1/10x

3/10x + 3 = -1

Step 3: Subtract 3 from both sides.

3 /10x + 3 - 3 = -1 - 3

3/10x = -4

Step 4: Multiply both sides by 10/3.

(10/3) * (3/10x) = (10/3) * (-4)

x = -40/3

3 0

3 years ago