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gizmo_the_mogwai [7]

3 years ago

15

Transformations

1 answer:

Sergio [31]3 years ago

5 0

Answer:

a

0

=

44

XXX

a

1

=

?

XXX

a

2

=

?

XXX

a

3

=

?

XXX

a

4

=

92

Step-by-step explanation:

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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

Alice's book has 200 pages . Alic has read 75%of the pages in her book Nina has read the same number of pages but only 50% of th

kirza4 [7]

Answer:

I Believe the answer is 300

Step-by-step explanation:

75% of 200 is 150 and Nina also read 150 pages. They said Nina only read 50% of her book so that means there's 150 more pages left.

I Hope this helped and i explained it well enough for you to understand

(Correct me if i'm wrong)

8 0

2 years ago

If 7 less than 4 times a number is two more than that number, what is the result when the number is subtracted from 50?

Tasya [4]

Answer:

4x-7=x+2

3x=9

x=3

3-50=-47

Step-by-step explanation:

8 0

3 years ago

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Plzzzzz help!!!!! I will give brainliest

Vitek1552 [10]

Answer:

<h2>10.88inches</h2>

Step-by-step explanation:

3 0

2 years ago

What’s domain and range

antoniya [11.8K]

Domain is all the x values and range is the y values

7 0

3 years ago