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2 years ago

What letter on this number line represents -(3/2)?

Mathematics

1 answer:

Rina8888 [55]2 years ago

6 0

Answer:

Step-by-step explanation:

- 3/2 is - 1.5 , and B is - 1.5

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Differentiate with respect to X <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

Explain why 30 divided by x is the same as 30 -x-x-x-x-x-x equal 0

sattari [20]

The value would be zero (0) bcuz if all ends up being 0 no matter how many zeros then yes it would be 0 as the value

7 0

2 years ago

Solve for x.

REY [17]

The answer is A) b/(c+a)
Hope this helps

4 0

3 years ago

Josh $600 into an account that pays simple interest at a rate of 4% per year. How much interest will he be paid in the first 4 y

galben [10]

Answer:

i think its 96 dollars

Step-by-step explanation:

600 × .06 = 24

24 × 4 = 96

6 0

3 years ago

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Find tan(B) in the triangle. Choose 1 answer A 15/8 B 8/17 C 8/15 D 15/17

erastova [34]

Answer: C
Explanation: tan = opposite/adjacent. 8 is the opposite length from angle B and 15 is the adjacent length from angle B. so tan(B) = 8/15

6 0

3 years ago

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