What is the circumference of circle T

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

and what is distance jeremy jumps from the ramp to the fire escape is _______ feet (round to the nearest tenth of a foot)

Cloud [144]

Answer:

sin(70°) =10/x

The distance Jeremy jumps from the ramp to the fire escape is <u>10.6</u> feet

Step-by-step explanation:

From the question shown in the picture attached, the vertical height Jeremy has to jump is: 15 - 5 = 10 ft

A right triangle is formed, where the angle between the hypotenuse (called x) and one of the legs is: 160° - 90° = 70°, and the vertical height Jeremy has to jump, is the leg opposite to that angle.

From sine definition:

sin(70°) = opposite/hypotenuse

sin(70°) = 10/x

x = 10/sin(70°)

x = 10.6 ft

4 0

3 years ago

Please help ASAP!! Will mark brainliest!!

Sergio [31]

The answer is 10 because all the angles are equal making it a equilateral triangle.

Therefore, the sides are all equal to one another, 3x - 8 = 5x - 20.

You just solve for x and get 6. You then plug in 6 for x and evauluate the equation, getting 10.

3 0

3 years ago

Read 2 more answers

what is the answer to this The sixth grade teachers ordered 54 bags of candy to be split among 12 students. How many bags of can

nadya68 [22]

Answer:

The answer is 4.5 and 9/2

Step-by-step explanation:

First

54 / 12 = 4.5

Then

Change it into a fraction

Write is fraction form 4.5 / 1

Multiply both numerator and denominator by 10 for every number after the decimal point

4.5 × 10

1 × 10

Which will equal 45/10

Then Reduce the fraction gives 9/2

3 0

3 years ago

(9\times100)+(8\times10)+\left (7\times\dfrac{1}{1000} \right )(9×100)+(8×10)+(7×

Tanya [424]

Answer:

7,980

Step-by-step explanation:

900 + 80 + (7 x 1000)

3 0

3 years ago