Find the volume of the rectangular prism: F. 36x G. 48x H. 72x J. 24x

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

2 years ago

An online ticket seller charges $44 for each ticket to a concert, plus a fixed handling fee of $12. Define the unknown variables

const2013 [10]

The unknown variables are how many tickets are being bought and the total.

t=tickets

x=total

44t+12=x

6 0

3 years ago

1) Which of the following is NOT the same as 4 : 20 ?* 8:40 6:50 5:25 1:5

adoni [48]

6:50 is the answer! Hope this helps. You can figure this out by crossing out the ones you KNOW are factors of 4 and 20. And 6:50 is NOT a factor of them . Hope this helped!!

4 0

2 years ago

A club decides to sell t-shirts for 15 as a fundraiser. It costs 20 plus 9 per t-shirt to make the t-shirts. Write and solve an

zepelin [54]

The club needs to make and sell 29 t-shirts in order to profit at least 150.

Explanation

Suppose , the number of t-shirts the club needs to make and sell is $x$

Selling price of each t-shirt is 15, so the total selling price of $x$ t-shirts $= 15x$

It costs 20 plus 9 per t-shirt to make the t-shirts. So, the total making cost of $x$ t-shirts $= 20+9x$

Now for getting profit at least 150 , the equation will be.....

$15x-(20+9x)= 150\\ \\ 15x-20-9x=150\\ \\ 6x-20=150\\ \\ 6x=150+20=170\\ \\ x= \frac{170}{6}=28.333....$

It means the value of x should be at least 28.333...

As here x is the number of t-shirts and it can't be in decimal , so the minimum value of x will be 29.

4 0

3 years ago

True or false:(6.9×10^8) (3.1×10^8)=2.139×10^17. A true B false

insens350 [35]

Answer:

True

Step-by-step explanation:

3 0

3 years ago

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