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3 years ago

In how many ways can 10 people wait in line for concert tickets

Mathematics

2 answers:

Mrrafil [7]3 years ago

8 0

10 * 1 *2 *3*4*5*6*7*8*9
3628800 is the answer

BabaBlast [244]3 years ago

4 0

Use a permutation. There are 20,274,200 combinations of ways to wait in line for ten people.

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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

2 years ago

Jamya is making a rectangular blanket. The length of the blanket is 10inches greater than it's worth, W, in inches. Write the fu

natta225 [31]

Answer: (w² + 10)inches²

Step-by-step explanation:

Since the width of the rectangular blanket is given as w and the length of the blanket is 10inches greater than it's width, therefore the length will be:

= 10 + w.

Therefore,

length = 10 + w

width = w

Area = length × width

Area = (10 + w) × w

Area = 10w + w²

Therefore, the area of the blanket will be (w² + 10)inches².

3 0

2 years ago

AD is a common internal tangent to circles B and C. Find the length of the radius of circle B. Round to the nearest hundredth.

ycow [4]

ΔABE ~ ΔDCE
AB=AE*DC/DE=18*4/6=12

8 0

3 years ago

Read 2 more answers

Solve each equation. 2y=7(y−2)+4 y = 4x=6−2(2−x) x =

aliya0001 [1]

Answer:

y=2 and x=1

Step-by-step explanation:

2y=7y-14+4

2y-7y=-14+4

-5y=-10/-5

y=2

4x=6-4+2x

4x-2x=6-4

2x=2/2

x=1

5 0

2 years ago

A reactangular court measures 600 cm wide and 700 cm long find the perimeter?

Tcecarenko [31]

Answer:

2(l+b)

2(600cm+700cm)

2(1300cm)

2600cm

Therefore, the perimeter of the rectangular court is 2600cm.

4 0

2 years ago