All categories

2 years ago

Combinations- how to show that 10C2=10C8

Mathematics

1 answer:

Black_prince [1.1K]2 years ago

7 0

By definition,

${}^nC_k=\dbinom nk=\dfrac{n!}{k!(n-k)!}$

We have

$\dbinom{10}2=\dfrac{10!}{2!(10-2)!}=\dfrac{10!}{2!8!}=\dfrac{10!}{(10-8)!8!}=\dbinom{10}8$

and so

${}^{10}C_8={}^{10}C_2$

You might be interested in

Answer this now please :)

natta225 [31]

9514 1404 393

Answer:

E. 384 cu ft

Step-by-step explanation:

The sum of length and width is half the perimeter, so the width is ...

(40/2) -12 = 8 . . . feet

The depth is half that, so is 8/2 = 4 feet.

The volume is ...

V = LWH = (12 ft)(8 ft)(4 ft) = 384 ft³

4 0

2 years ago

Find the complex fourth roots of 81(cos(3pi/8) + i sin(3pi/8))

BartSMP [9]

By using De Moivre's theorem:

If we have the complex number ⇒ z = a ( cos θ + i sin θ)
∴ $\sqrt[n]{z} = \sqrt[n]{a} \ (cos \ \frac{\theta + 360K}{n} + i \ sin \ \frac{\theta +360k}{n} )$
k= 0, 1 , 2, ..... , (n-1)

For The given complex number ⇒ z = 81(cos(3π/8) + i sin(3π/8))


Part (A) find the modulus for all of the fourth roots

∴ The modulus of the given complex number = l z l = 81

∴ The modulus of the fourth root = $\sqrt[4]{z} = \sqrt[4]{81} = 3$

Part (b) find the angle for each of the four roots

The angle of the given complex number = $\frac{3 \pi}{8}$
There is four roots and the angle between each root = $\frac{2 \pi}{4} = \frac{\pi}{2}$
The angle of the first root = $\frac{ \frac{3 \pi}{8} }{4} = \frac{3 \pi}{32}$
The angle of the second root = $\frac{3\pi}{32} + \frac{\pi}{2} = \frac{19\pi}{32}$
The angle of the third root = $\frac{19\pi}{32} + \frac{\pi}{2} = \frac{35\pi}{32}$
The angle of the fourth root = $\frac{35\pi}{32} + \frac{\pi}{2} = \frac{51\pi}{32}$

Part (C): find all of the fourth roots of this

The first root = $z_{1} = 3 ( cos \ \frac{3\pi}{32} + i \ sin \ \frac{3\pi}{32})$
The second root = $z_{2} = 3 ( cos \ \frac{19\pi}{32} + i \ sin \ \frac{19\pi}{32})$

The third root = $z_{3} = 3 ( cos \ \frac{35\pi}{32} + i \ sin \ \frac{35\pi}{32})$
The fourth root = $z_{4} = 3 ( cos \ \frac{51\pi}{32} + i \ sin \ \frac{51\pi}{32})$

7 0

3 years ago

As a promotion, the first 50 customers who entered a certain store at a mall were asked to choose from one of two discounts. The

julsineya [31]

Answer: rerere

Step-by-step explanation: rerer

3 0

2 years ago

The quotient of x and 7 is equal to 13. Define variable and then write an expression to model the situation

wolverine [178]

X = the dividend

x ÷ 7 = 13
x = 13x7
x = 91

6 0

3 years ago

If 5 boxes of cereal cost $27.50, how much does one box of cereal cost? a) $5.50 b) $5.05 c) $550 d) .55

olga_2 [115]

}

Answer:B

Step-by-step explanation: I said that because you have 27 and 50 Cent so basically you won't have that $5 in that picture because you still going to have that $0.04 and then you still have to have that much so I I think I am right but if I'm not I'm so sorry but I'm taking not even to get I'm trying to get back on track but I think is b for a reason like I think you could be because you have 27 and 50 Cent so if you got twenty-seven fifty cents you just rounding it down

8 0

2 years ago

Read 2 more answers