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ehidna [41]
3 years ago
7

Calculate the coefficient of x4y18 in the expansion of (x − y)22

Mathematics
1 answer:
Oksana_A [137]3 years ago
4 0
Binomial theorem:

(x-y)^n=\displaystyle\sum_{k=0}^n\binom nkx^k(-y)^{n-k}

The term with x^4y^{18} corresponds to n=18+4=22 and k=4 (or k=18, since \dbinom nk=\dbinom n{n-k}).

So, the coefficient of this term is

\dbinom{22}4(-1)^{18}=\dbinom{22}4=\dfrac{22!}{4!(22-4)!}=7315
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X= 7 cm hope this helps
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Gnoma [55]
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1 year ago
Determine whether the ordered pairs (1,4) and 6,
devlian [24]

Answer:

Not solutions.

Step-by-step explanation:

-5x+6y=-5

6y=-5+5x

6y=5x-5

y=5/6x-5/6

-5/6 is about -0.833

And the slope is 5/6.

So for every x there is 5/6y.

This means (1, 4) won't work cause it's too low.

Also 5/6*6=5. this is too low too.

So they aren't solutions.

3 0
1 year ago
Select Exponential growth or Exponential decay for each function.
Lena [83]

Answer:

f(x)=(1.023) ⋅ 3^x  Growth

f(x)=3 ⋅ (0.072)^x      Decay

f(x)=4 ⋅ (0.035)^x      Decay

f(x)=2 ⋅ (1.34)^x         Growth

Step-by-step explanation:

An exponential function at its heart has a base number of rate. If the rate is less than 1, then the function decays. If the base number or rate is greater than 1, then the function grows and increase.

f(x)=(1.023) ⋅ 3^x Rate 3 -  Growth

f(x)=3 ⋅ (0.072)^x      Rate 0.072 - Decay

f(x)=4 ⋅ (0.035)^x      Rate 0.035 - Decay

f(x)=2 ⋅ (1.34)^x         Rate 1.34 - Growth

7 0
3 years ago
A quadratic equation is shown below: 2x2 − 10x − 8 = 0 Part A: Describe the solution(s) to the equation by just determining the
dangina [55]
PART A:

The given quadratic equation is 2x²-10x-8=0

The radicand is given by b²-4ac where a, b, and c are the constants in a quadratic form ax²+bx+c

From the given equation, we have
a = 2
b = -10
c = -8

Radicand b²-4ac = (-10)² - 4(2)(-8) = 100 + 64 = 164

The radicand is >0 hence the quadratic equation has two distinct roots

PART B:

4x²-12x+5 = 0

We can use the factorization method to solve the equation
Firstly, we multiply 4 by 5 to get 20
Then we find the pair of numbers that multiply gives 20 and sum gives -12

The pair of number is -2 and -10
Rewriting the equation 
4x²-2x-10x+5 = 0
2x(2x-1)-5(2x-1) = 0
(2x-1)(2x-5) = 0

2x-1 = 0 and 2x-5 = 0
x = 1/2 and x = 5/2
6 0
3 years ago
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