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Lera25 [3.4K]
2 years ago
14

The coefficient of x^ky^n-k in the expansion of (x+y)^n equals (nk). True or false.

Mathematics
1 answer:
AVprozaik [17]2 years ago
7 0

Answer:

The correct option is;

False

Step-by-step explanation:

The coefficient of x^k·y^(n-k) is nk,   False

The kth coefficient of the binomial expansion, (x + y)ⁿ is  \dbinom{n}{k} = \dfrac{n!}{k!\cdot (n-k)!} = C(n,k)

Where;

k = r - 1

r = The term in the series

For an example the expansion of (x + y)⁵, we have;

(x + y)⁵ = x⁵ + 5·x⁴·y + 10·x³·y² + 10·x²·y³ + 5·x·y⁴ + y⁵

The third term, (k = 3) coefficient is 10 while n×k = 3×5 = 15

Therefore, the coefficient of x^k·y^(n-k) for the expansion  (x + y)ⁿ = C(n,k) not nk

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Answer:

I believe it would be 1

Step-by-step explanation:

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2 years ago
Does it seem plausible that employment has a normal distribution for each gender
Debora [2.8K]

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6 0
3 years ago
Find m∠STU and m∠TUA
PIT_PIT [208]

Answers:

  • angle STU = 65 degrees
  • angle TUA = 123 degrees

=========================================================

Explanation:

Let's find the expression for angle TUS in terms of x

Angle TUA has the expression 11x+2. It will add to angle TUS to get 180 degrees

(angle TUS) + (angle TUA) = 180

angle TUS = 180 - (angle TUA)

angle TUS = 180 - (11x + 2)

angle TUS = 180 - 11x - 2

angle TUS = -11x + 178

Now focus on the interior angles of triangle TUS. We have these three angles

  • T = 5x+10
  • U = -11x+178
  • S = 58

For any triangle, the interior angles always add to 180, so,

T+U+S = 180

(5x+10) + (-11x+178) + (58) = 180

(5x-11x) + (10+178+58) = 180

-6x + 246 = 180

-6x = 180-246

-6x = -66

x = -66/(-6)

x = 11

Use this x value to find the angle measures we're after:

  • angle STU = 5x+10 = 5*11+10 = 55+10 = 65 degrees
  • angle TUA = 11x+2 = 11*11+2 = 121+2 = 123 degrees

--------------------------

As an alternative route, you can apply the remote interior angle theorem. This says that adding two interior angles leads to the exterior angle that isn't adjacent to either one.

In this case, we would say

(angle STU) + (angle TSU) = angle TUA

that leads to the equation

(5x+10) + (58) = 11x+2

Solving this should lead to x = 11 to generate the angles mentioned earlier.

6 0
2 years ago
Solve and graph 4x<40
allochka39001 [22]
I am sorry , i no have graph

7 0
3 years ago
In how many years will $7000 yield an interest of $4620 at 22% simple interest?
meriva

Answer:

3 Years

Step-by-step explanation:

7000*22% = 1540

4620/1540 = 3

1540 = the yearly interest

so it will take 3 years of $1540 of interest to get $4620.

Normally you would also have to take into account the interest plus the base varible but since it specifically says 7000 it makes it a simple problem.

hope this helped

6 0
2 years ago
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