1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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

You might be interested in
I NEED HELP ASAP!!!PLEASE EXPLAIN THE ANSWER
Dimas [21]

Answer:

Below

Step-by-step explanation:

To find surface area, you can just find the area of each side and add them up!

11 ft x 9 ft x 2 = 198 ft^2 (this is the surface area of the front and back)

12 ft x 9 ft x 2 = 216 ft^2 (this is the surface area of the sides)

12 ft x 11 ft x 2 = 264 ft^2 (this is the surface area of the top and bottom)

Surface area = 198 + 216 + 264

                      = 678 ft^2

Hope this helps! Best of luck <3

5 0
2 years ago
Island A is 150 miles from Island B. A ship captain travels 310 miles from Island A and then finds that he is off course and 200
wolverine [178]

Answer:

156.37°

Step-by-step explanation:

We solve this above question, using Cosine rule which is given as:

Cos C = a² + b² - c²/2ab

Let the Angle be represented as: x

Cos x = 310² + 200² - 150²/2 × 310 × 200

x = arc cos [ 310² + 200² - 150²/2 × 310 × 200]

x = 23.63°

The angle, in degrees, that he must turn through to head straight for Island B is given as:

180° - 23.63°

= 156.37°

4 0
2 years ago
Solve using a2 + b2 = c2 <br> show ur work please :)
Brrunno [24]
So 90^2+90^2=c^2
8100+8100=c^2
16200=c^2
C= ~127.28
5 0
3 years ago
If you dont answer all I won't give brain list...(If you do I will!)
Goryan [66]

Answer:

dude bace times hight 4×2×3

3 0
3 years ago
Read 2 more answers
At a candy store, 3 giant lollipops sell for $7.59 and 2 small packets of bubblegum cost $4.82. Which is a better buy?
galben [10]
2 small backs of bubble gum is your answer because it costs less!!
3 0
3 years ago
Other questions:
  • What is the rate of change for the set of ordered pairs?
    12·1 answer
  • What is the explicit formula for this geometric sequence?
    12·1 answer
  • Solve.<br><br><br><br> 4w – 8 = 24<br><br><br><br> 10<br><br> 6<br><br> –7<br><br><br> 8
    12·1 answer
  • Al's Awesome Autos advertised a special sale on cars - Dealer cost
    8·1 answer
  • Which transformation describes the photograph? Select all that apply. The panels on the right side are a translation of those on
    15·1 answer
  • Can u help<br> if three times a number is increased by 4 the results is -8 . find the number
    8·2 answers
  • Jennifer pays $8 delivery fee and $20 per box for fruits, if she has at least $100 how many boxes of fruit can she order?
    13·2 answers
  • Please solve!!! <br> In a hurry!
    12·1 answer
  • The area of a circle, in terms of <br> π<br> , is 36<br> π<br> m2.<br> Find the value of the radius.
    10·1 answer
  • Need help with this math question 30 points correct answers only pls
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!