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
Jet001 [13]
2 years ago
5

In the expansion (ax+by)^7, the coefficients of the first two terms are 128 and -224, respectively. Find the values of a and b

Mathematics
1 answer:
madam [21]2 years ago
5 0

Answer:

a = 2, b = 3.5

Step-by-step explanation:

Expanding (ax+by)^7 using Binomial expansion, we have that:

(ax+by)^7 =

(ax)^7(by)^0 + (ax)^6(by)^1 + (ax)^5(by)^2 + (ax)^4(by)^3 + (ax)^3(by)^4 + (ax)^2(by)^5 + (ax)^1(by)^6 + (ax)^0(by)^7

= (a)^7(x)^7+ (a)^6(x)^6(b)(y) + (a)^5(x)^5(b)^2(y)^2 + (a)^4(x)^4(b)^3(y)^3 + (a)^3(x)^3(b)^4(y)^4 + (a)^2(x)^2(b)^5(y)^5 + (a)(x)(b)^6(y)^6 + (b)^7(y)^7\\\\\\= (a)^7(x)^7+ (a)^6(b)(x)^6(y) + (a)^5(b)^2(x)^5(y)^2 + (a)^4(b)^3(x)^4(y)^3 + (a)^3(b)^4(x)^3(y)^4 + (a)^2(b)^5(x)^2(y)^5 + (a)(b)^6(x)(y)^6 + (b)^7(y)^7

We have that the coefficients of the first two terms are 128 and -224.

For the first term:

=> a^7 = 128

=> a = \sqrt[7]{128}\\ \\\\a = 2

For the second term:

a^6b = -224

b = \frac{-224}{a^6}

b = \frac{-224}{2^6} \\\\\\b = \frac{-224}{64} \\\\\\b = 3.5

Therefore, a = 2, b = 3.5

You might be interested in
The area of a rectangle is 56 cm. The length is 2cm more than x and width is 5 cm less than twice x. Solve for x. Round to the n
ra1l [238]
Area = Length * Width = l * w
l = x + 2
w = 2x - 5
Area = (x + 2)(2x - 5) = 56
Area = 2x^2 -x  - 10 = 56
Area = 2x^2 - x - 66 = 0 Now you have to factor this thing.
Area = (2x + 11)( x - 6) = 0 This is more or less done by guessing. 
2x + 11 = 0 can't work. x would be negative.
x - 6 = 0
x = 6.

Check
=====
l = x + 2
l = 6 + 2
l = 8

w = 2*x - 5
w = 2*6 - 5
w = 12 - 5
w = 7

l*w = 8*7 = 56. It checks.
If this is the best answer you get, could you consider a Brainly? I need 2 of them to move up.
3 0
3 years ago
30÷10 divide until you find the ten thousand digit
klemol [59]

Answer:

The ten thousandth digit would be 0.

Step-by-step explanation:

30/10=3

3 is a whole number so there would be no decimal which means that in the ten thousandth place would be 0

30/10=3.0000

4 0
2 years ago
Hey could someone helpp me pls
Minchanka [31]

Answer: $5.54

Step-by-step explanation: 63 divided by 100 is 0.63, 0.63 x 8.8 is 5.544 and 5.544 rounded to the nearest cent is $5.54

5 0
2 years ago
What is 1,200/2,000 in a fraction
andreev551 [17]
1200/200 in a simplified form is
3/5
7 0
3 years ago
Select all equations that have at least one integer solution.
Anit [1.1K]

Answer:

b and d

Step-by-step explanation:

5 0
2 years ago
Other questions:
  • What is 4 / 3/7? Is it 28/3? Or 4/21?
    6·2 answers
  • Use table to compute the product below.
    13·1 answer
  • What does it mean if a scatterplot has a positive negative or no association
    8·1 answer
  • There are 20 students in the high school glee club. They need to pick four students to serve as
    13·2 answers
  • Two people working together can complete a job in 5 hours. If one of them works
    15·2 answers
  • This section of guttering can hold up to 20 litres of rainwater. work out the length of guttering in meters. The diameter is 11.
    12·1 answer
  • Please answer ASAP! An explanation is a MUST requirement in order to receive points and the Brainliest answer. Thank you.
    8·1 answer
  • Which option below describes the polynomial 10x^3?
    9·2 answers
  • You and a friend are playing a game by tossing two coins. If both coins are heads or both are tails, you win. Otherwise, your fr
    15·1 answer
  • Given: g ∥ h and ∠2 ≅ ∠3
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!