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
sweet [91]
3 years ago
9

Can someone tell me how

Mathematics
1 answer:
gulaghasi [49]3 years ago
7 0

the way I get the subsequent term, nevermind the exponents, the exponents part is easy, since one is decreasing and another is increasing, but the coefficient, to get it, what I usually do is.

multiply the current coefficient by the exponent of the first-term, and divide that by the exponent of the second-term + 1.

so if my current expanded term is say 7a³b⁴, to get the next coefficient, what I do is (7*3)/5   <----- notice, current coefficient times 3 divided by 4+1.

anyhow, with that out of the way, lemme proceed in this one.

\bf ~~~~~~~~\textit{binomial theorem expansion} \\\\ \qquad \qquad (1+ax)^n\implies \begin{array}{llll} term&coefficient&value\\ \cline{1-3}&\\ 1&+1&(1)^n(ax)^0\\\\ 2&+\frac{(1)(n)}{1}\to n&(1)^{n-1}(ax)^1\\\\ 3&+\frac{n\cdot (n-1)}{2}&(1)^{n-2}(ax)^2 \end{array}

so, following that to get the next coefficient, we get those equivalents as you see there for the 2nd and 3rd terms.

so then, we know that the expanded 2nd term is 24x therefore

\bf n(1)^{n-1}(ax)1 = 24x\implies n(1)(ax)=24x\implies nax=24x\implies n=\cfrac{24}{a}

we also know that the expanded 3rd term is 240x², therefore we can say that

\bf \cfrac{n(n-1)}{2}~~(1)^{n-2}(ax)^2 = 240x^2\implies \cfrac{n(n-1)}{2}(1)(a^2x^2) = 240x^2 \\\\\\ \cfrac{(n^2-n)(a^2x^2)}{2}=240x^2\implies \cfrac{(n^2-n)(a^2)}{2}=\cfrac{240x^2}{x^2}\implies \cfrac{a^2n^2-a^2n}{2}=240 \\\\\\ a^2n^2-a^2n=480

but but but, we know what "n" equals to, recall above, so let's do some quick substitution

\bf a^2n^2-a^2n=480\qquad \boxed{n=\cfrac{24}{a}}\qquad a^2\left( \cfrac{24}{a} \right)^2-a^2\left( \cfrac{24}{a} \right)=480 \\\\\\ a^2\cdot \cfrac{24^2}{a^2}-24a=480\implies 24^2-24a=480\implies 576-24a=480 \\\\\\ -24a=-96\implies a=\cfrac{-96}{-24}\implies \blacktriangleright a = 4\blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ n=\cfrac{24}{a}\implies n=\cfrac{24}{4}\implies \blacktriangleright n=6 \blacktriangleleft

You might be interested in
Solve the linear system below using the substitution method. <br> y = 5x – 22<br> 3x +2y=34
insens350 [35]

Answer:

Use photo math, it will explain all the steps

6 0
3 years ago
Read 2 more answers
Find a single expression that represents the distance from Adam's house to the corner if the distance between Adam's house and J
kvasek [131]
Just subtract the distance between the corner and jims house from 23x - 2 and you'll get your answer. I just got the correct answer.
7 0
2 years ago
What is the probability of drawing a heart or a club? <br> A)0%<br> B)50%<br> C)100%
zlopas [31]

Answer:

b = 50%

Step-by-step explanation:

P(Heart or Club)

= P(Heart) + P(Club)

= 13/52 + 13/52

= .25 + .25

= .5 --> 50%

5 0
3 years ago
Pls help with these questions I can give brainliest thank you all! 9 a and b
nata0808 [166]

Answer:

A. 8 1/4 * 11 1/2 * 14=1328 1/4 ft^2

OR

8 1/4 height times 11 1/2 width times 14 in length equals 1328 1/4 feet squared

B. 8 1/4 * 14 1/2 * 14=1674 3/4

OR

8 1/4 height times 11 1/2 width plus 3 so 14 1/2 width times 14 equals 1674 3/4 feet squared

Step-by-step explanation:

7 0
3 years ago
How was basic math used
dmitriy555 [2]
It was used to see how your basic math skills
4 0
2 years ago
Read 2 more answers
Other questions:
  • 100 POINTS NO BEGGINERS AND AMBITIOUS, VIRTUOSO AND UP ONLY OR I WILL REPORT U
    10·2 answers
  • 3/2 x 3 x 1/5 please help me
    12·1 answer
  • Ms. Fraser's car can go 19.21 miles on .85 gallons of gas.if gas cost $2.17 per gallon, how much will a 3,000 mile trip cost Ms.
    14·1 answer
  • Combing like terms in an quadiatic expression <br><br>2x2-10x-8+7x
    9·1 answer
  • You might need:
    13·1 answer
  • What is the rate of 4 shirts for $32
    10·2 answers
  • Q1<br> Q2 - Using ratios<br> Complete the table for this pattern.<br> 8
    5·1 answer
  • Which of the following 2D shapes compose the net of a square pyramid? Select all that apply.
    7·2 answers
  • Which graph represents the function f(x) = 3
    8·1 answer
  • Help me:-
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!