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
CaHeK987 [17]
4 years ago
6

What is the numerical coefficient of the a^8*b^2 term in the expansion of ((1/3)a^2 - 3b)^6 ?

Mathematics
1 answer:
zhuklara [117]4 years ago
7 0

In the binomial development, the main problem is calculation of binomial coefficients.

If we want to get term a∧8*b∧2 we see that this is the third member in binomial development (n 2) a∧n-2*b∧2

The given binomial  is ((1/3)a∧2 - 3b)∧6, the first element is (1/3)a∧2, the second element is (-3b) and n=6 when we replace this in the formula we get

(6 2) * ((1/3)a∧2)∧(6-2) * (-3b)2 = (6*5)/2 * ((1/3)a∧2)∧4 *9b∧2= 15*(1/81)*9 *(a∧8b∧2) =

= 15*9* a∧8b∧2 = 135*a∧8b∧2

We finally get numerical coefficient 135

Good luck!!!


You might be interested in
Lionfish are considered an invasive species, with an annual growth rate of 67%. A scientist estimates there are 8,000 lionfish i
natita [175]

<em>Answer:</em>

<em>There would be 173,535 lionfish after 6 years.</em>

<em>Step-by-step explanation:</em>

<em>Since lionfish are considered an invasive species, with an annual growth rate of 67%, ya scientist estimates there are 8,000 lionfish in a certain bay after the first year, A) to write the explicit equation for f (n) that represents the number of lionfish in the bay after n years; B) determine how many lionfish will be in the bay after 6 years; and C) if scientists remove 1,200 fish per year from the bay after the first year, determine what is the recursive equation for f (n); the following calculations must be performed:</em>

<em></em>

<em>A)</em>

<em>8000 x 1.67 ^ n = f  </em>

<em>B)</em>

<em>8000 x 1.67 ^ 6 = X</em>

<em>8000 x 21.691961596369 = X</em>

<em>173,535.692770952 = X  </em>

<em>C)</em>

<em>(8000 - 1200 x 1 ^ n) x 1.67 ^ n = f</em>

<em>Therefore, there would be 173,535 lionfish after 6 years.</em>

5 0
2 years ago
Pls help will give brainliest
Shtirlitz [24]

Answer:

C, C, C

Hope This Helps!    Have A Nice Day!!

8 0
3 years ago
Item 32 On three 150-point geography tests, you earned grades of 88%, 94%, and 90%. The final test is worth 250 points. What per
stira [4]
97.2% on the final.
Find the total amount of points needed to get a 93%. 150+150+150+250 = 700 total points. 700*.93 = 651 total points needed to get 93%. find the points received from the other quizzes and subtract the sum from 651 to find how many points need to be scored on the final.
150*.88=132 (test 1)
150*.94=141 (test 2)
150*.90=135 (test 3)
132+141+135= 408

651-408 = 243 points to score on the final exam.
243/250 =.972 or 97.2%
3 0
3 years ago
How do you use unit rates to help you solve a word problem
OleMash [197]
Answer:

You could find the unit rate by dividing the first term of the ratio by the second term.
4 0
3 years ago
Statement "if a and b are both positive integer numbers, then a +b &gt; a
bezimeni [28]

Answer:

Always

Step-by-step explanation:

Subtracting a from both sides yields b>0, which is always true since b is a positive integer.

3 0
1 year ago
Other questions:
  • 50+24/(6x2) <br> Please solve and show work. Thank you.
    8·1 answer
  • X and Y intercept equations x +2y =18
    8·1 answer
  • Find the first five terms of the sequence in which a1 = 6 and an = –3an – 1 – 12, if n ≥ 2.
    7·1 answer
  • Solve the following equation. x/8 = .42
    15·2 answers
  • Helppppp 78 squared to the 3rd
    5·1 answer
  • The table shows elevations at various locations.
    10·2 answers
  • mercer middle school has 1400 students last year this year there are 1,120 students enrolled. Find the percent of change in the
    9·1 answer
  • Can someone please help me with this question?
    12·2 answers
  • Write an inequality relating m
    12·1 answer
  • Which pair or pairs of polygons are congruent?
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!