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aksik [14]
3 years ago
14

Find the coefficient of x^7 in the expansion of (3x+4)^11

Mathematics
1 answer:
devlian [24]3 years ago
6 0

Use the binomial theorem:

(a+b)^n=\displaystyle\sum_{k=0}^n\binom nka^{n-k}b^k

In this case,

(3x+4)^{11}=\displaystyle\sum_{k=0}^{11}\binom{11}k(3x)^{11-k}4^k

The x^7 term occurs for k=4:

\dbinom{11}4(3x)^{11-4}4^4=\dfrac{11!}{4!(11-4)!}3^74^4x^7=184,757,760x^7

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Find the first four terms of the sequence given a1=31 and an+1=an−3
Alex

Step-by-step explanation:

Given the formula

a(n+1)=an−3

The first term a(1) = 31

<u>For</u><u> </u><u>the</u><u> </u><u>second</u><u> </u><u>ter</u><u>m</u>

a(2)

We have

a( 1 + 1) = a(1) - 3

a(2) = 31 - 3

a(2) = 28

<u>For</u><u> </u><u>the</u><u> </u><u>thir</u><u>d</u><u> term</u>

a(3)

We have

a(2+1) = a(2) - 3

a(3) = 28 - 3

a(3) = 25

<u>For</u><u> </u><u>the</u><u> </u><u>four</u><u>th</u><u> term</u>

a(4)

That's

a(3+1) = a(3) - 3

a(4) = 25 - 3

a(4) = 22

Hope this helps you

4 0
3 years ago
The sum of three integers is 193. The sum of the first and second integers exceeds the third by 13. The third integer is 11 less
aleksandrvk [35]

Answer:

<em>Answer</em><em> </em><em>is</em><em> </em><em>given</em><em> </em><em>in</em><em> </em><em>the image</em><em>. </em>

Step-by-step explanation:

HAVE A NICE DAY

THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.

5 0
3 years ago
0.13391963118/17(3.78)
erma4kov [3.2K]

Answer:

Simplify the expression.

0.02977742

Step-by-step explanation:

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7 0
2 years ago
A sample of bacteria is decaying according to a half-life model. If the sample begins with 700 bacteria, and after 10 minutes th
Papessa [141]

Answer:

18 minutes

Step-by-step explanation:

A = A₀ (½)^(t / T)

where A is the final amount,

A₀ is the initial amount,

t is the time,

and T is the half life.

A = 140 when t = 10.  Solve for the half life:

140 = 700 (½)^(10 / T)

0.2 = ½^(10 / T)

log 0.2 = (10 / T) log 0.5

10 / T = 2.32

T = 4.31

When A = 40, t is:

40 = 700 (½)^(t / 4.31)

0.057 = ½^(t / 4.31)

log 0.057 = (t / 4.31) log 0.5

t / 4.31 = 4.13

t = 17.8

Rounded to the nearest whole number, it takes 18 minutes.

4 0
4 years ago
Solve the following two equation X+Y=5<br> X-2Y=2
White raven [17]

Step-by-step explanation:

x=4 and y= 1 because of 4+1=5 and add 2y to both sides

x-2y+2y=2+ 2y

x=2y+2

4-2=2

8 0
3 years ago
Read 2 more answers
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