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Oduvanchick [21]
3 years ago
13

Given the polynomial : (3x+4)^5. find the coefficient of x³ !​

Mathematics
1 answer:
stiv31 [10]3 years ago
3 0

Answer:

\displaystyle 4320 {x }^{3}

Step-by-step explanation:

to solve binomials like this there's a way called<u> </u><u>binomial</u><u> theorem</u><u> </u>given by

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

but for this question we need the following part

\displaystyle   \boxed{ \binom{n}{k}  {a}^{n - k}  {b}^{k} }

from the question we obtain that a,b and n is 3x,4 and 5 since we want to find the coefficient <em>x³</em><em> </em><em> </em>k should be (5-3) = 2 so we have determined the variables now just substitute

\displaystyle  \binom{5}{2}  {(3x)}^{5 - 2} \cdot  {4}^{2}

simplify which yields:

\displaystyle \boxed{ \bold{4320 {x }^{3}} }

and we are done!

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F(x) = 3x - 5; Find f(-4)
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Answer:

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Step-by-step explanation:

given, f(x) = 3x ‐ 5

or, f(‐4) =( 3 × ‐4 ) ‐5

or, f(‐4) = ‐12 ‐5

or, f(‐4) = ‐17

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3 years ago
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3 years ago
Use the Ratio Test to determine whether the series is convergent or divergent. [infinity] n! 112n n = 1 Identify an. Correct: Yo
MakcuM [25]

Answer:

Step-by-step explanation:

Recall that the ratio test is stated as follows:

Given a series of the form \sum_{n=1}^{\infty} a_n let L=\lim_{n\to \infty}\left|\frac{a_{n+1}}{a_n}\right|

If L<1, then the series converge absolutely, if L>1, then the series diverge. If L fails to exist or L=1, then the test is inconclusive.

Consider the given series \sum_{n=1}^{\infty} n! \cdot 112n. In this case, a_n =n! \cdot 112n, so , consider the limit

\lim_{n\to\infty} \frac{(n+1)! 112 (n+1)}{n! 112 n} = \lim_{n\to\infty}\frac{(n+1)^2}{n}

Since the numerator has a greater exponent than the numerator, the limit is infinity, which is greater than one, hence, the series diverge by the ratio test

7 0
4 years ago
How do you solve this math problem-2(x+3y)=18
ss7ja [257]
Greetings!

Solve for <em>x</em>.
-2(x+3y)=18
Distribute the Parenthesis. <em>How?</em> Multiply all of the terms inside the parenthesis by the number outside the parenthesis.
(-2)*x+(-2)*3y=18
-2x-6y=18
Add 6y to both sides.
(-2x-6y)+6y=(18)+6y
-2x=18+6y
Divide both sides by -2.
(-2x)/-2=(18+6y)/-2
The Answer Is:
x=-9-3y
x=-3y-9

Hope this helps.
-Benjamin
7 0
3 years ago
When adding 35.64 to a certain number, the sum is 38.24, as seen below. What number should go in the box to complete the additio
Lunna [17]

Answer:

it would be 2

Step-by-step explanation:

5he answer is two so you subtract and then add and then multiply to get your answer 6ou divide it by pie

6 0
3 years ago
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