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3 years ago

1.) Mathman wants to join a book club. Books-for-less costs $40 to join and $10 per book. Book-Buddy cost $15 per

Mathematics

1 answer:

diamong [38]3 years ago

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Hey can you send me a dollar or...

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Law Incorporation [45]

Recall the binomial theorem.

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

1. The binomial expansion of $\left(1+\frac x3\right)^7$ is

$\left(1 + \dfrac x3\right)^7 = \displaystyle\sum_{k=0}^7 \binom 7k 1^{7-k} \left(\frac x3\right)^k = \sum_{k=0}^7 \binom 7k \frac{x^k}{3^k}$

Observe that

$k = 1 \implies \dbinom 71 \left(\dfrac x3\right)^1 = \dfrac73 x$

$k = 2 \implies \dbinom 72 \left(\dfrac x3\right)^2 = \dfrac73 x^2$

When we multiply these by $8-9x$ ,

• $8$ and $\frac73 x^2$ combine to make $\frac{56}3 x^2$

• $-9x$ and $\frac73 x$ combine to make $-\frac{63}3 x^2 = -21x^2$

and the sum of these terms is

$\dfrac{56}3 x^2 - 21x^2 = \boxed{-\dfrac73 x^2}$

2. The binomial expansion is

$\left(2a - \dfrac b2\right)^8 = \displaystyle \sum_{k=0}^8 \binom 8k (2a)^{8-k} \left(-\frac b2\right)^k = \sum_{k=0}^8 \binom 8k 2^{8-2k} a^{8-k} b^k$

We get the $a^6b^2$ term when $k=2$ :

$k=2 \implies \dbinom 82 2^{8-2\cdot2} a^{8-2} b^2 = 28 \cdot2^4 a^6 b^2 = \boxed{448} \, a^6b^2$

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1 year ago

What is 2,400 milliliters converted into liters

BARSIC [14]

Answer:

2.4 liters

Step-by-step explanation:

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3 years ago

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19.214÷13 <br> pls someone help me

slava [35]

Answer:

1.478

Step-by-step explanation:

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3 years ago

Joshua Bennett purchased a television for $245.95 with 40.25% down. He will make 6 payments of $25.83 each. What is the total am

brilliants [131]

(245.95×0.4025)+(6×25.83)=253.97

253.97-245.95=8.02

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3 years ago

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2hours to 1day as a ratio in its simplest form

Murrr4er [49]

Answer:

Step-by-step explanation:

convert 1 day into hours

1 day=24 hour

2/24

=1/12

3 0

3 years ago

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