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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!!!


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If f(x)=5x+a and f-1(10)=-1, find a
zhenek [66]

Answer:

15

Step-by-step explanation:

Given the function

f(x)=5x+a

and f^{-1} (10)=-1(f^{-1} \text{is the inverse function of f})

let f(x)=y

Substitute in f(x)

y=5x+a\\y-a=5x\\x=\frac{y-a}{5}

From the definition inverse function

if f(x)=y    ⇒   f^{-1} (y)=x

Substitute this in the above expression

f^{-1} (y)=\frac{y-a}{5}

Substitute y=10

⇒

f^{-1} (10)=\frac{10-a}{5}\\-1=\frac{10-a}{5}\\-5=10-a\\a=10+5\\a=15

Therefore a=15

4 0
3 years ago
Laquita had 5 7/9 yards of fabric. She used 3 2/3 to make a blouse.Write and slove an expresstion to find how much fabric has be
enyata [817]

Answer: \frac{11}{3}\ yards

Step-by-step explanation:

Given

Laquita has 5 \frac{7}{9}\ yards of fabric i.e.

\Rightarrow \dfrac{5\times9+7}{9}=\dfrac{45+7}{9}=\dfrac{52}{9}\ yards

She used  3\ \frac{2}{3} yards to make a blouse i.e.

\Rightarrow \dfrac{3\times 3+2}{3}=\dfrac{11}{3}\ yards

Left fabric

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8 0
3 years ago
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SpyIntel [72]

Answer:

<em>x² - 28x√x + 294x - 1372√x + 2404 </em>

Step-by-step explanation:

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g(x) = x - 7

h(x) = √x

f(g(h(x))) - ?

g(h(x)) = √x - 7

f(g(h(x))) = (\sqrt{x} -7) ^{4} + 3 = ( √x - 7 )² × ( √x - 7 )² + 3 =

= (x - 14√x + 49)(x - 14√x + 49) + 3 =

= x² - 14x√x + 49x - 14x√x + 196x - 686√x + 49x - 686√x + 2401 + 3 =

=  <em>x² - 28x√x + 294x - 1372√x + 2404</em>

8 0
3 years ago
Harriet is cultivating a strain of bacteria in a petri dish. Currently, she has 103 bacteria in the dish. The bacteria divide ev
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Answer:

D

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I think

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Round 149,640 to the nearest thousand.
love history [14]
150,000 I believe is the answer
6 0
3 years ago
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