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taurus [48]
3 years ago
12

Find the term indecent of x in the expansion of (x^2-1/x)^6

Mathematics
1 answer:
Mars2501 [29]3 years ago
3 0

By the binomial theorem,

\displaystyle \left(x^2-\frac1x\right)^6 = \sum_{k=0}^6 \binom 6k (x^2)^{6-k} \left(-\frac1x\right)^k = \sum_{k=0}^6 \binom 6k (-1)^k x^{12-3k}

I assume you meant to say "independent", not "indecent", meaning we're looking for the constant term in the expansion. This happens for k such that

12 - 3k = 0   ===>   3k = 12   ===>   k = 4

which corresponds to the constant coefficient

\dbinom 64 (-1)^4 = \dfrac{6!}{4!(6-4)!} = \boxed{15}

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38

Step-by-step explanation:

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kvasek [131]
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yawa3891 [41]
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See the picture below!!
Darya [45]

Answer:

Q1) x = 17.3

y = 8.7

Q2) d = 19

Step-by-step explanation:

Question 1

Angle = 60°

Hypotenuse = x

Adjacent = y

Opposite = 15

<u>Step 1: Find x</u>

Sin (angle) = opposite/hypotenuse

Sin (60°) = 15/x

x = 10√3 = 17.3

<u>Step 2: Find y</u>

Tan (angle) = opposite/adjacent

Tan (60°) = 15/y

y = 5√3 = 8.7

Question 2

<u>Step 1: Find the diagonal of the base</u>

c² = a²+b²

c² = 6² + 10²

c = 2√34 = 11.7

<u>Step 2: Find diagonal d</u>

c² = a² + b²

d² = 11.7² + 15²

d = 19

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7 0
3 years ago
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