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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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A regular pentagonal prism has a volume of 2,850 cubic millimeters. what is the height of the prism? a regular pentagonal prism
zlopas [31]

Answer:

Height = 19mm.

Step-by-step explanation:

Area of a regular polygon =  (A * P) / 2 where A = side / (2 * Tan (π / N)) where, N = Number of sides, A = Apothem,  P = Perimeter.

Here A = 5, P = 5*12 = 60 so

Area  of the base  = (5 * 60) / 2 = 150 mm^2.

Volume = area base * height so

Height = volume / area of base

            = 2850 / 150

            = 19 mm.

5 0
1 year ago
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scoray [572]
The first one is a reflection over the x-axis :)
5 0
3 years ago
PLZ SOMEONE HELP ME
Sphinxa [80]

Answer:

9 teaspoons of cocoa

Step-by-step explanation:

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6 0
2 years ago
Least common multiple of 2,7, and 13
san4es73 [151]


To work out the LCM, we need their prime factors. So:

2 is simple 2 x 1.

7 is also 7 x 1.

13 is also 13 and 1.

They all have in common "1" - so we keep that aside as 1 figure, rather than 3.

We still have the 2, 7 and 13 leftover.

We then multiply the 1 with the other figures.

So 1 x 2 x 7 x 13 is our answer.

Which is = 182.


Hope I helped:)


~FabSafxo

6 0
3 years ago
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