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hammer [34]
4 years ago
6

Find the sum of the coefficients in the expansion of (x+1)^12

Mathematics
1 answer:
MariettaO [177]4 years ago
4 0

Answer:

<h2>2¹²</h2>

Step-by-step explanation:

The sum of the coefficients in the expansion of (x+1)^12:

= 12C0 + 12C1 + 12C2 + . . . + 12C11 + 12C12

the formula says that this sum equal to 2¹².

Other examples

The sum of the coefficients in the expansion of (x+1)^3:

3C0+3C1+3C2+3C3

=8 = 2³

The sum of the coefficients in the expansion of (x+1)^4:

4C0+4C1+4C2+4C3+4C4

=16 = 2⁴

:)

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5 0
3 years ago
PLEASE HELP!!! Use sigma notation to represent the following series for the first 12 terms.
MariettaO [177]
If you notice, in the sum the terms are 2, -8, 32, -128....

we can always get the "common ratio" of a geometric sequence by dividing the "following term by the previous term", namely like in this case say -8/2, which is -4, so r = -4, and we know the first term is 2.

so, notice, the pattern will then be

 \bf \stackrel{2(-4)^0}{2}~~\stackrel{2(-4)^1}{-8}~~\stackrel{2(-4)^2}{32}~~\stackrel{2(-4)^3}{-128}\qquad \implies \qquad \sum\limits_{k=0}^{11}~2(-4)^k
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3 years ago
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jeka94

In most approximate way it can never be the area of the circle (Accurate area)

This is why because after creating base lines of each triangle it forms an inscribed polygon .

  • Some little spaces left over each side or b_n

So

h is already approaching to r

  • and b_1+b_2..b_n is approaching to the perimeter i.e 2πr

Option B

5 0
2 years ago
Find the perimeter of the polygon
pychu [463]

Answer:

Answer 60

Step-by-step explanation:

The distance from an exterior point to the incircle is equal to the tangent length in both cases.

So the 19 is made up of 9 and 10.

The length of the other portion of the tangent from the end of 19 to the tangent point on the right is also 10.

By a similar argument the lower length of the line to the tangent point is 11.

So you have

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6 0
3 years ago
The royal fruit company produces two types of fruit drinks the first type is 70% pure fruit juice and the second type is 95% pur
Ipatiy [6.2K]
This is a typical mixture problem where using a table is the best thing.
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juice A            x                  .70          =        .70x
juice B        60-x                 .95          =    .95(60-x)
total              60                  .75          =    60(.75)

The last row gives you a total that you need to use, so do that multiplication to get 45. You now to need to add the last columns together for rows 1 and 2 and set them equal to 45: .7x +.95(60-x) = 45. When you do that math, you'll get that x = 48. This means that you need 48 pints of juice A and 60-48 pints of juice B, which is 12 pints.
6 0
3 years ago
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