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pishuonlain [190]
3 years ago
15

Find the middle term of (

" title="( x^{2}+2) ^{20} 
" alt="( x^{2}+2) ^{20} 
" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
Alla [95]3 years ago
7 0
So... when expanding a binomial, recall we get as many terms as the exponent plus 1, so, in this case will be 20 + 1, so 21 terms.

now, the middle guy in 21 terms, will be the 11th term.

using the binomial theorem, is simple to get the terms themselves, since all we're doing is, beginning at the highest with first element and going down by 1 each term, and with the second starting at 0 and going up, surely you already know that.

So, all that's left is what the dickens is the coefficient of each term in the expansion?

well, is "the current coefficient, times the exponent of the 1st element, divided all that by the exponent of the 2nd element on the next term", now, that's a mouthful but lemme post quick and explain a couple.

\bf (x^2+2)^{20}\implies 
\begin{array}{llll}
term&coefficient&value\\
-----&-----&-----\\
1&&(x^2)^{20}(+2)^0\\
2&+20&(x^2)^{19}(+2)^1\\
3&+190&(x^2)^{18}(+2)^2\\
4&+1140&(x^2)^{17}(+2)^3\\
5&+4845&(x^2)^{16}(+2)^4\\
6&+15504&(x^2)^{15}(+2)^5\\
7&+38760&(x^2)^{14}(+2)^6\\
8&+77520&(x^2)^{13}(+2)^7\\
9&+125970&(x^2)^{12}(+2)^8\\
10&+167960&(x^2)^{11}(+2)^9\\
11&+184756&(x^2)^{10}(+2)^{10}\\
\end{array}

so, how did we get the coefficient for say the 5th term, the coefficient of 4845?   well, is just 1140 * 17 / 4.

and how about the 6th term with 15504?  well 4845 * 16 / 5.

another example, say the 10th term's coefficient of 167960?  well is just 125970 * 12 / 9.

and now simply expand and combine the factors for the 11th term.
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Solve this problem thanks
vovikov84 [41]

The three missing lengths are the left hypotenuse, x, the middle altitude, y, and the right hypotenuse, z.


9/y = y/16


y^2 = 9 * 16


y^2 = 144


y = 12


9^2 + 12^2 = x^2


x^2 = 225


x = 15


12^2 + 16^2 = z^2


z^2 = 400


z = 20


From left to right, the sides measure 15, 12, and 20 units.

5 0
3 years ago
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<img src="https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B14%7D%20%2F%20%5Cfrac%7B4%7D%7B3%7D" id="TexFormula1" title="\frac{9}{14} / \
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3 years ago
Ms. Chen is planning to take her camp group on a field trip to Pottery Bayou where each person will create her own piece of art
erica [24]

Answer:

1. C=21x.

2. C=(8x+104).

Step-by-step explanation:

Let the number of people in the group be x. Denote the total cost as C.

1. If the regular cost is $21 per person, then the total regular cost for x people is C=21x.

2. If the special cost is $8 per person, then the total special cost for x people is \$8x. There is an additional $104 fee for a private room, thus the total special cost is C=(8x+104).

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3 years ago
Please factorise 16p²-9q² for me<br>​
kirill115 [55]

Answer:

a ^ 2 - b ^ 2 = ( a + b ) ( a - b ) where a = 4p and b = 3q.

( 4p + 3q ) ( 4p - 3q )

7 0
3 years ago
Least to greatest -6.8,|-23/4|,0,-14.4,|-1.9|,5.4
IrinaVladis [17]

Answer:

From Least to Greatest: -14.4, -6.8, -23/4, -1.9, 0, 5.4

Step-by-step explanation:

3 0
3 years ago
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