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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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Finding a parametric description of the solution set of a linear system is the same as solving the system.Choose the correct ans
Grace [21]

Answer:

The answer is "Choice B".

Step-by-step explanation:

Please find the complete question in the attached file.

In this question, in all choices, the choice (B) is Correct because in the declaration of the statement Only when the process has had at least another answer could a candidate solution for more than just a linear model explicitly uses a parametric description that's why the given statement is true.

7 0
3 years ago
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room.
neonofarm [45]
The third one. width=y-5
6 0
3 years ago
B<br> [2 0]<br> -2 5<br> What is the determinant of B?<br> Your answer
Marianna [84]

Answer:

10

Step-by-step explanation:

Determinant = ad - bc

\det\begin{pmatrix} 2 & 0 \\-2 & 5\end{pmatrix} =\begin{vmatrix} 2 & 0 \\-2 & 5\end{vmatrix} = 2\times5 + 0\times2 = 10

8 0
3 years ago
Find the distance between points A (10,-1) and B (-2,5). Round to the nearest tenth
bija089 [108]

Answer:

<h2>The answer is 13.4 units</h2>

Step-by-step explanation:

The distance between two points can be found by using the formula

d =  \sqrt{ ({x1 - x2})^{2}  +  ({y1 - y2})^{2} }  \\

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

A (10,-1) and B (-2,5)

The distance is

|AB|  =  \sqrt{ ({10 + 2})^{2} +  ({ - 1 - 5})^{2}  }  \\  =  \sqrt{ {12}^{2}  +  ({ - 6})^{2} }  \\  =  \sqrt{144 + 36}  \:  \:  \:  \:  \:  \:  \:   \\  =  \sqrt{180}  \\  = 6 \sqrt{5}  \:  \:  \\  =13.416407

We have the final answer as

<h3>13.4 units to the nearest tenth</h3>

Hope this helps you

7 0
3 years ago
Translate the statement into an equation: the difference of four times a number and eight is equal to twenty-three less than tha
neonofarm [45]
Let, the number be "x"
Now,
according to the question,
4x -8 = x -23....................This is your equation.

Now solving it,
4x - 8 = x - 23
4x - x = -23 + 8
3x = -15
x = -15 / 3
x = -5

Checking the answer,
4 (-5) - 8 = (-5) - 23
-20 - 8 = -5 - 23
-28 = -28......................................true



6 0
3 years ago
Read 2 more answers
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