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ss7ja [257]
3 years ago
14

In the function, 9 (2-) = 9 - 5x, what is the value of g (3)?

Mathematics
1 answer:
vekshin13 years ago
3 0

Answer: 53

Step-by-step explanation:

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Use the summation formulas to rewrite the expression without the summation notation. summation_k = 1^n 12k(k - 1) / n^3 Use the
kvasek [131]

Answer:

Sum=4*[\frac{n^2-1}{n^2}]

For n=10:

Sum=3.96

For n=100:

Sum=3.9996

For n=1000:

Sum=3.999996

For n= 10000:

Sum=3.99999996

Step-by-step explanation:

Formula:

\sum_{k=1}^n \frac{12k(k-1)}{n^3}

Rearranging the above formula:

\sum_{k=1}^n \frac{12}{n^3}*k(k-1)\\\sum_{k=1}^n \frac{12}{n^3}*(k^2-k)            Eq (1)

According to summation formula:

\sum_{k=1}^n\ k= \frac{n(n+1)}{2}\\ \sum_{k=1}^n\ k^2= \frac{n(n+1)(2n+1)}{6}\\

Putt these in Eq (1), and we will get:

=\frac{12}{n^3}[\frac{n(n+1)(2n+1)}{6}-\frac{n(n+1)}{2}]\\Taking\ n\ as\ common\\=n*\frac{12}{n^3}[\frac{(n+1)(2n+1)}{6}-\frac{(n+1)}{2}] \\=\frac{12}{n^2}*[\frac{(n+1)(2n+1)}{6}]-\frac{12}{n^2}*[\frac{(n+1)}{2}] \\=\frac{2*(n+1)(2n+1)}{n^2}-\frac{6(n+1)}{n^2}\\

Taking 2(n+1) as common:

=2(n+1)*\frac{2n+1-3}{n^2} \\=(2n+2)*\frac{2n-2}{n^2}\\=\frac{4n^2-4}{n^2}

After more simplifying,

Sum=4*[\frac{n^2-1}{n^2}]

Now ,for n=10:

Sum=4[\frac{(10^{2})-1}{10^{2}}]\\Sum=3.96

For n=100:

Sum=4[\frac{(100^{2})-1}{100^{2}}]\\Sum=3.9996

For n=1000

Sum=4[\frac{(1000^{2})-1}{1000^{2}}]\\Sum=3.999996

For n=10000:

Sum=4[\frac{(10000^{2})-1}{10000^{2}}]\\Sum=3.99999996

4 0
3 years ago
Devaughn is 5 years older than Sydney. The sum of their age is 87. What is Sydney’s age?
sp2606 [1]
41

87=41+46

I don’t know how the person before me got 56 because 56+61=117
3 0
3 years ago
Express √-225 in its simplest terms
Montano1993 [528]

Answer:

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Look at the triangle:
Tamiku [17]
<h3>Answer:   12/13</h3>

The sine of an angle is equal to the opposite over hypotenuse

sin(angle) = opposite/hypotenuse

sin(x) = 12/13

7 0
3 years ago
Write a story problem that represents 252÷14
7nadin3 [17]
There were a total of 252 cans of soda given the the camp "turken" There was 14 campers. How many cans of soda would each kid get if you equally divided the soda between all 14 campers?
8 0
3 years ago
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