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allochka39001 [22]

4 years ago

8

N divided by 5 plus negative 6 equals 9. whats n?

2 answers:

Natali5045456 [20]4 years ago

7 0

So,

$\frac{n}{5} + -6 = 9$
$\frac{n}{5} - 6 = 9$

Add 6 to both sides
$\frac{n}{5} = 15$

Multiply both sides by 5
$n = 75$

Check
$\frac{75}{5} - 6 = 9$
$15 - 6 = 9$
$9 = 9\ This\ checks.$

S = {75}

Bond [772]4 years ago

5 0

N/5 -6 = 9 simplifies to n/5 = 15 then you can cross multiply and that comes out to 75 so n = 75

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3 years ago

Evaluate 1^3 + 2^3 +3^3 +.......+ n^3

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We have

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You might already know that

$\displaystyle\sum_{i=1}^n1=n$

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so from these formulas we get

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$\implies\displaystyle\sum_{i=1}^ni^3=\frac{(n+1)^4-1-n(n+1)(2n+1)-2n(n+1)-n}4$

$\implies\boxed{\displaystyle\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}4}$

If you don't know the formulas mentioned above:

The first one should be obvious; if you add $n$ copies of 1 together, you end up with $n$ .
The second one is easily derived: If $S=1+2+3+\cdots+n$ , then $S=n+(n-1)+(n-2)+\cdots+1$ , so that $2S=n(n+1)$ or $S=\dfrac{n(n+1)}2$ .
The third can be derived using a similar strategy to the one used here. Consider the expression $(n+1)^3-n^3=3n^2+3n+1$ , and so on.

7 0

4 years ago