jesussanchez1445

26.01.2021 •

Mathematics

Evaluate
81.4% of 58.81km
Give your answer rounded to 2 DP.
km

Solved

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Ответ:

bee3176

10.08.2022

Mathematics

n = 8

Step-by-step explanation:

Given

$3(^nP_2 + 24) = ^{2n}P_2$

Required

Find n

To do this, we simply apply permutations formula

$nP_r = \frac{n!}{(n -r)!}$

So, we have:

$3 * [\frac{n!}{(n -2)!} + 24] = \frac{2n!}{(2n -2)!}$

Expand

$3 * [\frac{n * (n - 1) * (n - 2)!}{(n -2)!} + 24] = \frac{2n * (2n - 1) * (2n - 2)}{2n - 2}$

3 * [n * (n - 1) + 24] = 2n * (2n - 1)

3 * [n^2 - n + 24] = 4n^2 - 2n

Open bracket

3n^2 - 3n + 72 = 4n^2 - 2n

Collect like terms

3n^2 - 4n^2- 3n+2n + 72 = 0

-n^2- n + 72 = 0

Expand

-n^2 -9n + 8n + 72 = 0

Factorize

-n(n +9) - 8(n + 9) = 0

Factor out n + 9

(-n -8)(n + 9) = 0

Split

$(-n -8)= 0 \ or\ (n + 9) = 0$

Solve for n

$n =8\ or\ n = -9$

The positive value is n = 8

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Evaluate 81.4% of 58.81km Give your answer rounded to 2 DP. km