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GenaCL600 [577]
3 years ago
8

The sum of w and 84 is 125. What is the value of w?

Mathematics
2 answers:
Ymorist [56]3 years ago
4 0
The value of w is 41.
84 + 41 = 125
Lilit [14]3 years ago
4 0

w + 84 = 125

w = 125 - 84

w = 41

--------------------

41 + 84 = 125


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For this case we have the following expression:

\frac {216 ^ {n-2}} {(\frac {1} {36}) ^ {3n}} = 216

We multiply both sides by: (\frac {1} {36}) ^ {3n}

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We divide both sides by 216:

\frac {216 ^ {n-2}} {216} = (\frac {1} {36}) ^ {3n}

To divide powers of the same base, we place the same base and subtract the exponents:

216 ^ {n-2-1} = (\frac {1} {36}) ^ {3n}\\216 ^ {n-3} = (\frac {1} {36}) ^ {3n}

Rewriting:

(6 ^ 3) ^ {n-3} = (\frac {1} {6 ^ 2}) ^ {3n}\\6 ^ {3n-9} = \frac {1} {6 ^ {6n}}\\6^{ 3n-9} * 6^{ 6n} = 1

To multiply powers of the same base, we place the same base and add the exponents:

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9n-9 = 0\\9n = 9\\n = \frac {9} {9}\\n = 1

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Essentially, there are five way because there are five "positions" where the tail could be.

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