Complete the equation to show how many twelfths are equivalent to 5/6

Mathematics

1 answer:

quester [9]3 years ago

3 0

Answer:

Step-by-step explanation:

<u>Let the required number be x, then we have the following equation:</u>

1/12x = 5/6
1/12x = 10/12
1/12x = 1/12*10
x = 10

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840/7 = 120.

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form a 6 digit number divisible by 1 first 2 divisible by 2, first 3 digits divisible by 3, first 4 digits divisible by 4, first

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Answer:

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Step-by-step explanation:

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The function g has an inverse. The function g − 1 determines the number of folds needed to give the folded paper a thickness of

Amanda [17]

Answer:

$\mathbf{g^{-1} (t) = log _2 \ 20 \ t}$

Step-by-step explanation:

Here is the full question

A standard piece of paper is 0.05 mm thick. Let's imagine taking a piece of paper and folding the paper in half multiple times. We'll assume we can make "perfect folds," where each fold makes the folded paper exactly twice as thick as before - and we can make as many folds as we want.

Write a function g that determines the thickness of the folded paper (in mm) in terms of the number folds made, n. (Notice that g(0) 0.05,)

$g(n )= (05)2^n$

The function g has an inverse. The function g⁻¹ determines the number of folds needed to give the folded paper a thickness of t mm. Write a function formula for g⁻¹).

<u>SOLUTION:</u>

If we represent g(n) with t;

Then

$\mathbf{t = (0.05)2^n} \\ \\ \mathbf{\dfrac{t}{0.05} = 2^n} \\ \\ \mathbf{\dfrac {100 \ t }{ 5} = 2^n} \\ \\ \mathbf{20 t = 2^n}$

Taking logarithm of both sides; we have :

$\mathbf{log (20 t) = n log 2} \ \ \ \mathbf{(since \ , log \ a^b = b \ log \ a) } \\ \\ \mathbf{n = \dfrac{log \ 20 t }{log \ 2 }} \\ \\ \mathbf{g^{-1} (t) = \dfrac{log \ 20 t }{log \ 2 }} \\ \\ \mathbf{g^{-1} (t) = log _2 \ 20 \ t}$