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Goryan [66]
3 years ago
15

8/15 64/? What would the value of the ? Be?

Mathematics
1 answer:
Naya [18.7K]3 years ago
4 0

120

for \frac{8}{15} to be equal to \frac{15}{?}

consider the numerators 8 × 8 = 64, the numerator of the second fraction

We must therefore multiply the denominator by 8

15 × 8 = 120

thus \frac{8}{15} = \frac{64}{120}


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Suppose the Tower of Hanoi rules are changed so that stones may only be transferred to an adjacent clearing in one move. Let In
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Answer:

l_n=3^n-1

Step-by-step explanation:

We will prove by mathematical induction that, for every natural n,  

l_n=3^n-1

We will prove our base case (when n=1) to be true:

Base case:

As stated in the qustion, l_1=2=3^1-1

Inductive hypothesis:  

Given a natural n,  

l_n=3^n-1

Now, we will assume the inductive hypothesis and then use this assumption, involving n, to prove the statement for n + 1.

Inductive step:

Let´s analyze the problem with n+1 stones. In order to move the n+1 stones from A to C we have to:

  1. Move the first n stones from A to C (l_n moves).
  2. Move the biggest stone from A to B (1 move).
  3. Move the first n stones from C to A (l_n moves).
  4. Move the biggest stone from B to C (1 move).
  5. Move the first n stones from A to C (l_n moves).

Then,

l_{n+1}=3l_n+2.

Therefore, using the inductive hypothesis,

l_{n+1}=3l_n+2=3(3^n-1)+2=3^{n+1}-3+2=3^{n+1}-1

With this we have proved our statement to be true for n+1.    

In conlusion, for every natural n,

l_n=3^n-1

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A punch recipe that serves 24 people calls for 4 liters of lemon-lime soda, 2 pints of sherbet, and 6 cups of ice. How much of e
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1 = (-1/3)(0) + b
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