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3 years ago

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

Svet_ta [14]

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:

Move the first n stones from A to C ( $l_n$ moves).
Move the biggest stone from A to B (1 move).
Move the first n stones from C to A ( $l_n$ moves).
Move the biggest stone from B to C (1 move).
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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Which is the equation of a line with a slope of -1/3 and a yintercept at (0, 1)?

posledela

Y = mx + b

m is -1/3

plug in your given values for x and y to find b

1 = (-1/3)(0) + b
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make equation
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4 years ago