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3 years ago

Find the smallest non-zero whole number n such that 756n is a perfect cube.

Mathematics

1 answer:

Kitty [74]3 years ago

5 0

Step-by-step explanation:

756 = 2² * 3³ * 7.

For 756n to be a perfect cube, all of its prime factors must have a power that is a multiple of 3.

How to get from 2² to 2³: Multiply by 2.

3³ has already a power that is a multiple of 3.

How to get from 7 to 7³: Multiply by 7².

Hence n = 2 * 7² = 98.

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3 years ago

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Answer:

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3 years ago

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3 years ago

5/8 of the 64 musicians in a music contest are guitarists. Some of the guitarists play jazz solos, and the rest play classical s

motikmotik

The first thing we must do for this case is find the number of total guitarists.

We have then:

$(\frac{5}{8}) * (64) = 40$

We now look for the relationship between the number of guitarists playing jazz alone to the total number of guitarists.

We have then:

$\frac{x}{40} = \frac{1}{4}$

Where,

x: number of guitarists playing jazz alone

From here, we clear the value of x.

$x = (\frac{1}{4}) * (40)\\x = 10$

Then, the number of guitarists who play classical solo is:

$40 - 10 = 30$

Answer:

30 guitarists play classical solos in the contest

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4 years ago

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