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Viktor [21]
2 years ago
12

Find the smallest positive integer k such that 360k is a cube number.

Mathematics
2 answers:
MAXImum [283]2 years ago
8 0

Answer: k = 75

<u>Step-by-step explanation:</u>

                360

                  ∧

             36   10

              ∧     ∧

           6  6   2  5

          ∧    ∧

        2 3  2 3

Prime factorization of 360 is: 2³ · 3² · 5

Since we want a perfect cube, every number must be to the power of 3.

That means we need  a 3 and 2 more 5s  to make a cube

k = 3 × 5 × 5

  = 75

Luden [163]2 years ago
5 0

Answer:

k = 75

Step-by-step explanation:

Factorize 360

360 = 36 * 10

      = 2 * 2 * 3 * 3 * 2 * 5

As 360k is cube number, k = 3 * 5 * 5

k = 75

360k = 360 * 75 = 27000 is a perfect cube

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Which linear equation has no solution?
olga_2 [115]

Answer:

Option A

Step-by-step explanation:

Given:

  • a. 3x-5= 3x + 5
  • b. 3x-5= 3x - 5
  • c. 3x - 5 = 2x+5
  • d. 3x-5 = 2x + 10

To find:

  • Which one of the linear equations have no solution.

Solution:

a)  3x-5= 3x + 5

Add 5 to both sides

3x-5= 3x + 5

3x - 5 + 5 = 3x + 5 + 5

Simplify

(Add the numbers)

3x - 5 + 5 = 3x + 5 + 5

3x = 3x + 5 + 5

(Add the numbers)

3x  = 3x + 5 + 5

3x = 3x + 10

Subtract 3x from both sides

3x = 3x + 10

3x - 3x = 3x + 10 - 3

Simplify

(Combine like terms)

3x -3x = 3x + 10 - 3

0 = 3x + 10 - 3

(Combine like terms)

0 = 3x + 10 - 3

0 = 10

The input is a contradiction: it has no solutions

b)  3x-5= 3x - 5

Since both sides equal, there are infinitely many solutions.

c)  3x - 5 = 2x+5

Add 5 to both sides

3x = 2x + 5 + 5

Simplify  2x + 5 + 5 to 2x + 10

3x = 2x + 10

Subtract 2x from both sides

3x - 2x = 10

Simplify 3x - 2x to x.

x = 10

d) 3x-5 = 2x + 10

Add 5 to both sides

3x = 2x + 10 + 5

Simplify 2x + 10 + 5 to 2x + 15

3x = 2x + 15

Subtract 2x from both sides

3x - 2x = 15

Simplify 3x -2x to x.

x = 15

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

Answer:

As you can see all c and d both have solutions, eliminating them as options. Option B has infinite solutions leaving Option A which has no solutions.

Therefore, <u><em>Option A</em></u> is the linear equation that has no solution.

3 0
2 years ago
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The graph shows the distance a ball has traveled x seconds after it was thrown. What is the average speed between 2 seconds and
Arlecino [84]

Answer:

0.5 meters per second

Step-by-step explanation:

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3 years ago
The equation y = 15.5x represents the number of dollars, y, Worker B earns in x hr.
ira [324]

Answer:

The correct answer is y = 20x.

Step-by-step explanation:

6 0
3 years ago
PLEASE HELP!! IM HAVING A HARD TIME UNDERSTANDING THIS QUESTION.
kondor19780726 [428]

Answer:

14.6

Step-by-step explanation:

8 0
2 years ago
I think it’s b but I may be wrong
leonid [27]

Answer:

D, not B

Step-by-step explanation:

So using Pythagorean Theorem:

C^{2} =A^{2} +B^{2} \\x^{2} =144+265\\x^{2} =400\\x=20

Yep, It's not B, But D.

Hope this helps!

Stay Safe!

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