1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Viktor [21]
3 years ago
12

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

Mathematics
2 answers:
MAXImum [283]3 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]3 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

You might be interested in
Technetium-99m is used as a radioactive tracer for certain medical tests. It has a half-life of 1 day. Consider the function T w
Alinara [238K]

Answer:

The expression that represents the number of days until only 10% remains is T((d) 10 %) =100×(\frac{1}{2} )^{3.322}.

Step-by-step explanation:

The equation for half life is of the form

A = A₀×(\frac{1}{2} )^{\frac{t}{h} }.........................................................................(1)

Where

A = Final amount

A₀ = Initial amount

t = Time

h = Half life

For the equation T(d) = 100×2⁽⁻²⁾....................................(2)

We have by comparison with the equation for half life

2 ≡ \frac{t}{h}  and and the equation (2) can be written as

Percentage remaining after 2 half lives is

\frac{A}{A_0} ×100=100×(\frac{1}{2} )^{2 }

However if the half life of Technetium-99m is 6 hours then we have for one day

\frac{A}{A_0} ×100=100×(\frac{1}{2} )^{2 *2}

Therefore an expression that represents the number of days until only 10% remains is

\frac{A}{A_0} ×100=100×(\frac{1}{2} )^{\frac{d}{h}  } = 10 %

(\frac{1}{2} )^{\frac{d}{h}  } =\frac{1}{10}

= ㏑(\frac{1}{2} )^{\frac{d}{h}  }  = ㏑(\frac{1}{10})

= \frac{d}{h}×㏑(\frac{1}{2} ) = ㏑(\frac{1}{10})

\frac{d}{h} = \frac{ln(\frac{1}{10}) }{ln(\frac{1}{2} )} = 3.322

Therefore the expression for the number of days 10 % of Technetium-99m will be remaining is

T((d) 10 %) =100×(\frac{1}{2} )^{3.322}

3 0
4 years ago
What is 52,437 rounded to the nearest thousand?
saul85 [17]
<h3>What is 52,437 rounded to the nearest thousand?</h3>

Answer:  52,000

Step-by-step explanation:

We have to look at the number in the hundredth place and if it is less than five we round down, but if it is five or more, we round up.

In this case, since we have 52,437, the number of hundreds is 4, so we have to <u>round down</u>. 52,000.

\textit{\textbf{Spymore}}​​​​​​

7 0
4 years ago
Determine if the following side lengths could form a triangle.
kykrilka [37]

Answer: Determine if the following side lengths could form a triangle.

Prove your answer with an inequality.

8,17,24

Step-by-step explanation:

Determine if the following side lengths could form a triangle.

Prove your answer with an inequality.

8,17,24

4 0
3 years ago
How I can answer this question, NO LINKS, If you answer correctly I will give u brainliest!
Nat2105 [25]

Answer:

the slope is 3 and you can put points on (1,3) and (2,6) to demonstrate this in the graph

5 0
3 years ago
A bag contains 9 red marbles, 6 white marbles, and 8 blue marbles. You draw 4 marbles out at random, without replacement. Find t
____ [38]

Step-by-step explanation:

here are the answers bae. Feel free to ask for more

4 0
3 years ago
Other questions:
  • Hannah factored the expression 24xy + 15y. Her work is shown below. 1. GCF (24xy, 15y) = 3y 2. 24xy/3 = 8xy, 15y/3 = 5y 3. 3(24x
    9·3 answers
  • Select the correct answer.
    10·1 answer
  • Let a = x2 + 4Rewrite the following equation in terms of a and set it equal to zero (x2+4)2+32=12x2+48
    7·1 answer
  • The polynomial below is NOT in standard form: - 4 + 7x² + 3x Rearrange the terms so that the polynomial is in standard form: Sub
    10·1 answer
  • Please help and add steps!!
    9·2 answers
  • WILL MARK BRAINLIEST!!!
    15·1 answer
  • 36
    7·1 answer
  • 33/7,158 A) 7,158/33= or B) 7,158 /33 = _ R _
    9·1 answer
  • Logan made 6 pounds of trail mix. If he puts 3/4 pounds into each bag, how many bags can Logan fill?
    12·2 answers
  • Mr. Parker spent $96.30 on 3 hats and 6 key chains. if each hat cost $15.50 how much did each key chain cost?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!