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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

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3 years ago
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To model this situation, we are going to use the exponential function: f(t)=P(1+ \frac{r}{n} )^{nt}
where
P is the initial number of cars
r is the growing rate in decimal form 
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t is the time in years

To convert the growing rate to decimal form, we are going to divide the rate by 100%
r= \frac{12}{100}
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Since the growing rate is increasing quarterly, n=4. We also know that the initial number of cars is 920, so P=920. Lets replace all those values in our function:
f(t)=920(1+ \frac{0.12}{4} )^{4t}
f(t)=920(1+0.03)^{4t}
f(t)=900(1.03)^{4t}

We can conclude that:
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Exponent --------> The compound periods multiplied by the number of years                                 is 4t
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3 0
3 years ago
Read 2 more answers
Please hurry <br> Select all the points that are on the graph of the line<br> 3x + 5y = 20 ?
Lynna [10]

Answer:

x=5

y=1

Step-by-step explanation:

3*5=15

5*1=5

15+5=20

8 0
2 years ago
A principal of $2600is invested at 6.75% interest, compounded annually. How much will the investment be worth after 14 years
dedylja [7]

Answer:

$6488.19

Step-by-step explanation:

To solve this problem we use the compounded interest formula:

amount  =  principal(1 + (r \n))^({n}{t})

a = $2600(1+(0.0675/1))¹*¹⁴

a = $6488.19

8 0
3 years ago
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