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Murrr4er [49]
2 years ago
12

What is the smallest positive integer $n$ such that $3n$ is a perfect square and $2n$ is a perfect cube?

Mathematics
1 answer:
Agata [3.3K]2 years ago
6 0

Answer:

108

Step-by-step explanation:

Since 3n is a perfect square, that means that n has to be a multiple of 3. Since 2n is a perfect cube, then n has to be divisible by 2^2=4. Since n is a multiple of 3, then n also has to be divisible by 3^3=27. Therefore, the smallest value for n is 4*27=108.

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I want to run 4 1/2 miles tonight. If I know running around my block is 3/5 of a mile, how many times should I run around the bl
sukhopar [10]
3/5 block mile is also 0.6 block mile
4 1/2 miles is also 4.5 miles

How many 0.6mi blocks do you run to run 4.5 miles?

4.5miles/0.6block mi = 7.5 or 7 1/2 blocks will equal 4.5 or 4 1/2 miles.

Check 7.5 blocks x 0.6 block mi = 4.5 miles

Same as you know one quarter equals $0.25 cent. And how many do you need to make one dollar that equals $1.00 ?

1/ .25 = 4 quarters

3 0
3 years ago
A bird flies 2/3 of a mile per minute. How many miles per hour is it flying?
Snowcat [4.5K]

Answer:

40 MPH (Miles Per Hour)

Step-by-step explanation:

Well i will put it in simple terms. Put 2/3 into a decimal point, which for this fraction is 0.66666666667 (the 6 is infinite basically). Then you multiply it by 60, because you know it goes in that distance in one minute and 60 minutes makes a hour, which equals 40. So the answer is 40 MPH.

6 0
3 years ago
Multiply the polynomial <br><br> (4d-3)(-2d+1)
Nutka1998 [239]
If this an it my bad Gee

8 0
3 years ago
Each year for 4 years, a farmer increased the number of trees in a certain orchard by of the number of trees in the orchard the
Neko [114]

Answer:

The number of trees at the begging of the 4-year period was 2560.

Step-by-step explanation:

Let’s say that x is number of trees at the begging of the first year, we know that for four years the number of trees were incised by 1/4 of the number of trees of the preceding year, so at the end of the first year the number of trees wasx+\frac{1}{4} x=\frac{5}{4} x, and for the next three years we have that

                             Start                                          End

Second year     \frac{5}{4}x --------------   \frac{5}{4}x+\frac{1}{4}(\frac{5}{4}x) =\frac{5}{4}x+ \frac{5}{16}x=\frac{25}{16}x=(\frac{5}{4} )^{2}x

Third year    (\frac{5}{4} )^{2}x-------------(\frac{5}{4})^{2}x+\frac{1}{4}((\frac{5}{4})^{2}x) =(\frac{5}{4})^{2}x+\frac{5^{2} }{4^{3} } x=(\frac{5}{4})^{3}x

Fourth year (\frac{5}{4})^{3}x--------------(\frac{5}{4})^{3}x+\frac{1}{4}((\frac{5}{4})^{3}x) =(\frac{5}{4})^{3}x+\frac{5^{3} }{4^{4} } x=(\frac{5}{4})^{4}x.

So  the formula to calculate the number of trees in the fourth year  is  

(\frac{5}{4} )^{4} x, we know that all of the trees thrived and there were 6250 at the end of 4 year period, then  

6250=(\frac{5}{4} )^{4}x⇒x=\frac{6250*4^{4} }{5^{4} }= \frac{10*5^{4}*4^{4} }{5^{4} }=2560.

Therefore the number of trees at the begging of the 4-year period was 2560.  

7 0
3 years ago
What is 117/320 simplified to a mixed fraction
Alex

Answer:

hope this helps 229 999 0523

117 /320 ≈ 0.366

Step-by-step explanation:

Step 1 of 1: Simplify.

Simplify

117 over 320

117

320

Step 1 of 1: Simplify, sub-step a: Reduce fraction to lowest terms.

Reduce fraction to lowest terms

1 is the greatest common divisor of 117 and 320. The result can't be further reduced.

8 0
3 years ago
Read 2 more answers
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