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2 years ago

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

Step-by-step explanation:

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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ax + by = c

y = -5x + 3
Add 5x to both sides.

5x + y = 3
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2 years ago

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Pachacha [2.7K]

Answer:

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Step-by-step explanation:

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1 year ago

Read 2 more answers

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mamaluj [8]

I don't know if this is right, but I'm pretty sure it's B.

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2 years ago

A sample of 20 joint specimens of a particular type gave a sample mean proportional limit stress of 8.41 mpa and a sample standa

nignag [31]

For this problem, the confidence interval is the one we are looking for. Since the confidence level is not given, we assume that it is 95%.

The formula for the confidence interval is: mean ± t (α/2)(n-1) * s √1 + 1/n

Where:

α= 5%

α/2 = 2.5%

t 0.025, 19 = 2.093 (check t table)

n = 20

df = n – 1 = 20 – 1 = 19

So plugging in our values:

8.41 ± 2.093 * 0.77 √ 1 + 1/20

= 8.41 ± 2.093 * 0.77 (1.0247)

= 8.41 ± 2.093 * 0.789019

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2 years ago

Help out?? Mathematics image.

Brilliant_brown [7]

Answer: (12) ∠1 = 20° (13) ∠2 = 50° (14) ∠3 = 15° (15) UV = 80° (16) AB = 40° (17) ABC or 180° - CD (18) BC - 140° (19) ABC = 150°

Step-by-step explanation:

12) $\frac{1}{2}$ (UV - ST) = ∠1

$\frac{1}{2}$ (80 - 40) = ∠1

$\frac{1}{2}$ (40) = ∠1

20 = ∠1

13) $\frac{1}{2}$ (UV + ST) = ∠2

$\frac{1}{2}$ (70 + 30) = ∠2

$\frac{1}{2}$ (100) = ∠2

50 = ∠2

14) $\frac{1}{2}$ (VB - BS) = ∠3

$\frac{1}{2}$ (60 - 30) = ∠3

$\frac{1}{2}$ (30) = ∠3

15 = ∠3

15) $\frac{1}{2}$ (UV - ST) = ∠1

$\frac{1}{2}$ (UV - 20) = 30

UV - 20 = 60

UV = 80

16) ∠1 = arc AB

∠1 = 40

arc AB = 40

17) arc AB + arc BC = arc AC

= 180 = arc CD

18) ∠1 + ∠2 + ∠3 = 180

20 + ∠2 + 20 = 180

∠2 + 40 = 180

∠2 = 140

19) ∠1 + ∠ 2 = arc ABC

∠1 + ∠2 + ∠3 = 180

arc ABC + 30 = 180

arc ABC = 150

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2 years ago