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Marianna [84]
2 years ago
8

The most economical proportion for a right circular cone is to have its height three times long as its base diameter. What later

al area of the cone would produce a volume of 100m^3.
Mathematics
1 answer:
defon2 years ago
5 0

9514 1404 393

Answer:

  ∛(2500π)√37 m² ≈ 120.911 m²

Step-by-step explanation:

If the height is 3 times the diameter, it is 6 times the radius. Then the volume is ...

  V = 1/3πr²h

  V = 1/3πr²(6r) = 2πr³

For a volume of 100 m³, the radius is ...

  100 m³ = 2πr³

  r = ∛(50/π) m

The lateral area of the cone is computed from the slant height. For this cone, the slant height is found using the Pythagorean theorem:

  s² = r² +(6r)² = 37r²

  s = r√37

Then the lateral area is ...

  LA = πrs

  LA = π(∛(50/π) m)(∛(50/π) m)√37

  LA = ∛(2500π)√37 m² ≈ 120.911 m²

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2 years ago
Gavin likes biking. He never misses a chance to go for a ride when the weather is nice. This week his goal is to bike about 65 t
andreyandreev [35.5K]

Answer:

How far should he ride on each of the four days to reach his goal?

1st day: 8 miles

2nd day: 12 miles

3rd day: 18 miles

4th day: 27 miles

Step-by-step explanation: As the problem says, x is the number of miles he rides on the first day. Let's start off with that.

1st day: x miles

He want to ride 1.5 times as far as he rode the day before... no 1.5 more, but 1.5 <em>times</em> as far as he rode the day before; you would multiply 1.5 with the previous day's length.

2nd day: 1.5x

Then you multiply 1.5 to 1.5x to get the third day's.

3rd day: 2.25x

4th day: 3.375x

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

Phew! Gavin wants to ride a total of 65 miles over these four days, so if Gavin added all the miles of the four days, he should get 65...

1st+2nd+3rd+4th=65

x+1.5x+2.25x+3.375x=65

8.125x=65

\frac{8.125x}{8.125}=\frac{65}{8.125}

x=8

Yes! Now that we've got the hard part done... substitute 8 for ever single x.

1st day: 8 miles

2nd day: 1.5(8)=12 miles

3rd day: 2.25(8)=18 miles

4th day: 3.375(8)=27 miles

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

Checking my answer:

Just add the miles!

8+12+18+27=65

65=65

✓

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

Hope that helps! :D



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Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 21 days and
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Answer:

0.33411

The probability that a particular criminal trial lasted atleast 24 days is 0.33411

Step-by-step explanation:

The random variable X is normally distributed with a mean of 21 and standard deviation of 7

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X ~ N(μ = 21 ; σ = 7)

X ~ N(21, 7)

Probability that a trial lasted atleast 24 days :

P(X ≥ 24) :

The standardized score :

Z = (x - μ) / σ ; (24 - 21) / 7 ; 3 / 7 = 0.4286

Hence,

P(Z ≥ 0.4286) = 0.33411

The probability that a particular criminal trial lasted atleast 24 days is 0.33411

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