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natka813 [3]
3 years ago
8

The diameter of the clock face of Big Ben in London measures 29 feet. The minute hand is 14 feet long and the hour hand is 9 fee

t long.
As the minute hand moves from 12 to 5, how many more feet does it travel than the hour hand as it moves from 12 to 5?

Use π≈3.14 and round your answer to the nearest foot.
Mathematics
1 answer:
Svetach [21]3 years ago
8 0

Answer:

13 feet

Step-by-step explanation:

The first step in determining the distance each hand moves is to determine the angle their movement form, going from 12 to 5.

From 12 to 5, that represent a movement of 5... out of a possible movement of 12 (to reach 12 again)...  so their movement is equal to 5/12 of a circle.

Now that we have the fraction of the circle we need, we can calculate the distance run by each hand.  We'll start with the minute hand, which is 14 feet long:

The length of the arc of a full circle is calculated by the formula 2 * π * r where r is the radius of the circle.  In our case, the radius of the circle is the length of the hand drawing the circle.  And since we don't want to know the all the circumference of the circle, but only the 5/12 of it, representing the movement from 12 to 5, we'll factor it in:

d = \frac{5}{12} * 2 * \pi * 14 = 36.63

Now, let's do the same calculation for the hour hand which measures 9 feet:

d = \frac{5}{12} * 2 * \pi * 9 = 23.55

The difference is then 36.63 - 23.55 = 13.08 feet.

Which we round down to 13 feet.

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Answer:

r = 5.848cm, h = 11.696cm

Step-by-step explanation:

Surface area: SA=2\pi rh+2\pi r^2

Volume: V=\pi r^2h

Therefore, the height of a cylinder given its volume would be h=\frac{V}{\pi r^2}, thus:

SA=2\pi r(\frac{V}{\pi r^2})+2\pi r^2\\\\SA=\frac{2V}{r}+2\pi r^2\\\\SA=\frac{2(400\pi)}{r}+2\pi r^2\\\\SA=\frac{800\pi}{r}+2\pi r^2

We now find the derivative of the surface area of the cylinder with respect to its radius and set it equal to 0, solving for the radius:

\frac{d(SA)}{dr}=-\frac{800\pi}{r^2}+4\pi r

0=-\frac{800}{r^2}+4\pi r

0=800\pi+4\pi r^3

-800\pi=4\pi r^3

-200=r^3

r\approx5.848

If 0If [tex]r>5.848, then the surface area of the cylinder increases

Therefore, the surface area is minimized when the radius is r=5.848cm, making the minimum height h=\frac{V}{\pi r^2}=\frac{400\pi}{\pi(5.848)^2}\approx11.696cm.

In conclusion, the 2nd option is correct.

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2 years ago
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Answer:

x = 15

Step-by-step explanation:

Bisects means divide in two equal parts.

Therefore, 74/2 = 37

37 = 2x+7

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15 =  x

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3 years ago
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4. In a sample of 1000 people, 130 can wiggle their ears. Two unrelated people are
Elina [12.6K]

Using the hypergeometric distribution, it is found that there is a 0.7568 = 75.68% probability that neither can wiggle his or her ears.

The people are chosen from the sample without replacement, which is why the <u>hypergeometric distribution</u> is used to solve this question.

Hypergeometric distribution:

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}

C_{n,x} = \frac{n!}{x!(n-x)!}

The parameters are:

  • x is the number of successes.
  • N is the size of the population.
  • n is the size of the sample.
  • k is the total number of desired outcomes.

In this problem:

  • 1000 people means that N = 1000
  • 130 can wiggle their ears, thus k = 130
  • Two are selected, thus n = 2.

The probability that neither can wiggle his or her ears is P(X = 0), thus:

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}

P(X = x) = h(0,1000,2,130) = \frac{C_{130,0}C_{870,2}}{C_{1000,2}} = 0.7568

0.7568 = 75.68% probability that neither can wiggle his or her ears.

A similar problem is given at brainly.com/question/24826394

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