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yanalaym [24]
3 years ago
13

A boy wants to jump onto a carousel that is spinning at a rate of 14 revolutions per minute. If the carousel is 23 feet in diamt

er, how fast must the boy run to match the speed of the carousel and jump on?A) 2.68 feet per second.B) 1,011.59 feet per second.C) 33.72 feet per second.D) 16.86 feet per second.
Mathematics
1 answer:
nirvana33 [79]3 years ago
6 0

Answer:

16.86 ft/s

Step-by-step explanation:

Given that

Speed of the carousel, s = 14 rpm

Distance from the carousel, d = 23 ft

To start with, we convert the given speed to revolution per second, so that

s = 14/60 rev/sec

To find the needed speed, we use the formula

v =2πnR, remember that Diameter = 2R, so we substitute D for 2R and get πnD

v = πnD, and we use this to find our needed velocity

v = 3.142 * 14/60 * 23

v = 72.266 * 14/60

v = 16.86 ft/s

Therefore the boy must run at a speed of 16.86 ft/s in order to be able to match the carousel and jump on it

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Answer:

81 adult tickets

Step-by-step explanation:

Step 1:

Set up a system of equations

Since the adult tickets and student tickets add to 243, we can do

a+s=243

and the student tickets sold were 2x the adult tickets, we can do

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We can replace s in the first equation adding to 243 with 2a

a+s(2a)=243\\3a=243\\

Step 2:

Solve for a. We can divide both sides by 3.

a=81

Therefore, there were 81 adult tickets sold.

Step 3:

We can check our work! Since we learned earlier the student tickets are 2x adult tickets, we can multiply 81 by 2 and add that to 81 to see if it equals 243!

s=2a\\s=2(81)\\s=162

And...

162+81=243

So, 81 must be the answer!

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