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BabaBlast [244]
3 years ago
5

Mai runs around a 400-meter track at a constant speed of 250 meters per minute. How many minutes does it take Mai to complete 4

laps of the track? Explain or show your reasoning​
Mathematics
1 answer:
Artyom0805 [142]3 years ago
8 0

Answer:

6.4 minutes

Step-by-step explanation:

<u>Given information:</u>

- Track is 400m long

- Mai runs at a constant speed of 250 meters/minute

- - - - - -

To find how many minutes it takes for Mai to complete 4 laps, we need to find the total distance Mai is running for:

400\times4=1600 meters

To find how many minutes Mai is running for, we divide by the distance Mai travels per minute:

1600\div250=6.4 minutes

∴ Mai takes 6.4 minutes to run 4 laps around the track.

Hope this helps :)

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Step-by-step explanation:

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tiny-mole [99]

Ok, so the question is based on geometric progression. Remember, the formula for calculating the nth-term of a geometric progression is: a*r^{n-1}. The a in the expression stands for the 1st term of the sequence, and r is the common ratio of the elements of the sequence. Now let's take a look at the problem.

"A ping pong ball has a 75% rebound ration". We can infer that our common ratio, r, is 75% which is 0.75.

"When you drop it from a height of k feet...", this means the first height you drop it from, a.k.a, the first term.

Now going back to the expression, the nth-term = a*r^{n-1}, we can substitute our common ration, 0.75 with r, and our 1st term, k, with a. This becomes: k * 0.75^{n-1}. This becomes our expression.

a. The highest height achieved by the ball after six bounces. Our nth-term here is 6, so let's use our expression to find the 6th term. n_{6} = 235 * 0.75^{6-1} = 235*0.75^{5} = 235*0.2373 = 55.7655ft

b. The total distance travelled by the ball when it strikes the ground for the 12th time. This involves the use of the sum of elements in the geometric progression. The formula for that is \frac{a(1 - r^{n})}{1-r}, provided that r is less than 1, which it is in this case, since 0.75 is less than one. Our nth-term here is 12, so we substitute.

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