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omeli [17]
3 years ago
13

A tortoise and a hare are competing in a race around a 1600-meter track. The arrogant hare decides to let the tortoise have a 78

0-meter head start. When the start gun is fired the hare begins running at a constant speed of 10 meters per second and the tortoise begins crawling at a constant speed of 5.3 meters per second.
Mathematics
2 answers:
Sindrei [870]3 years ago
6 0
I am presuming that the question is who won or by how much did the winner win. 

distance equals rate times time, or d = r*t
For the Hare d = 1600 and r = 10
   1600 = 10 t 
Divide both sides by 10 
t = 160
The hare finished in 160 seconds

For the tortoise d = 1600 - 780 = 820 (due to the head start) and r = 5.3
820= 5.3 t
Divide both sides by 5.3
t = 154.72 (rounded to the hundredths place)

The tortoise won by 5. 28 seconds (160-154.72)
 
Nutka1998 [239]3 years ago
3 0
<span>The tortoise wins. The tortoise takes 154.7 seconds to finish the race. The hare takes 160 seconds to finish the race. There really isn't a question here, but I'm going to assume the unasked question is one of "Who wins?" "How long does it take the tortoise to complete the race?" or "How long does it take the hare to complete the race?" And thankfully, in determining the answer to "Who wins?" will have as a side effect the answers to the other two questions. First, how many seconds does it take for the hare to complete the race. Just divide the distance by the speed and you'll have the answer. So 1600 m / 10 m/s = 160 s Now, how many seconds does it take the tortoise to finish the race? Same thing. Distance divided by speed. But there's a twist, you need to figure out the distance. And that is just the track length minus the head start. So (1600 m - 780 m) / 5.3 m/s = 820 m / 5.3 m/s = 154.717 s And since the tortoise took less time than the hare, the tortoise wins.</span>
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Answer:

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Step-by-step explanation:

Let h represent the number of hamburgers. Then h+63 is the number of cheeseburgers, and the combined total is ...

  h +(h +63) = 813

  2h = 813 -63 = 750

  h = 750/2 = 375

375 hamburgers were sold on Saturday.

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<em>Additional comment</em>

In a "sum and difference" problem like this, the smaller number is half the difference between the sum and the difference. h = (813 -63)/2 = 375. This generic solution applies to all "sum and difference" problems.

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Read 2 more answers
1. A ball's position, in meters, as it travels every second is represented by the position function s(t) = 4.9t2+ 450.
bezimeni [28]
1) The ball's position is described by:
s(t) = 4.9t² + 450
We want to find the velocity, which is the 1st-order derivative of the displacement function (I assume this is an introductory calculus class)
s'(t) = v(t) = 9.8t           
We get this by multiplying 4.9 x 2 and reducing the exponent by 1. Now we simply plug 5 in for t.
v(5) = 9.8* 5
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2) Our cost function is C(x) = x² - 10,000
To find the average rate of change between these units, we use this formula:
( C(101) - C(100) ) ÷1 .
We find the change in C, and divide by the change in x, which is just one. 
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C(101) - C(100) = 201 
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3 years ago
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