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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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Solve for x: 3x − 2 &gt; 5x + 10. (5 points)
velikii [3]

Answer:

Option 2.. x > -6

Step-by-step explanation:

3x -5x - 2 > 5x -5x + 10

-2x - 2 + 2 > 10 + 2

-2x/-2 > 12/-2

<u>x > -6</u>

5 0
2 years ago
Y=5x-1 and -15x-3y=3 how many solutions does this have
Artemon [7]
No solutions. The equation would be
-15x-3(5x-1)=3
-15x-15x-3=3
No Solution

Hope this helped?
4 0
3 years ago
12 buses bring a total of 420 people to the Alharbra in Granada, Spain. Each bus carries the same number of people. How many peo
Kobotan [32]
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8 0
3 years ago
The geometric sequence a i a i ​ a, start subscript, i, end subscript is defined by the formula: a 1 = 8 a 1 ​ =8a, start subscr
frozen [14]

Question:

The geometric sequence ai is defined by the formula: a₁ = 8, aᵢ = aᵢ₋₁(-1.5 ).

Find the sum of the first 20 terms in the sequence. Choose 1 answer:

Answer:

The sun of 20 terms of the progress is -10,637.621536256

Step-by-step explanation:

Given

Geometric Sequence

a₁ = 8

aᵢ = aᵢ₋₁(-1.5 )

First, the common ratio needs to be calculated.

The common ratio is the ratio of a term to its previous term.

In other words,

Ratio = 2nd term ÷ 1st term or 3rd term ÷ 2nd term, ...... Etc.

We can calculate the common ratio from aᵢ = aᵢ₋₁(-1.5 ) by dividing both sides by aᵢ₋₁. This gives

aᵢ / aᵢ₋₁ = aᵢ₋₁(-1.5 ) / aᵢ₋₁

aᵢ / aᵢ₋₁ = -1.5

So, the common ratio, r = -1.5

Now that we've had the common ratio and first term to be -1.5 and 8 respectively, the sum of 20 terms can then be calculated using the sum of n terms formula.

Sₙ = a(1 - rⁿ)/(1 - r)

We're making use of this formula because r is less than 1

Where n = 20

a = first term = 8

r = -1.5

By substituting these values; we get

S₂₀ = 8(1 - (-1.5)²⁰)/(1 - (-1.5))

S₂₀ = 8(1 - (-1.5)²⁰)/(1 + 1.5))

S₂₀ = 8(1 - (-1.5)²⁰)/(1 + 1.5))

S₂₀ = 8(1 - (3325.25673008

))/(2.5)

S₂₀ = 8(1 - 3325.25673008

)/(2.5)

S₂₀ = 8(-3324.25673008

)/(2.5)

S₂₀ = -10,637.621536256

5 0
3 years ago
Monday 2/3 of the team practiced, Tues 7/8, Wed 1/2,Thurs 3/4. On which day were the most team members present at practice?
MrMuchimi
Tuesday.

1/2 =50%, 3/4=75% 2/3=66.6% and so forth.
8 0
3 years ago
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