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mojhsa [17]
2 years ago
12

After heating up in a teapot, a cup of hot water is poured at a temperature of

Mathematics
1 answer:
xxTIMURxx [149]2 years ago
3 0

Answer:

  • k ≈ 0.060
  • T(4) ≈ 178 °F

Step-by-step explanation:

The desired formula parameters for Newton's Law of Cooling can be found from the given data. Then the completed formula can be used to find the temperature at the specified time.

__

<h3>Given:</h3>

  T(t)=T_a+(T_0-T_a)e^{-kt}\\\\T_a=68,\ T_0=208,\ (t,T)=(3,185)

<h3>Find:</h3>

  k

  T(4)

<h3>Solution:</h3>

Filling in the given numbers, we have ...

  185 = 68 +(208 -68)e^(-k·3)

  117/140 = e^(-3k) . . . . . subtract 68, divide by 140

  ln(117/140) = -3k . . . . . . take natural logarithms

  k = ln(117/140)/-3 ≈ 0.060

__

The temperature after 4 minutes is about ...

  T(4) = 68 +140e^(-0.060·4) ≈ 68 +140·0.787186

  T(4) ≈ 178.205

After 4 minutes, the final temperature is about 178 °F.

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Answer:

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Step-by-step explanation:

All three of these ratios are equivalent to 15:5. Here's how:

Let's look at the first ratio, 9:3. Did you notice something common? 3 x 3 = 9. 9/3 = 3. 5 x 3 = 15. 15/3 = 5. Both of these numbers are divisible by 3,  so these ratios are equivalent.

Second. 6:2. 2 x 3 = 6. 6/3 = 2. 5 x 3 = 15. 15/3 = 5. See the similarity? The same applies to the next problem, number three, although it does slightly differentiate.

Third, 3:1. See, here, since the ratio is smaller than the problem, we can't multiply, since this ratio is smaller than the original number. But, it's still the same thing. A ratio is a number that compares a value to another value. This means that 3:1 is 3 compared to one. Now, let me clarify. 15:5. 3:1. These are the exact same values, except they are just written in a different form, and simplified. Since 5 x 3 = 15, we know that we can divide 15 evenly by 5, which makes it 3, and divide 5 evenly by 5, which equals one. So here we have our answer for the third problem. 5:1.

Ratios are basically division, except simplified. Every single ratio problem works this way. Once you get the hang of it, it's immensely easy. Hope this helped!

6 0
3 years ago
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Step-by-step explanation:

According to the graph :

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Step-by-step explanation:

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