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oee [108]
2 years ago
13

A clothier who only makes shirts and pants can make a shirt in 4 hours and a pair of pants in 6

Mathematics
1 answer:
Novay_Z [31]2 years ago
7 0

The amount of shirts and pants the clothier makes is an illustration of a linear equation

The equation that represents the number of shirts, and the number of pants is 4s + 6p = 40

<h3>How to determine the equation</h3>

The rates are given as:

Shirts = 4 hours

Pants = 6 hours

In time t, the shirts and pants made is represented with:

t = 4s + 6p

Given that the time is 40 hours, the equation becomes

4s + 6p = 40

Hence, the equation that represents the number of shirts, and the number of pants is 4s + 6p = 40

Read more about linear equations at:

brainly.com/question/14323743

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Newton's Law of Cooling states that the rate of change of the temperature of an object, T, is proportional to the difference of
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Answer:

  305 °F

Step-by-step explanation:

The core temperature of the object after 4 hours can be found using an exponential decay formula to model the decay of the difference between core temperature and ambient.

<h3>Cooling Model</h3>

The solution to the differential equation described by Newton's law of cooling is the exponential equation ...

  y = ab^t +c

where 'a' is the initial core temperature difference from ambient, 'b' is the decay factor of that difference in 1 unit of time period t. 'c' is the ambient temperature.

For this problem, the ambient temperature is c=80, and the differences of interest are ...

  a = 1200 -80 = 1120

  b = (830 -80)/1120 = 75/112

Using these values in the model gives ...

  y = 1120(75/112)^t +80 . . . . . . where y(t) is the core temperature at time t

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<h3>Application</h3>

We want y when t=4.

  y = 1120(75/112)^4 +80 ≈ 1120(0.20108) +80 ≈ 305.212

The core temperature after 4 hours is about 305 °F.

__

<em>Additional comment</em>

The differential equation will have a solution of the form ...

  T-T_R=(T_0-T_R)e^{kt}

where k = ln(75/112) ≈ -0.40101

In the above, we defined b = e^k = 75/112. Accuracy with this fraction can be better than using a truncated value of k.

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