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zmey [24]
3 years ago
13

you place a cup of 200f coffee on a table in a room that is 67f and 10 minutes later it is 195f. approximately how long will it

be before the coffee is 180f

Mathematics
1 answer:
kompoz [17]3 years ago
7 0
Newton's law of cooling says the rate of change of temperature is proportional to the difference between the object's temperature and the temperature of the environment.

Here, the object starts out at 200 °F, which is 133 °F greater than the environment temperature. 10 minutes later, the object is 195 °F, so is 128 °F greater than the environment. In other words, the temperature difference has decayed by a factor of 128/133 in 10 minutes.

The solution to the differential equation described by Newton's Law of Cooling can be written as the equation
   T(t) = 67 + 133*(128/133)^(t/10)
where T is the object's temperature in °F and t is the time in minutes from when the object was placed in the 67 °F environment.

The equation 
   T(t) = 180
can be solved analytically, but it can be a bit easier to solve it graphically. A graphing calculator shows it takes 42.528 minutes for the temperature of the coffee to reach 180 °F.

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Leah claims that these figures are not similar. When she compared the heights, she wrote 27. Then she compared the bases and got
Flauer [41]

Answer:

<h2>Leah is actually wrong, because those rectangles are similar.</h2>

Step-by-step explanation:

Remember that similarity is about having proportional sides and congruent angles. When we have congruent sides, then those rectangles are congruent not similar.

In this case, to find the similarity, Leah should compare bases and heights thorugh division, because the ratio between heights and the ratio between bases must be equal. So, let's divide.

\frac{21}{6}=3.5

\frac{7}{2}=3.5

As you can observe, both ratios are equal.

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4 0
3 years ago
If the temperature was -4 yesterday and 23 today what is the change in temperature
Bess [88]
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7 0
3 years ago
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Which word problem below could be represented by the number sentence 6 X 4= ?
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O D. Luis had 6 pencils. He placed them in 4 groups. How many were in each group?

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6 0
2 years ago
At a farm, there are two huge pits for storing hay. 90 tons of hay is stored in the first pit, 75 tons in the second pit. Then,
Travka [436]

Answer:

63 tons

Step-by-step explanation:

The problem statement asks for the tons of hay removed from the first pit. It is convenient to let a variable (x) represent that amount. This is said to be 3 times the amount removed from the second pit, so that amount must be x/3.

The amount remaining in the first pit is 90-x.

The amount remaining in the second pit is 75 -x/3.

Since the first pit remaining amount is half the second pit remaining amount, we can write the equation ...

... 90 -x = (1/2)(75 -x/3)

... 180 -2x = 75 -x/3 . . . . multiply by 2

... 105 - 2x = -x/3 . . . . . . subtract 75

... 315 -6x = -x . . . . . . . . multiply by 3

... 315 = 5x . . . . . . . . . . . add 6x

... 63 = x . . . . . . . . . . . . . divide by 5

63 tons of hay were taken from the first pit.

_____

<em>Check</em>

After removing 63 tons from the first pit, there are 27 tons remaining. After removing 63/3 = 21 tons from the second pit, there are 54 tons remaining. 27 is half of 54, so the answer checks OK.

6 0
3 years ago
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