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ExtremeBDS [4]
2 years ago
11

The temperature of a cup of coffee varies according to Newton's Law of Cooling: dT dt equals negative k times the quantity T min

us A, where T is the temperature of the coffee, A is the room temperature, and k is a positive constant. If the coffee cools from 100°C to 90°C in 1 minute at a room temperature of 25°C, find the temperature, to the nearest degree Celsius of the coffee after 4 minutes.
74
67
60
42
Mathematics
1 answer:
denis23 [38]2 years ago
4 0

Answer:

  (b)  67

Step-by-step explanation:

A solution to the differential equation describing the temperature according to Newton's Law of Cooling could be written as ...

  T = (final temp) + (initial difference)×(decay factor)^t

where the decay factor is the fraction of change during 1 unit of time period t.

__

Here, the initial difference of 100-25 = 75 degrees decays to 90-25 = 65 degrees in 1 minute. So, the units of t are minutes, the decay factor is 65/75, the initial difference is 75 degrees, and the final temperature is 25 degrees. That lets us write the equation as ...

  T = 25 +75(65/75)^t

Then for t=4, the temperature is ...

  T = 25 +75(13/15)^4 ≈ 67.3 . . . . degrees

After 4 minutes the temperature of the coffee is about 67 degrees.

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charle [14.2K]

Add the exponents and keep the same base. Then reciprocal it and change the sign of the exponent. Then the value of the exponent expression is 0.5.

<h3>What is an exponent?</h3>

Exponential notation is the form of mathematical shorthand which allows us to write complicated expressions more succinctly. An exponent is a number or letter is called the base. It indicates that the base is to raise to a certain power. X is the base and n is the power.

The exponent expression is 2³ × 2⁻⁴ can be simplified.

Add the exponents and keep the same base. Then we have

2³ × 2⁻⁴  = 2⁽³⁻⁴⁾

2³ × 2⁻⁴  = 2⁻¹

Then find the reciprocal and change the sign of the exponent.

2^3* 2^{-4} = 2^{-1}\\\\2^3* 2^{-4} = \dfrac{1}{2}\\\\2^3* 2^{-4} = 0.5

The value is 0.5.

More about the exponent link is given below.

brainly.com/question/5497425

7 0
2 years ago
Mr. Sasha teaches 4 math classes, with the same number of students in each class. Of those students, 80 are sixth graders and 40
STatiana [176]
80=6th graders
40=5th graders

80+40=120
120/22= 60/11
120/25=24/5
120/30= 4

There are 30 students in each class because he teaches 4 class and 120/30 will give you 4.
6 0
3 years ago
Five metal cubes with sides of 18 cm are melted and casted into a spherical ball. Find the volume of the sphere that is formed.
liberstina [14]

Answer:

29160cm³

Step-by-step explanation:

(18*18*18) *5 = 29160

6 0
3 years ago
Jay is hanging 160 feet of Christmas garland on the three sides (two on the width and one on the length) of fencing that enclose
Setler [38]

The length of the fencing is 62.4 feet.

The width of the fencing is 17.6 feet.

Given,

The measurement of the Christmas garland = 160 feet

The width of the fencing = w

The length of the fencing, l = 4w - 8

We have to find the length and width of the fencing.

Here,

Perimeter can be taken as 160. Because garland will cover the entire fencing.

Perimeter = 2(l + w)

160 = 2(4w - 8 + w)

160 = 2(5w - 8)

160/2 = 5w - 8

80 + 8 = 5w

88/5 = w

width = 17.6 feet

Now,

l = 4w - 8

l = 4 × 17.6 - 8

l = 70.4 - 8

length = 62.4 feet

That is,

The length of the fencing is 62.4 feet.

The width of the fencing is 17.6 feet.

Learn more about perimeter here:

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3 0
1 year ago
How do I use the substitution method to find the point of intersection of
Goshia [24]
To substitute, solve for one variable and then plug it into the other equation you have. In this problem, y is already solved for on the top equation (y=x+2), so you just stuff it into the second equation.

y = x + 2
3y = 4x - 2

3(x + 2) = 4x - 2
3x + 6 = 4x - 2
-x = -8
x = 8
y = x + 2 = 8 + 2 = 10

solution:
x = 8 
y = 10

hope this helps!! :)
7 0
3 years ago
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