1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
tensa zangetsu [6.8K]
2 years ago
8

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

T and the temperature of the region, TR or dT over dt equals k times the quantity T minus T sub R end quantity. An object with core temperature of 1200°F is removed from a fire and placed in a region with a constant temperature of 80°F. After 1 hour, its core temperature is 830°F. What is the object's core temperature 4 hours after it is taken off the fire? (1 point)
Mathematics
1 answer:
maria [59]2 years ago
5 0

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

Note that units of time are hours.

<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.

You might be interested in
What is the hypotenuse?
olga55 [171]

Answer:

he longest side of a right triangle, opposite the right angle.

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Formulate the situation as a system of inequalities. (Let x represent the number of dinghies the company can manufacture and y r
kirill [66]

Answer:

x (smallest to largest) = 0,45 ,55

y (smallest to largest) = 0,10,40

Step-by-step explanation:

(hours)        Dinghy Rowboat        Labor Available

Metal Work 2             3                       120

Painting         2              2                        110

Let x represent the number of dinghies the company can manufacture and y represent the number of rowboats.

So, total hours for metal work = 2x+3y

So, total hours for Painting = 2x+2y

So, equation becomes:

2x+3y\leq 120

2x+2y\leq 110

x\geq 0

y\geq 0

Plot the inequalities

Refer the attached figure

So, the vertices of the feasible region are (0,40),(45,10) and (55,0)

So, x values are 0 , 45 and 55

x represents the number of dinghies

So, x (smallest to largest) = 0,45 ,55

y values are 40,10,0

y represent the number of rowboats.

So, y (smallest to largest) = 0,10,40

3 0
3 years ago
A 4" by 6" by 8" rectangular solid is cut by slicing through the midpoint of three adjacent edges. What is the number of inches
Triss [41]

Answer:

22.078

Step-by-step explanation:

I have attached the images above

7 0
3 years ago
Which expression is equivalent to 3m+1-m?
Lisa [10]

Answer:

option  (a) is correct.

2 + m - 1 + m is an equivalent expression  to the given expression  3m+1-m

Step-by-step explanation:

 Given expression  3m+1-m

We have to choose an equivalent expression from given options.

Equivalent expression are those expression that looks different but are same.

Like 4+2 = 6  and 3+ 3 = 6

Both have same value but looks differently.

Like terms are term having same variable with same degree.

Consider the given expression  3m+1-m

Simplify by adding like terms,

3m + 1 - m = (3-1) m + 1

Thus, (3-1) m + 1  = 2m + 1

Also 2m + 1 can be written as m + m + 2 - 1

Thus, option  (a) is correct.

6 0
3 years ago
Read 2 more answers
Determine the perimeter of quadrilateral CGHI
Murljashka [212]

Answer:

if the sides are 2, 3, 4.2, 2.6 then the perimeter is 11.8

Step-by-step explanation:

just add them together

5 0
2 years ago
Other questions:
  • Find the volume for the problem
    13·1 answer
  • Evaluate the expression.
    5·1 answer
  • Which of these is the longest<br> 1 foot<br> 1 yard<br> 3 feet<br> 39 inches<br> 2.5 feet
    15·1 answer
  • PLEASE HELP! The trail around Mirror Lake in Yosemite National park is 5 miles long. What fraction describes how much more of th
    6·1 answer
  • X + 2y = 2<br><br>A, B, C, or D​
    13·2 answers
  • The difference of a number and 10 is equal to eleven times the number
    11·1 answer
  • The figure below shows triangle NRM with r2 = m2 + n2:
    9·1 answer
  • PLEASE ANSWER THE QUESTION BELOW
    12·1 answer
  • A ship captain is mapping a trip and wants to know the distance the ship will
    11·1 answer
  • What is the slope of this scenario? The bowling alley charges $4 per game and a one time fee of $7 for bowling shoes. *
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!