![daltondespain2](/avatars/36548.jpg)
daltondespain2
01.09.2019 •
Mathematics
Factoring equation of the problem
Solved
Show answers
More tips
- F Food and Cooking 10 Reasons Why You Should Avoid Giving Re-Gifts: An Informative Guide...
- S Sport How to wrap boxing hand wraps? Everything you need to know!...
- A Animals and plants 5 Tips for Taking Care of Yews to Keep Them Green and Beautiful...
- H Health and Medicine How to Calm Your Nerves? Expert Tips That Actually Work...
- O Other What is a Disk Emulsifier and How Does it Work?...
- S Sport How to Pump Your Chest Muscle? Secrets of Training...
- C Computers and Internet How to Get Rid of 3pic Infector: Everything You Need to Know...
- S Style and Beauty How to Grow Hair Faster: Real Methods and Advice...
- C Computers and Internet How to Top Up Your Skype Account Without Losing Money?...
- C Computers and Internet How to Get Rid of Spam in ICQ?...
Answers on questions: Mathematics
- M Mathematics In the past year pablo watched 12 movies that he thought were very good. he watched 60 movies over the whole year. of the movies he watched, what percentage did he rate...
- M Mathematics Which set of angles are corresponding angles?...
- M Mathematics On a particular day, the wind added 4 miles per hour to alfonso s rate when he was cycling with the wind and subtracted 4 miles per hour from his rate on his return trip....
- M Mathematics Find the missing side of the triangle...
- M Mathematics $452.91 rounded to the nearest cent?...
- M Mathematics Find the missing side lengths. leave your answers as radicals in simplest form...
- M Mathematics If the sales tax rate is 7.25% in california, then how much would you pay in los angeles for a coat that cost $120.00?...
- M Mathematics Find the missing side of the triangle...
- M Mathematics Askin care manufacture produces 85 g canister of skin balm. any canister whose weight differs by more that 0.05 g cannot be shipped out. choose the equation that would...
- M Mathematics The ratio of boys to girls in ms. farley’s class is 2: 3. there are 18 boys in class. what is the total number of students in ms. farley’s class?...
Ответ:
A) It will get to a temperature of 125°F at 9:19 PM
B) It will get to a temperature of 150°F at 9:16 PM
C) as time passes temperature approaches the initial temperature of 450°F
Step-by-step explanation:
We are given;
Initial temperature; T_i = 450°F
Room temperature; T_r = 70°F
From Newton's law of cooling, temperature after time (t) is given as;
T(t) = T_r + (T_i - T_r)e^(-kt)
Where k is cooling rate and t is time after the initial temperature.
Now, we are told that After 5 minutes, the temperature is 300°F.
Thus;
300 = 70 + (450 - 70)e^(-5k)
300 - 70 = 380e^(-5k)
230/380 = e^(-5k)
e^(-5k) = 0.6053
-5k = In 0.6053
-5k = -0.502
k = 0.502/5
k = 0.1004 /min
A) Thus, at temperature of 125°F, we can find the time from;
125 = 70 + (450 - 70)e^(-0.1004t)
125 - 70 = 380e^(-0.1004t)
55/380 = e^(-0.1004t)
In (55/380) = -0.1004t
-0.1004t = -1.9328
t = 1.9328/0.1018
t ≈ 19 minutes
Thus, it will get to a temperature of 125°F at 9:19 PM
B) Thus, at temperature of 150°F, we can find the time from;
150 = 70 + (450 - 70)e^(-0.1004t)
150 - 70 = 380e^(-0.1004t)
80/380 = e^(-0.1004t)
In (80/380) = -0.1004t
-0.1004t = -1.5581
t = 1.5581/0.1004
t ≈ 16 minutes.
Thus, it will get to a temperature of 150°F at 9:16 PM
C) As time passes which means as it approaches to infinity, it means that e^(-kt) gets to 1.
Thus,we have;
T(t) = T_r + (T_i - T_r)
T_r will cancel out to give;
T(t) = T_i
Thus, as time passes temperature approaches the initial temperature of 450°F