Saul the college calculus student wants to reheat some soup between study sessions. Saul puts the...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Saul the college calculus student wants to reheat some soup between study sessions. Saul puts the bowl in the microwave straight from the refrigerator. When the soup has been heating up for t minutes, its temperature is given by r(t) = 2t4 +37 where r(t) is measured in degrees Fahrenheit. We will use calculus to study how fast the soup heats up. a) (2 points) What was the temperature of the soup when Saul took it out of the refrigerator? (Include units.) Temperature: b) (2 points) Saul wants the soup to be 199°. How long should he microwave the soup to hit this temperature? (Include units.) Time: c) (4 points) Find the average rate of change of the temperature of the soup during the first two minutes. (Include units.) Average rate of change: d) (4 points) Find the average rate of change of the temperature of the soup during the time interval [1,2]. (Include units.) Average rate of change: e) (4 points) Let An denote the average rate of change of the temperature during the time interval [2, 2+ h] if h > 0, and the average rate of change of the temperature during the time interval [2 + h, 2] if h < 0. Find an expression for A₁. SIMPLIFY your result. f) (3 points) Evaluate the limit lim A₁. (Include units). h→0 An lim Ah h→0 = = g) (3 points) Explain what the value found in the previous part means in the context of the problem. (Don't forget units.) h) (2 points) The soup bowl might crack if its temperature ever changes at a rate faster than 50°/min. Is the bowl in danger of cracking at time t = 2? Explain. Saul the college calculus student wants to reheat some soup between study sessions. Saul puts the bowl in the microwave straight from the refrigerator. When the soup has been heating up for t minutes, its temperature is given by r(t) = 2t4 +37 where r(t) is measured in degrees Fahrenheit. We will use calculus to study how fast the soup heats up. a) (2 points) What was the temperature of the soup when Saul took it out of the refrigerator? (Include units.) Temperature: b) (2 points) Saul wants the soup to be 199°. How long should he microwave the soup to hit this temperature? (Include units.) Time: c) (4 points) Find the average rate of change of the temperature of the soup during the first two minutes. (Include units.) Average rate of change: d) (4 points) Find the average rate of change of the temperature of the soup during the time interval [1,2]. (Include units.) Average rate of change: e) (4 points) Let An denote the average rate of change of the temperature during the time interval [2, 2+ h] if h > 0, and the average rate of change of the temperature during the time interval [2 + h, 2] if h < 0. Find an expression for A₁. SIMPLIFY your result. f) (3 points) Evaluate the limit lim A₁. (Include units). h→0 An lim Ah h→0 = = g) (3 points) Explain what the value found in the previous part means in the context of the problem. (Don't forget units.) h) (2 points) The soup bowl might crack if its temperature ever changes at a rate faster than 50°/min. Is the bowl in danger of cracking at time t = 2? Explain.
Expert Answer:
Answer rating: 100% (QA)
a The temperature of the soup when Saul took it out of the refrigerator can be found by substituting t 0 into the equation rt 2t 37 r0 20 37 r0 37 The... View the full answer
Related Book For
Fundamentals Of Electric Circuits
ISBN: 9780073301150
3rd Edition
Authors: Matthew Sadiku, Charles Alexander
Posted Date:
Students also viewed these accounting questions
-
Solve the following differential equations using Laplace transform A d2y (t)/dt2 + 2dy(t)dt +y (t) =e-2t, y (0) = y t (0) = 0 A d2y (t)/dt2 + 4dy (t)/dt) +4y (t) =u(t), y (0) 0;y (0) = 1
-
Solve the following differential equations by integrating both side of the equation w.r.t the given unknown: 2.1 dy %D x - 1 dx
-
Solve the following differential equations by integrating both side of the equation w.r.t the given unknown: dy - x- 2; y(0) = 1 2.2 %3D dx
-
What conditions must be met for revenue to be recorded? Can pledges meet those conditions?
-
A franchisor has granted a license to a franchisee to offer hamburgers and other deli-style foods under its mark. What types of quality control provisions should a license agreement include?
-
There is a 0.9968 probability that a randomly selected 50-year-old female will live through the year. A life insurance company charges $226 for insuring that the female will live through the year. If...
-
Why is the executive summary an important part of the report?
-
1. Do you think a country the size of Iceland a Lilliputian is more or less sensitive to the potential impacts of global capital movements? 2. Many countries have used interest rate increases to...
-
Jeremy is thinking of starting up a small business selling NASCAR memorabilia. He asks his friend, Carmen, if she'd like to join him in setting up a partnership to start the business. What is one...
-
The owner of Neros company has hired you to analyze her company's performance and financial position, as well as the positions of Iits competitors, Centar and Xermix. However, the data Neros abtained...
-
A voltage source inverter is supplied from a 620-V de source and feeds a balance load. At a certain instant, the inverter is in state 3and the output currents in phase A and B are -72 and 67A,...
-
Describe the materials in the environment, Real Objects versus Open-Ended Materials
-
Kevin, CPA is performing on audit on RST Company. Kevin decides to sample the additions to the equipment account. Kevin determines that the population size is 100 transactions and 25 of these...
-
What will help managers further distinguish product costs? Explain.
-
1. What is a "Bull Market?" 2. What got so many people interested in buying and selling stocks? 3. Why did the stock market rise so rapidly between March 1928 and September 1929? 4. How could average...
-
what literary methods were used within the oracle. What is the main message of the oracle?
-
As a financial accountant for a public widget manufacturing company, you are given a data file and asked to calculate and record month-end adjusting journal entries. You must calculate the warranty...
-
A company produces earbuds. The revenue from the sale of x units of these earbuds is R = 8x. The cost to produce x units of earbuds is C = 3x + 1500. In what interval will the company at least break...
-
Given the transmission parameters Obtain the other five two-port parameters. 3 20 1-1 7 [T] =
-
Two capacitors (20 F and 30 F) are connected to a 100-V source. Find the energy stored in each capacitor if they are connected in: (a) Parallel (b) Series
-
For the circuit in Fig. 8.101, find v(t) for t > 0 . Assume that v(0+) = 4 V and i(0+) = 2A. 2 1 0.5 F
-
Which of the following approaches is used to study management? Art Process Science Profession
-
Management is Ongoing process Social process Integrated process All the above
-
Which is the correct order for the process of management? Planning, organizing, staffing, directing, and controlling Planning, organizing, directing, staffing, and controlling Planning,...
Study smarter with the SolutionInn App