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?
-
The coefficient of static friction s is the same between block B and the horizontal surface and between the rope and support C. Knowing that WA = WB, determine the smallest value of s for which...
-
What are the benefits and drawbacks of oral and written communication?
-
A machine is bought for 18,000, plus 3,000 installation costs. It is to be depreciated on a diminishing balance basis using a rate of 60% p.a. What is the depreciation to be charged in the second...
-
The chief engineer at a university that is constructing a large number of new student dormitories decides to install a counter flow concentric tube heat exchanger on each of the dormitory shower...
-
5-26 Find the most general antiderivative of the function. (Check your answer by differentiation.) 5. f(x)=4x+7 7. f(x) = 2x-3x + 5x == 6. f(x) = x-3x+2 8. f(x)=6x- 8x4 - 9x2
-
Perform the test in Problem 8.44 using both the raw and ln scale, and report a p-value. Are there any advantages to using the raw or the ln scale? Renal Disease Ten patients with advanced diabetic...
-
3. Company A announces it will pay all shareholders of Company B $44 per share they own. On that date, the value of Company B shares on the public stock exchanges was $32. This action by Company A is...
-
In the figure three identical conducting spheres form an equilateral triangle of side length d = 27.5 cm. The sphere radii are much smaller than d and the sphere charges are q = -3.68 nC, qB = -3.13...
-
A US stock paying a $20 dividend in two months is trading at $2,000. Assume the US interest rate is 5% with continuous annual compounding. (a). If the dividend is instead paid in three months, the...
-
Oriole Trucking purchased a tractor trailer for $141000. Oriole uses the units-of-activity method for depreciating its trucks and expects to drive the truck 1000000 miles over its 10-year useful...
-
Tomas began carrying on a home-based business as a sole proprietor on January 1, 2023. In 2023, he received $40,000 cash for services rendered and paid $33,000 in business expenses. On December 31,...
-
What are the principles behind advanced seismic design strategies in civil engineering, and how do they incorporate innovative technologies such as base isolation and damping systems to enhance the...
-
Problem 7-2 (IFRS) Awesome Bank granted a loan to a borrower on January 1, 2021. The interest rate on the loan is 10% payable annually starting December 31, 2021. The loan matures in five years on...
-
A company produces earbuds. The revenue from the sale of x units of these earbuds is R = 8x. The cost to produce x units of earbuds is C = 3x + 1500. In what interval will the company at least break...
-
Given the transmission parameters Obtain the other five two-port parameters. 3 20 1-1 7 [T] =
-
Two capacitors (20 F and 30 F) are connected to a 100-V source. Find the energy stored in each capacitor if they are connected in: (a) Parallel (b) Series
-
For the circuit in Fig. 8.101, find v(t) for t > 0 . Assume that v(0+) = 4 V and i(0+) = 2A. 2 1 0.5 F
-
Does Russias BOP balance? Use the following balance of payments data for Russia (Russian Federation) from the IMF to answer this problem. Assumptions (million US$) 2000 2001 2002 2003 2004 2005 2006...
-
Is the Euro Area experiencing a net capital inflow? Use the following balance of payments data for the Euro Area from the IMF to answer this problem. Assumptions (billion US$) 2000 2001 2002 2003...
-
What is the Euro Areas total for Groups A and B? Use the following balance of payments data for the Euro Area from the IMF to answer this problem. Assumptions (billion US$) 2000 2001 2002 2003 2004...
Study smarter with the SolutionInn App