Question

The temperature at time t, y(t) in units of 100◦F of a room in the winter...

The temperature at time t, y(t) in units of 100◦F of a room in the winter satisfies the differential equation

dy/dt ={ −y + 1, if heating unit is on

   −y, if heating unit is off }

Suppose the initial temperature is y(0) = 0 at 9a.m.

(Let the time t = 0 corresponds to 9a.m., t = 1 corresponds to 10a.m. and so on.) The heating unit is on from 9 to 10a.m., off from 10 to 11a.m., on again from 11a.m. to noon and so on. What is the room temperature at noon? (Hint: the answer is 71.8◦F.)

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
1. Solve the given initial value problem. dy/dt = (t^3 + t)/(y^2); y(0) = 2 ....
1. Solve the given initial value problem. dy/dt = (t^3 + t)/(y^2); y(0) = 2 . 2. We know from Newton’s Law of Cooling that the rate at which a cold soda warms up is proportional to the difference between the ambient temperature of the room and the temperature of the drink. The differential equation corresponding to this situation is given by y' = k(M − y) where k is a positive constant. The solution to this equation is given...
Consider the linear equation y' + by = f(t). Suppose that b > 0 is constant,...
Consider the linear equation y' + by = f(t). Suppose that b > 0 is constant, and |f| is bounded by some M > 0 (Namely, |f(t)| < M for every real number t). Show that if y(t) is a solution of the equation then there is a constant C such that |y(t)| ≤ C + (M/ b) for all t ≥ 0. (Hint: Use the fact µ(t) = ebt is an integrating factor, and that | ∫f(t) · µ(t)dt...
Logistic Equation The logistic differential equation y′=y(1−y) appears often in problems such as population modeling. (a)...
Logistic Equation The logistic differential equation y′=y(1−y) appears often in problems such as population modeling. (a) Graph the slope field of the differential equation between y= 0 and y= 1. Does the slope depend on t? (b) Suppose f is a solution to the initial value problem with f(0) = 1/2. Using the slope field, what can we say about fast→∞? What can we say about fast→−∞? (c) Verify that f(t) =11 +e−tis a solution to the initial value problem...
A cup of tea is cooling in a room that has a constant temperature of 70...
A cup of tea is cooling in a room that has a constant temperature of 70 degrees Fahrenheit (F). If the initial temperature of the tea, at time t=0 minutes, is 200 F and the temperature of the tea changes at the rate: R(t) -6.89e^(-.053t) degrees Fahrenheit per minute, what is the temperature, to the nearest degree, of the tea after 4 minutes? 2. On the closed interval [2, 4], which of the following could be the graph of a...
Write a matlab script file to solve the differential equation dy/dt = 1 − y^3 with...
Write a matlab script file to solve the differential equation dy/dt = 1 − y^3 with initial condition y(0)=0, from t=0 to t=10. matlab question
a) A fluid flows from the top of a cylinder to the bottom through a hole....
a) A fluid flows from the top of a cylinder to the bottom through a hole. Given Bernoulli's equation and that the fluid's level is at height y(t) in a cylinder, derive the form dy/dt = −f(y). For Bernoulli’s equation, the kinetic energy term of the fluid’s top surface can be considered zero. b) The previous differential equation may be integrated as integral from 0 to ∆t dt = integral from 0 to h0 of (1/f(y)) dy. Use this to...
Consider the differential equation L[y] = y′′ + p(t)y′ + q(t)y = f(t) + g(t), and...
Consider the differential equation L[y] = y′′ + p(t)y′ + q(t)y = f(t) + g(t), and suppose L[yf] = f(t) and L[yg] = g(t). Explain why yp = yf + yg is a solution to L[y] = f + g. Suppose y and y ̃ are both solutions to L[y] = f + g, and suppose {y1, y2} is a fundamental set of solutions to the homogeneous equation L[y] = 0. Explain why y = C1y1 + C2y2 + yf...
1. Use Euler’s method with step size ∆x = 1 to approximate y(4), where y(x) is...
1. Use Euler’s method with step size ∆x = 1 to approximate y(4), where y(x) is the solution of the initial value problem: y' = x2+ xy y(0) = 1 2. The coroner arrives at a murder scene at 9:00 pm. He immediately determines that the temperature of the body is 83◦F. He waits one hour and takes the temperature of the body again; it is 81◦F. The room temperature is 68◦F. When was the murder committed? Assume the man...
Let be the problem with initial value f(t,y) = yt3   , y(0)=1 Write the general formula...
Let be the problem with initial value f(t,y) = yt3   , y(0)=1 Write the general formula for Picard iterations. Then start with the function y0 (t) = y (0) = 1 and calculate the iterations y1 (t) and y2 (t).
1. A roast turkey is taken from an oven when its temperature has reached 185°F and...
1. A roast turkey is taken from an oven when its temperature has reached 185°F and is placed on a table in a room where the temperature is 75°F. (Round your answer to the nearest whole number.) (a) If the temperature of the turkey is 150°F after half an hour, what is the temperature after 60 minutes? T(60) =  °F (b) When will the turkey have cooled to 95°? t =  min 2. Let c be a positive number. A differential equation...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT