Questions from Calculus

Q: Solve the initial-value problem. ty’ + y =

Solve the initial-value problem. ty’ + y = sin t, y(π/2) = 0, t > 0

Q: A certain piece of news is being broadcast to a potential audience

A certain piece of news is being broadcast to a potential audience of 200,000 people. Let f (t) be the number of people who have heard the news after t hours. Suppose that y = f (t) satisfies y' = ....

Q: Consider the initial-value problem y’ = - y/(

Consider the initial-value problem y’ = - y/(1 + t) + 10, y(0) = 50. (a) Is the solution increasing or decreasing when t = 0? (b) Find the solution and plot it for 0 ≤ t ≤ 4.

Q: Find an integrating factor for each equation. Take t > 0

Find an integrating factor for each equation. Take t > 0. y' - 2y = t

Q: Find an integrating factor for each equation. Take t > 0

Find an integrating factor for each equation. Take t > 0. y’ + ty = 6t

Q: Find an integrating factor for each equation. Take t > 0

Find an integrating factor for each equation. Take t > 0. t3y’ + y = 0

Q: Twenty years ahead of her retirement, Kelly opened a savings account

Twenty years ahead of her retirement, Kelly opened a savings account that earns 5% interest rate compounded continuously, and she contributed to this account at the annual rate of $1200 per year for 2...

Q: Answer the question in Exercise 5 if John contributed to his savings

Answer the question in Exercise 5 if John contributed to his savings account at the annual rate of $3000 per year for 10 years. Exercise 5: Twenty years ahead of her retirement, Kelly opened a saving...

Q: A person took out a loan of $100,000 from

A person took out a loan of $100,000 from a bank that charges 7.5% interest compounded continuously. What should be the annual rate of payments if the loan is to be paid in full in exactly 10 years? (...

Q: The National Automobile Dealers Association reported that the average retail selling price

The National Automobile Dealers Association reported that the average retail selling price of a new vehicle was $30,303 in 2012. A person purchased a new car at the average price and financed the enti...