Questions from General Calculus

Q: Find the solution of the differential equation that satisfies the given initial

Find the solution of the differential equation that satisfies the given initial condition.

Q: When a cold drink is taken from a refrigerator, its temperature

When a cold drink is taken from a refrigerator, its temperature is 50C. After 25 minutes in a 200C room its temperature has increased to 100C. (a). What is the temperature of the drink after 50 minute...

Q: A freshly brewed cup of coffee has temperature 950C in a 200C

A freshly brewed cup of coffee has temperature 950C in a 200C room. When its temperature is 700C, it is cooling at a rate of 10C per minute. When does this occur?

Q: The rate of change of atmospheric pressure P with respect to altitude

The rate of change of atmospheric pressure P with respect to altitude h is proportional to P, provided that the temperature is constant. At 150C the pressure is 101.3kPa at sea level and 87.14 kPa at...

Q: (a). If $1000 is borrowed at 8% interest

(a). If $1000 is borrowed at 8% interest, find the amounts due at the end of 3 years if the interest is compounded (i) annually, (ii) quarterly, (iii) monthly, (iv) weekly, (v) daily, (vi) hourly, and...

Q: (a). If $3000 is invested at 5% interest

(a). If $3000 is invested at 5% interest, find the value of the investment at the end of 5 years if the interest is compounded (i) annually, (ii) semiannually, (iii) monthly, (iv) weekly, (v) daily, a...

Q: Around 1910, the Indian mathematician Srinivasa Ramanujan discovered the formula

Around 1910, the Indian mathematician Srinivasa Ramanujan discovered the formula William Gosper used this series in 1985 to compute the first 17 million digits of π. (a). Verify that the...

Q: (a). How long will it take an investment to double

(a). How long will it take an investment to double in value if the interest rate is 6% compounded continuously? (b). What is the equivalent annual interest rate?

Q: Consider a population P = P (t) with constant relative

Consider a population P = P (t) with constant relative birth and death rates α and β, respectively, and a constant emigration rate m, where α, β, an...

Q: Let c be a positive number. A differential equation of the

Let c be a positive number. A differential equation of the form dy/dt = ky1+c where is a positive constant, is called a doomsday equation because the exponent in the expression is larger than the expo...