Questions from General Calculus

Q: Find the orthogonal trajectories of the family of curves. y

Find the orthogonal trajectories of the family of curves. y = e kx

Q: A planning engineer for a new alum plant must present some estimates

A planning engineer for a new alum plant must present some estimates to his company regarding the capacity of a silo designed to contain bauxite ore until it is processed into alum. The ore resembles...

Q: Cobalt-60 has a half-life of 5.24

Cobalt-60 has a half-life of 5.24 years. (a). Find the mass that remains from a 100-mg sample after 20 years. (b). How long would it take for the mass to decay to 1 mg?

Q: Let C (t) be the concentration of a drug in

Let C (t) be the concentration of a drug in the bloodstream. As the body eliminates the drug, C (t) decreases at a rate that is proportional to the amount of the drug that is present at the time. Thus...

Q: A patient is prescribed a drug and is told to take one

A patient is prescribed a drug and is told to take one 100-mg pill every eight hours. After eight hours, about 5% of the drug remains in the body. (a). What quantity of the drug remains in the body af...

Q: A cup of hot chocolate has temperature 800Cin a room kept at

A cup of hot chocolate has temperature 800Cin a room kept at 200C. After half an hour the hot-chocolate cools to 600C. (a). What is the temperature of the chocolate after another half hour? (b). When...

Q: (a). Write the solution of the initial-value problem

(a). Write the solution of the initial-value problem and use it to find the population when t = 20. (b). When does the population reach 1200?

Q: (a). Write a differential equation that expresses the law of

(a). Write a differential equation that expresses the law of natural growth. What does it say in terms of relative growth rate? (b). Under what circumstances is this an appropriate model for populatio...

Q: The von Bertalanffy growth model is used to predict the length L

The von Bertalanffy growth model is used to predict the length L (t) of a fish over a period of time. If L∞ is the largest length for a species, then the hypothesis is that the rate of growth in lengt...

Q: The Brentano-Stevens Law in psychology models the way that a

The Brentano-Stevens Law in psychology models the way that a subject reacts to a stimulus. It states that if R represents the reaction to an amount of stimulus, then the relative rates of increase are...