Math Answers

Determine the equation of the circle with radius 9

9 and center (-1,-8)

(−1,−8).

Find the general solution of the given differential equation.

(x + 1) dy/dx + (x + 2)y = 2xe^−x

You have 80 grams of a radioactive kind of tellurium. How much will be left after 8 months if its half-life is 2 months?

You have 80 grams of a radioactive kind of tellurium. How much will be left after 8 months if its half-life is 2 months?

Let P(t) be the population of a certain animal species. Assume the

P(t) satisfies the logistic growth equation,

dP

dt = 0.2P(t) (1 −

P(t)

200) , y(0) = 150

a) Is the above equation autonomous? if yes (explain your answer with

proper reasons), if no (justify you answer).

b) Solve the above initial value problem, and find the value of solution at

time t = 0.5 using separation of variables

Consider the autonomous DE xʹ = x(x − 1)(x+ 2). Determine the

critical points of the equation. Discuss a way of obtaining a phase portrait

of the equation.

in the new apartment, 2k new light bulbs are included in the lighting network. Each light bulb burns out within a year with probability p. Find the probability that less than half of the original light bulbs will have to be replaced with new ones within a year.

Separate the interval in which the function f defined on R by f(x)=2x3-15x2+36x+5 for all x∈R is increasing

4 independent shots are fired from the aircraft at the aircraft. The probability of hitting each shot is 0.3. Two hits are obviously enough to destroy (failure) an aircraft; with one hit, the aircraft is hit with a probability of 0.6. Find the probability that the aircraft will be hit.