x"+ 9x = -10 8 (1-2) Initial Conditions: x (0) = 1, x'(0) = 5 8 (t) = the Diract Delta Function Find x(2.5) to at least the nearest thousandth (3 decimal places).

Solve the ODE xdx + ydy = xdy - ydx a. ln [(y+x) / x] = C b. ln [(x-y) / x] = C c. arctan (y/x) - 0.5 ln [(y^2 + x^2) / x] = C d. arctan (y/x) - 0.5 ln [(y^2 + x^2) / x^2] - lnx = C e. none

Determine y' of 4 y = (2x +1)

Daily crude oil production by one particular oil company for 2014-2019 could be approximated by P(t)=0.018t^2−0.7t+5.82 million barrels, where t is time in years since the start of 2000. At what rate was oil production changing when t=16? (Round to four decimal places as needed.)

Suppose that the fish population P(t)in a lake is attacked by a disease at time t=0, with the result that the fish cease to reproduce (so that the birth rate is β=0) and the death rate δ(deaths per week per fish) is thereafter proportional to P^(-1/2). If there were initially 100,000 fish in the lake and 1984were left after 20weeks, how long did it take for the lake to contain 0 fish?What if the number of fish left after 20 weeks is 4891,how many fish do you have after 24 weeks?

The population of a​ city, in​ millions, since 1990 has grown at a rate of P′(t)=0.21e^ 0.027t million people per​ year, where t is the number of years after 1990. If there were 1.5 million people in​ 2000, estimate​ (to two decimal​places) the population in 2004.

Find f. (х + 1) f'(x) f(1) = 3 f(x) = %3D