Let c be a positive number. a differential equation of the form

dy
dt= ky1 + c
where k is a positive constant, is called a doomsday equation because the exponent in the expression ky1 + c is larger than the exponent 1 for natural growth.

(a) determine the solution that satisfies the initial condition

y(0) = y0.

ans: y=(-ckt+y0^-c)^(-1/c)

(b) show that there is a finite time
t = t
(doomsday) such that
lim t %u2192 t%u2212y(t) = infinity.
ans: y(t) --> infinity as 1-cy0^ckt--> 0 as t--> 1/cy0^ck
t=1/cy0^ck, them lim y(t)=infinity as t--> t-

Aregular pentagon with a perimeter of 21 inches is dilated by a scale factor of 5/3 to create a new pentagon. what is the perimeter of the new pentagon?

The school track has eight lanes. each lane is 1.25 meters wide. the arc at each end of the track is 180. the distance of the home straight and the radii for the arcs in the 1st 4 lanes are given. s=85m r1=36.5m r2=37.75m r3=39m r4=40.25m part one: find the radii of lanes 5 through 8 of the track. show your work. part two: if max ran around lane one, how far did he run? show your work and explain your solution. part three: max wants to run a total of three laps around the track, choose two additional lanes (2-8) for him to run and find the distance around those two lanes. show your work and round to the hundredths. part 4: based on your lane choices in part three, what was the total distance max ran in the three laps around the track?

One number is 4 less than 3 times a second number. if 3 more than two times the first number is decreased by 2 times the second number, the result is 11. use the substitution method. what is the first number?