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-

the answer is b.

step-by-step explanation:

by the trigonometric ratio tangent, tangent equals opposite divided by adjacent.

therefore, tan(50) equals ac/3

multiply each side by 3 to get: ac=3tan(50)

the answer is b.

x/3-10=8

x/3=18

x=48

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.