(a) Determine a differential equation for the velocity v(t) of a mass m sinking in water that imparts a resistance proportional to the square of the instantaneous velocity (with is given by Archimedes' principle, which states that the upward buoyant force has magnitude equal to the weight of the water displaced. Assume that the positive direction is
acceleration due to gravity.)
dv ku2
PV
dt
g-
m
m
(b) Solve the differential equation in part (a).
v(t) =
mg-PV
.2
k
mg -pykt
k
- +
m
X
(c) Determine the limiting, or terminal, velocity of the sinking mass.
lim v(t) =
mg - PV
k
t-
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its a straight line parallel to the time axis

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation:

you need to give us more information since we can't answer

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.