It's true that (2, 12) is a solution of 3x-1/2 y = 0 .
It's also true that (1, 6), (3, 18), (5, 30), (9, 54), (150, 900),
and (12 million, 72 million) are also perfectly correct solutions.
Any pair of numbers where the 'y' number is six times as much as
the 'x' number is a solution to that equation.
There are an infinite number of them.
Answer:
0.573 m
Step-by-step explanation:
a. To find the depth, x, we first solve the differential equation to find the expression for I
dI/dx = (-1.21)I
dI = (-1.21)Idx
dI/I = -1.21dx
Integrating both sides, we have
∫dI/I = ∫-1.21dx
㏑I = -1.21x + C
I = exp(-1.21x + C)
I = exp(-1.21x)exp(C) Let exp(C) = A
I =Aexp(-1.21x)
when x = 0, I = L. Substituting these into the equation, we have
L = Aexp(-1.21 × 0)
L = Aexp(0)
L = A
So, I = Lexp(-1.21x)
we want to find x when I = L/2.
So, L/2 = Lexp(-1.21x)
1/2 = exp(-1.21x)
-1.21x= ㏑(1/2)
-1.21x= -㏑2
x = -㏑2/-1.21
x = 0.693/1.21
x = 0.573 m
So.. if you notice the picture below.. .the length is that much
thus

take the derivative of A, zero it out, and then check the critica points for any maxima by using the first-derivative test
In this question, you know that the machine packs

of a box every

of a minute. Since it is constant, you simply have to double the half a minute to a full minute and then also double the rate to get

boxes packed per minute. And

is equal to