Answer:
d = 1.46 m
Step-by-step explanation:
We'll begin by obtaining the relationship between the force (F) and the distance (d). This can be obtained as follow:
From the question given above,
F is inversely proportional to square of d. This can be written as:
F ∝ 1/d²
F = K/d²
Cross multiply
K = Fd²
But:
Force (F) = 0.006 N
Distance (d) = 4 m
Constant (K) =?
K = Fd²
K = 0.006 × 4²
K = 0.006 × 16
K = 0.096 Nm²
Therefore, the relationship between the force (F) and the distance (d) is:
F = K/d²
F = 0.096 / d²
Finally, we shall determine the distance when the force is 0.045 N. This can be obtained as follow:
Force (F) = 0.045 N
Constant (K) = 0.096 Nm²
Distance (d) =?
F = K/d²
0.045 = 0.096 / d²
Cross multiply
0.045 × d² = 0.096
Divide both side by 0.045
d² = 0.096 / 0.045
Take the square root of both side.
d = √(0.096 / 0.045)
d = 1.46 m.
I see no reason for the aluminum foil to have lost any volume, matter, mass , etc.
If all pieces are retrieved for measuring. - &
If a clean cut was achieved- and the blade used to cut did not impede upon the proceedings by also being variable, then I reiterate that there should be no difference in volume, matter, mass, etc.
<span>let 2x be the length of rectangw where x is value of x of point on parabola width is represented as y is the length.
Area = 2x*y = 2x (5-x^2) = 10x -2x^3
maximize Area by finding x value where derivative is zero
dA/dx = 10 -6x^2 = 0
--> x = sqrt(5/3)
optimal dimensions: length = 2sqrt(5/3) width = 10/3</span>
