Let us say that x is the cut that we will make on the
sides to make a box, therefore the new dimensions are:
l = 15 – 2x
w = 8 – 2x
It is 2x since we cut on two sides.
We know that volume is:
V = l w x
V = (15 – 2x) (8 – 2x) x
V = 120x – 30x^2 – 16x^2 + 4x^3
V = 120x – 46x^2 + 4x^3
Taking the 1st derivative:
dV/dx = 120 – 92x + 12x^2
Set dV/dx = 0 to get maxima:
120 – 92x + 12x^2 = 0
Divide by 12:
x^2 – (92/12)x + 10 = 0
(x – (92/24))^2 = -10 + (92/24)^2
x - 92/24 = ±2.17
x = 1.66, 6
We cannot have x = 6 because that will make our w
negative, so:
x = 1.66 inches
So the largest volume is:
V = 120x – 46x^2 + 4x^3
V = 120(1.66) – 46(1.66)^2 + 4(1.66)^3
V = 90.74 cubic inches
In order to calculate the amount of energy required, we must first check the latent heat of vaporization of water from literature. The latent heat of vaporization of any substance is the amount of energy required per unit mass to convert that substance from a solid to a liquid. For water this is 2,260 J/g. We now use the formula:
Energy = mass * latent heat
Q = 50 * 2,260
Q = 113,000 J
113,000 Joules of heat energy are required.
Answer:
accelerating
Explanation:
If we consider(v > u) Acceleration:
final velocity(v)= 14m/s
initial velocity(u)=10m/s
time taken(t)= 2 seconds
a= 
=2m/s²
If we consider (v<u) Deceleration:
final velocity(v)= 3m/s
initial velocity(u)=9m/s
time taken(t)=2 seconds
a= 
= -3m/s²
Answer:
Final velocity v=19.83 m/sec
Explanation:
We have given initial velocity u =5.13 m/sexc
Acceleration of automobile 
Time t =4.9 sec
We have to find the final velocity v
According to first law of motion v = u+at ,here v is the final velocity , a is acceleration and t is time
So 
So the final velocity is 19.83 m/sec
