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
1. one-Half
2. Apogee
3. Any object that revolves around another object
4. Venus's gravitation pull
<h3>
Answer:</h3>
1.5 m/s²
<h3>
Explanation:</h3>
We are given;
Force as 60 N
Mass of the Cart as 40 kg
We are required to calculate the acceleration of the cart.
- From the newton's second law of motion, the rate of change in momentum is directly proportional to the resultant force.
- That is, F = ma , where m is the mass and a is the acceleration
Rearranging the formula we can calculate acceleration, a
a = F ÷ m
= 60 N ÷ 40 kg
= 1.5 m/s²
Therefore, the acceleration of the cart is 1.5 m/s²
Answer:
Explained
Explanation:
Compared to Jupiter, Saturn's atmosphere is more calm with fewer disturbances or storms.
The Atmosphere in Jupiter is highly violent and thinner as compared with Saturn.
The layers of atmosphere on Saturn is thicker because of lower gravity of Saturn and hence they are calmer.
Good morning.
We have:

Where
j is the unitary vector in the direction of the
y-axis.
We have that

We add the vector
-a to both sides:

Therefore, the magnitude of
b is
47 units.