Width of the rectangle is 16 cm
Step-by-step explanation:
- Step 1: Let the width of the rectangle be x. Then length = 4x. Find width.
Area of the rectangle = length × width
⇒ 1024 = x × 4x
⇒ 4x² = 1024
⇒ x² = 1024/4 = 256
⇒ x = √256 = 16
Answer:
D,x < 36 and x > 0, negative number cannot be in sq.root
Answer:
4.5 km
Step-by-step explanation:
3km times 1 = 3 and then 3km times .5 = 1.5
3+1.5= 4.5
Answer:
Step-by-step explanation:
Let the length of one side of the square base be x
Let the height of the box by y
Volume of the box V = x²y
Since the box is opened at the top, the total surface area S = x² + 2xy + 2xy
S = x² + 4xy
Given
S = 7500sq in.
Substitute into the formula for calculating the total surface area
7500 = x² + 4xy
Make y the subject of the formula;
7500 - x² = 4xy
y = (7500-x²)/4x
Since V = x²y
V = x² (7500-x²)/4x
V = x(7500-x²)/4
V = 1/4(7500x-x³)
For us to maximize the volume, then dV/dx = 0
dV/dx = 1/4(7500-3x²)
1/4(7500-3x²) = 0
(7500-3x²) = 0
7500 = 3x²
x² = 7500/3
x² = 2500
x = √2500
x = 50in
Since y = (7500-x²)/4x
y = 7500-2500/4(50)
y = 5000/200
y = 25in
Hence the dimensions of the box that will maximize its volume is 50in by 50in by 25in.
The Volume of the box V = 50²*25
V = 2500*25
V= 62,500in³
Hence the maximum volume is 62,500in³
Answer:
A random variable is a variable whose values are unknown. Random variable are mostly used in regression analysis to determine the statistical relationship between two entities.
Step-by-step explanation:
There are two types of random variable;
1. The discrete random variable and
2. The continuous random variable.
