Answer:
Hence the width, length is 20 cm and height is 10 cm
Step-by-step explanation:
Since the box has a square base, let length = width = x. Also, let the height = y, therefore:
The volume of box = width * length * height
4000 = x * x * y
4000 = x²y
y=4000/x²
The surface area (SA) = area of the base + sum of the area of each side
SA = x² + xy + xy + xy + xy
SA = x² + 4xy
substitute y = 4000/x²
SA = x² + 4x(4000/x²)
SA = x² + 16000/x
Taking the derivative:
SA' = 2x - 16000/x²
making SA' = 0:
0 = 2x - 16000/x²
2x = 16000/x²
2x³ = 16000
x³ = 8000
x = 20 cm
y = 4000 / x² = 4000 / 20² = 10 cm
Hence the width, length is 20 cm and height is 10 cm
The volume is 1012 cm³.
The volume of a right prism is found by multiplying the area of the base and the height. First we need to convert the height to centimeters.
1 dm = 10 cm
2.3 dm = 2.3(10) = 23 cm
Now we have 44(23) = 1012 cm³
2 2/3 pages=8/3 pages
1 hour=60 minutes
Let x represent the total pages in an hour
8/3 pages in 5 minutes
x pages in 60 minutes
Use cross multiply
x(5)=8/3(60)
5x=160
Divided 5 to each side
5x/5=160/5
x=32 pages per hour. As a result, there will be 32 pages per hour. Hope it help!
To check if an improper fraction like like 24/7 can still be simplified, you have to find similar factors that can divide both the numerator (24) and the denominator (7). However in this case, there are no longer any common factors that can divide both of them. However, improper fractions can be represented in a mixed fraction form.
A mixed fraction is made up of a whole number and a fraction. To change an improper fraction to a mixed fraction, divide the numerator by the denominator. The quotient should be a whole number and a remainder. The whole number in the quotient would be the whole number in the mixed fraction, and the remainder would be the numerator.
In the case of 24/7, dividing it would yield us 3 remainder 3. Therefore, the mixed fraction would be:
3 3/7
Answer:
(1)
(2)
Step-by-step explanation:
Solving (1):
Considering
We have:
This gives:
Solve for a
So:
To solve for b, we make use of Pythagoras theorem
This gives
Collect like terms
Take LCM and solve
Take square roots
Solving (2):
Considering
We have:
This gives:
Solve for a
So:
To solve for b, we make use of Pythagoras theorem
This gives
Collect like terms
Take square roots
