Prime numbers are numbers that have only one factor pair; 1 and themselves.
Let's start from 21.
21 = 1 x 21, 3 x 7.
This has two factor pairs, this is not prime.
Let's try 22.
22 = 1 x 22, 2 x 11.
This also has two factor pairs, this is not prime.
Let's try 23.
1 x 23.
This is a prime number, as it only has one factor pair; 1 and itself.
23 is your prime number.
I hope this helps!
Answer:
x = 2.354 in
Maximum volume = 228.162 in³
Step-by-step explanation:
Size of the metal sheet = (18 in × 12 in)
Let the height of the box = x in
Then length of the box = (18 - 2x) in
Width of the box = (12 - 2x) in
Now volume of the rectangular box (V) = Length × Width × height
= (18 - 2x) × (12 - 2x) × x
= x[18(12 - 2x) - 2x(12 - 2x)]
= x[216 - 36x - 24x + 4x²]
= x[216 - 60x + 4x²]
= (4x³ - 60x² + 216x) in³
For maximum volume, we will find the derivative of the volume and equate it to zero.
V' = 12x² - 120x + 216
V' = 0
12x² - 120x + 216 = 0
x² - 10x + 18 = 0
By quadratic formula,
x =
x = 5 ± √7
x = 7.646, 2.354
But for 7.646, volume of the box will be negative.
Therefore, (x = 2.354 in) will be value of x for maximum volume of the box.
Maximum volume of the box = 4(2.354)³ - 60(2.354)² + 216(2.354)
= 228.162 in³
Answer:
8.5
Step-by-step explanation:
25, 28, 32, 35, 40, 45, 48, 53, 56, 60
40+45 = 85 divided by 10 = 8.5
Answer:
-3
Step-by-step explanation: