<h3>Given</h3>
Two positive numbers x and y such that xy = 192
<h3>Find</h3>
The values that minimize x + 3y
<h3>Solution</h3>
y = 192/x . . . . . solve for y
f(x) = x + 3y
f(x) = x + 3(192/x) . . . . . the function we want to minimize
We can find the x that minimizes of f(x) by setting the derivative of f(x) to zero.
... f'(x) = 1 - 576/x² = 0
... 576 = x² . . . . . . . . . . . . multiply by x², add 576
... √576 = x = 24 . . . . . . . take the square root
... y = 192/24 = 8 . . . . . . . find the value of y using the above equation for y
The first number is 24.
The second number is 8.
Perimeter is the addition of all 4 sides and a square as all the same sides. so every side will be the same. so if you divide 216 by 4 you get 54. you can check this by adding 54+54+54+54=216 or 54x4=216
Let the two integers be x and x + 1, then
2(x + 1) + 9 = 3x
2x + 2 + 9 = 3x
3x - 2x = 11
x = 11
Therefore, the integers are 11 and 12.
Answer:
1,000,000
Step-by-step explanation:
10^3*10^3
Answer:
6 2/3
Step-by-step explanation:
2 2/5 * 2 7/9
Change each number to an improper fraction
2 2/5 = (5*2+2)/5 = 12/5
2 7/9 = (9*2+7) = 25/9
12/5 * 25/9
Rewriting
25/5 * 12/9
5/1 * 4/3
20/3
Now changing to a mixed number
3 goes into 20 6 times with 2 left over
6 2/3
