Answer:
1) Both 15.
2) 25 and -25.
Step-by-step explanation:
1) Let the 2 numbers be x and 30 - x.
The product = x(30 - x)
f(x) = x(30 - x)
f(x) = 30x - x^2
Finding the derivative:
f'(x) = 30 - 2x
Finding the maximum:
30 - 2x = 0
x = 15.
This gives a maximum f(x) because f"(x) = -2.
So the numbers are 15 and 30 - 15 = 15.
2). If one number is x the other is y.
x - y = 50
y = x - 50
The product =
x(x - 50)
= x^2 - 50x
Finding the derivative:
2x - 50 = 0 for a minimum value.
2x = 50
x = 25.
So the numbers are 25 and 25-50 = -25.
The LCM of 20 and 300 is 300.
<h3>How to find the LCM?</h3>
The multiple of 20 will be:
20 = 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, 220, 240, 260, 280, 300
The multiple of 300 will be:
300 = 300, 600, 900
Therefore, the lowest common multiple of 20 and 300 is 300.
Learn more about LCM on:
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Answer:
81.11 in decimal
81 1/9 in fraction
Step-by-step explanation:
Let the number be x
1.9 time a number is equal to 1.9x
1.7 plus 1.9 times a number is equal to 1.7 + 1.9x
Now given that
1.7 plus 1.9 times a number equals the sum of the number and 74.7
mathematically we have relation equation as
1.7 + 1.9x = x + 74.7
subtracting 1.7 from both side
1.7 + 1.9x - 1.7 = x + 74.7 - 1.7
=> 1.9x = x + 73
subtracting x from both side
1.9x - x = x + 73 - x
0.9x = 73
dividing both side by 0.9
0.9x/0.9 = 73/0.9
x = 81.11 or 81 1/9
Thus, the number is
81.11 in decimal
81 1/9 in fraction
Answer:
3600 ml
Step-by-step explanation:
A dozen = 12
12 * 300 = 3600