Answer:
<h3>36 and 12</h3>
Step-by-step explanation:
Let the two positive integers be x and y.
If their product is 432, then
xy = 432 ......... 1
Also if the sum of the first plus three times the second is a minimum, then;
p(x) = x + 3y
From 1;
y = 432/x ..... 3
Substitute 3 into 2;
p(x) = x+3y
p(x)= x + 3(432/x)
p(x) = x + 1296/x
Since the expression is at minimum when dp(x)/dx = 0
dp/dx = 1 + (-1296)/x²
dp/dx = 1 -1296/x²
0 = 1 -1296/x²
0 = (x²-1296)/x²
cross multiply
0 = x²-1296
x² = 1296
x = √1296
x = 36
Since xy = 432
36y = 432
y = 432/36
y = 12
Hence the two positive numbers are 36 and 12
The complement of an angle is 90 minus the angle, or
90 - x = complement angle
if x is 18 more than 3 times it's complement, then
x = 3(complement angle) + 18
We can substitute "90 - x" for the "complement angle" in the second equation:
x = 3(90 - x) + 18
distribute the 3 to the 90 and the x
x = 270 - 3x + 18
add 3x to both sides
4x = 270 - 18
4x = 252
x = 63
the measure of angle x is 63 degrees
Answer:
0.79
Step-by-step explanation:
Answer:
As number of gallons of gas minus 9 leaves 3 gallons, denote g as number of gallons: g - 9 >=3.
Then g>= 12
