Answer:
third one
Step-by-step explanation:
The perpendicular bisector goes through the midpoint.
What is the midpoint of the 2 points?
We simply add up the x points and divide by 2. Then we add up the y points and divide by 2.
So,
Midpoint is:
Also, the perpendicular bisector's slope is the negative reciprocal of the line's slope.
The slope of the line is change in y points divided by change in x points.
Slope =
The slope (m) of the perpendicular line (negative reciprocal) is basically:
Equation of line is:
m is the slope (what we got "2")
x1 and y1 are the respective point where it passes through (which is the midpoint, which is (-3,2)
So, equation of perpendicular bisector is:
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
5+8=13
52/13=4
4*5=20
4*8=32
20:32