Answer: k=36 and x2=24
Step-by-step explanation:
Answer:
y= -3x +40
Step-by-step explanation:
Properties of perpendicular bisector:
• perpendicular to the given line
• cuts through the center of the given line
The equation of a line can be written in the form of y=mx +c, where m is the gradient and c is the y -intercept.
Let's find the gradient of the given line first.
![\boxed{gradient = \frac{y1 - y2}{x1 - x2} }](https://tex.z-dn.net/?f=%5Cboxed%7Bgradient%20%3D%20%20%5Cfrac%7By1%20-%20y2%7D%7Bx1%20-%20x2%7D%20%7D)
Gradient of given line
![= \frac{6 - 2}{18 - 6}](https://tex.z-dn.net/?f=%20%3D%20%20%5Cfrac%7B6%20-%202%7D%7B18%20-%206%7D%20)
![= \frac{4}{12}](https://tex.z-dn.net/?f=%20%3D%20%20%5Cfrac%7B4%7D%7B12%7D%20)
![= \frac{1}{3}](https://tex.z-dn.net/?f=%20%3D%20%20%5Cfrac%7B1%7D%7B3%7D%20)
The product of the gradients of perpendicular lines is -1.
m(⅓)= -1
m= -1(3)
m= -3
Substitute m= -3 into the equation:
y= -3x +c
To find the value of c, substitute a pair of coordinates in which the perpendicular bisector passes through into the equation. Since perpendicular bisectors passes through the center of the segment, we can find the point in which the perpendicular bisector passes through using the mid- point formula.
![\boxed{midpoint = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )}](https://tex.z-dn.net/?f=%5Cboxed%7Bmidpoint%20%3D%20%28%20%5Cfrac%7Bx1%20%2B%20x2%7D%7B2%7D%20%2C%20%5Cfrac%7By1%20%2B%20y2%7D%7B2%7D%20%29%7D)
Midpoint
![= ( \frac{6 + 18}{2} , \frac{6 + 2}{2} )](https://tex.z-dn.net/?f=%20%3D%20%28%20%5Cfrac%7B6%20%2B%2018%7D%7B2%7D%20%2C%20%5Cfrac%7B6%20%2B%202%7D%7B2%7D%20%29)
![= ( \frac{24}{2} , \frac{8}{2} )](https://tex.z-dn.net/?f=%20%3D%20%28%20%5Cfrac%7B24%7D%7B2%7D%20%2C%20%5Cfrac%7B8%7D%7B2%7D%20%29)
![= (12,4)](https://tex.z-dn.net/?f=%20%3D%20%2812%2C4%29)
y= -3x +c
when x= 12, y= 4,
4= -3(12) +c
4= -36 +c
c= 4 +36
c= 40
Thus, the equation of the perpendicular bisector is y= -3x +40.
Answer:
This can be solved using a calculator
239323
Answer:
The cost of printing posters 2 to 100 is $9.
Step-by-step explanation:
The marginal cost of printing a poster when x posters have been printed is
We need to find the cost function.
Seprate the variables.
Integrate both sides.
where, C is an arbitrary constant.
We need to find the value of c(100)-c(1).
Substitute x=100 in the above function.
Substitute x=1 in the above function.
Therefore, the cost of printing posters 2 to 100 is $9.