Answer:
- 4x² + 6x - 3 remainder -12
Step-by-step explanation:
<u>Given:</u>
- (x) = 8x³ + 16x² − 15
- g(x) = 2x + 1
<u>To find:</u>
<u>Use long division:</u>
- (8x³ + 16x² − 15) / (2x + 1)
2x + 1 | (8x³ + 16x² − 15
<u>| 8x³ + 4x²</u>
12x² + 0x - 15
<u>12x² + 6x</u>
-6x - 15
<u>-6x - 3</u>
-12
4x² + 6x - 3 remainder -12
It would be: 360- (101+133+76)
360-310 = 50 degree
Answer:
8.5 units
Step-by-step explanation:
step 1
<em>Find the slope of the perpendicular line to the given line</em>
---> given line
The slope is ![m=1](https://tex.z-dn.net/?f=m%3D1)
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
![m_1*m_2=-1](https://tex.z-dn.net/?f=m_1%2Am_2%3D-1)
we have
![m_1=1](https://tex.z-dn.net/?f=m_1%3D1)
substitute
![(1)*m_2=-1](https://tex.z-dn.net/?f=%281%29%2Am_2%3D-1)
so
![m_2=-1](https://tex.z-dn.net/?f=m_2%3D-1)
step 2
Find the equation of the perpendicular line to the given line
The equation in point slope form is
![y-y1=m(x-x1)](https://tex.z-dn.net/?f=y-y1%3Dm%28x-x1%29)
we have
![m=-1](https://tex.z-dn.net/?f=m%3D-1)
![(x_1,y_1)=(-9,-3)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%3D%28-9%2C-3%29)
substitute
--> equation in point slope form
![y+3=-x-9](https://tex.z-dn.net/?f=y%2B3%3D-x-9)
![y=-x-9-3](https://tex.z-dn.net/?f=y%3D-x-9-3)
---> equation in slope intercept form
step 3
Find the intersection point between the given line and the perpendicular line to the given line
we have the system of equations
![y=-x-12](https://tex.z-dn.net/?f=y%3D-x-12)
Solve the system by graphing
The intersection point is (-3,-9)
see the attached figure
step 4
we know that
The distance between the point A and the point (-3,-9) is the same that the distance between point A and the line y=x-6
the formula to calculate the distance between two points is equal to
substitute the values
simplify
y=-2x
We know this because the slope is -2 (slope is found using rise/run, in this case the rise is 2 and the run is -1, so 2/-1=-2), and the y-intercept is at 0 (the y-intercept is the point at which a line crosses the y-axis).
:)