Find an equation of the plane that contains the points p(5,−1,1),q(9,1,5),and r(8,−6,0)p(5,−1,1),q(9,1,5),and r(8,−6,0).
topjm [15]
Given plane passes through:
p(5,-1,1), q(9,1,5), r(8,-6,0)
We need to find a plane that is parallel to the plane through all three points, we form the vectors of any two sides of the triangle pqr:
pq=p-q=<5-9,-1-1,1-5>=<-4,-2,-4>
pr=p-r=<5-8,-1-6,1-0>=<-3,5,1>
The vector product pq x pr gives a vector perpendicular to both pq and pr. This vector is the normal vector of a plane passing through all three points
pq x pr
=
i j k
-4 -2 -4
-3 5 1
=<-2+20,12+4,-20-6>
=<18,16,-26>
Since the length of the normal vector does not change the direction, we simplify the normal vector as
N = <9,8,-13>
The required plane must pass through all three points.
We know that the normal vector is perpendicular to the plane through the three points, so we just need to make sure the plane passes through one of the three points, say q(9,1,5).
The equation of the required plane is therefore
Π : 9(x-9)+8(y-1)-13(z-5)=0
expand and simplify, we get the equation
Π : 9x+8y-13z=24
Check to see that the plane passes through all three points:
at p: 9(5)+8(-1)-13(1)=45-8-13=24
at q: 9(9)+8(1)-13(5)=81+9-65=24
at r: 9(8)+8(-6)-13(0)=72-48-0=24
So plane passes through all three points, as required.
Answer:
a
Step-by-step explanation:
follows geometric sequence. starting value is 1/3 and is multiplied by 1/3 every time
The equation of the line in slope-intercept form is y = (1/2)x + 3 and the slope is 1/2.
<h3>What is a straight line?</h3>
A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
As we can see in the graph the line goes from (-6, 0) and (0, 3)
Finding the slope:
m = 3/6 = 1/2
y = mx + c
y = (1/2)x + c
c is the y-intercept
c = 3
The equation:
y = (1/2)x + 3
Thus, the equation of the line in slope-intercept form is y = (1/2)x + 3 and the slope is 1/2.
Learn more about the straight line here:
brainly.com/question/3493733
#SPJ1
Here's a good rhyming rule to keep in mind.
Zero to four, you get no more.
Five to nine, move up one time.
With this rule you can see that there is a 5 at the end, therefor you should round up. Your number is 720.
Answer:
D
Step-by-step explanation:
In the graph, there are only two values for a graph. In this case, those two values are crackers and calories.
