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:
42 tps
Step-by-step explanation:
I think
If correct pls give me brainliest
Answer: 38 over 49 can be written as 38/49. When divided, you will get 0.77551020408. It takes lots of regrouping, but it ends eventually.
If you are reducing it as a fraction, it is not possible because there is no other number to reduce it, so it will be in it's simplest form already.
Remember: when calculating percent it will always be over 100. With the given numbers 14 is your part out of the total (25). It should be written as part/whole.
As previously said, the percent is always over 100. (x/100)
In this problem you are given the part (14) and the whole (25). So it would be 14/25. The percent in this problem would be x/100. Now to find percent with the given part/whole, you would multiply 14 with 100. Then simply divide by 25.
Answer:
A. 0
E. -3
F. 9
Step-by-step explanation:
You can't divide by 0; it is undefined. So if x cannot equal zero, then anything that turns the denominator to zero is an asymptote. Therefore, the roots of the cubic expression would be excluded, and we get our final answers.
