Yes, it is.and I have to keep typing because I need a character at least 20
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.
See this solution/explanation (answer is '7 meters'):
1. According to the condition 'y' means the height, and 'x' - the length from the start of the lift hill.
2. The phrase 'height of 343 meters' means y=343.
3. From the another side y=x³. If to substitute 343 instead of 'y': 343=x³, - it is possible to find the value of 'x'.
x=<u>7 [m]</u> - how far from the start of the lift hill...
Hi there! Use the following identities below to help with your problem.
What we know is our tangent value. We are going to use the tan²θ+1 = sec²θ to find the value of cosθ. Substitute tanθ = 4 in the second identity.
As we know, sec²θ = 1/cos²θ.
And thus,
Since the given domain is 180° < θ < 360°. Thus, the cosθ < 0.
Then use the Identity of sinθ = tanθcosθ to find the sinθ.
Answer
- sinθ = -4sqrt(17)/17 or A choice.
You just answerd it yourself i think.......
