Answer:
It would be constant.
Step-by-step explanation:
Since there is no x value, the line will have no slope and just be horizontal about y= -2.
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:
the burgers be 3 and fries be 2
Step-by-step explanation:
The computation is shown below:
Let us assume burgers be x
And, the fries be y
Now according to the questiojn
1.25x + 0.50y = $4.75
1.50x + 0.99y = $6.48
Now multiply by 1.2 in the first equation
1.50x + 0.6y = $5.70
1.50x + 0.99y = $6.48
-0.39y = -0.78
y = 2
Now put the value of y in any of the above equation
1.25x + 0.50(2) = $4.75
x = 3
Hence, the burgers be 3 and fries be 2
Answer:
D) 20°
Step-by-step explanation:
Using the triangle sum theorem, you know that every triangle's interior angles add up to 180°. Therefore the bottom triangle's missing angle can be found by giving it the variable x.
57° + 30° + x = 180°
Simplify: 87° + x =180°
x=93°
By the vertical angles theorem, the vertical angle directly across this angle is congruent to this one. Meaning that the top triangle's angle are 67°, 93°, and unknown, which we can assign y. We can use the same method from above here.
67° + 93° + y = 180°
Simplify: 160° + y = 180°
y=20°
