The equation of the plane that goes through these points is:
6x + 2y + z = 10.
<h3>How to find the equation of a plane given three points?</h3>
The equation of the plane is found replacing the points into the following equation:
ax + by + c = z.
For point A, we have that:
3b + c = 4.
For point B, we have that:
a + 2b + c = 0.
For point C, we have that:
-a + 6b + c = 4.
Hence the system is:
From the first equation, we have that:
c = 4 - 3b.
Replacing in the second, we have that:
a + 2b + 4 - 3b = 0
a - b = -4.
Replacing in the third, we have that:
-a + 6b + 4 - 3b = 4.
-a + 3b = 0.
a = 3b.
We have that a - b = -4, hence:
3b - b = -4
2b = -4
b = -2.
a = 3b, hence a = -6.
c = 4 - 3b -> c = 10.
Hence the equation is:
ax + by + c = z.
z = -6x - 2y + 10
6x + 2y + z = 10.
More can be learned about the equation of a plane at brainly.com/question/13854649
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c^2 = 5^2 + 8^2 = 25 + 64 = 89
c = √89
Answer: c
Answer:
x=15/8
Step-by-step explanation:
Inverse variation is given by
xy = k
Substituting x=5 and y=12
5*12 = k
60 =k
Our original equation is xy = 60
Now let y=32
x*32 = 60
Divide each side by 32
32x/32 = 60/32
Divide top and bottom by 4
x = 15/8
Answer:
The correct option is (D).
Step-by-step explanation:
It is given that GIKMPR is regular hexagon. It means it has 6 vertices.
Since the central angle is 360 degree. Therefore the central angle between two consecutive vertices is
It is given that the dashed line segments form 30 degree angles.
We have rotated the hexagon about O to map PQ to RF. Since P and R are consecutive vertices, therefore the angle between them is 60 degree.
The vertex R is immediate next to the vertex P in clockwise direction.
So if we rotate the hexagon at 60 degree clockwise about O, then we can maps PQ to RF.
Therefore we can also rotate the hexagon at 300 degree counterclockwise about O, then we can maps PQ to RF.
Therefore option D is correct.
