The vector from the reference point on the line to the point is
.. (5-2, 1-3, 4-3) = (3, -2, 1)
The cross product of this with the line's direction vector (-1, 1, -3) is (5, 8, 1). The dot product of that with any of the points in the problem statement is 37. Your plane equation can be written as
.. 5x +8y +z = 37
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A suitable vector calculator is very handy for this. I used an HP-48 app on my phone.
Answer:
4m +3 marbles does Helena have in all.
Step-by-step explanation:
Here, m represents the marble in each bag.
She put them in 4 bags with m marbles in each bag.
In each bag she have m marbles
then, in 4 bag she have 4m marbles
⇒total number of marbles= 4m
Since, she had 3 marbles left over.
⇒She have total number of marbles = 4m + 3
Therefore, 4m +3 marbles does Helena have in all.
Answer:
-2
Step-by-step explanation:
From the position of 2 on the x axis, just trace down to the graph.
Where the trace intersects the graph, then trace this point to the y-axis
This gives -2
Answer:
16 + sqrt(128)
Step-by-step explanation:
find the lengths of all 3 sides:
the side from (-9,8) to (-9,16) will be 16-8=8 (x stays constant)
The side from (-9,8) to (-17,8) is 8 (-9- (-17)=8)
The side from (-9,16) to (-17,8) will be found from the distance formula
d=sqrt((-17-9)^2 + (8-16)^2))
= sqrt(128)
So the perimeter will be these 3 numbers added together
P=sqrt(128) + 8 + 8
= 16 + sqrt(128)
which can simplify to:
= 16 + 4sqrt(8)
= 16 + 8sqrt(2) = 8+ sqrt(2)