Please help! Select the graph for the solution of the open sentence. |x| < 1
1 answer:
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Answer:
angle of intersection: 5.2°
Step-by-step explanation:
The direction vector normal to the plane is ...
n = (1, 1, 3)
The direction vector of the line is ...
m = (1, -3, 1)
Then the angle θ between them can be found from the dot product:
n•m = |n|·|m|·cos(θ)
(1·1 +1(-3) +3·1) = 1 -3 +3 = 1 = √(1²+1²+3²)·√(1²+(-3)²+1²)·cos(θ)
1 = 11·cos(θ)
θ = arccos(1/11) ≈ 84.8°
This is the angle between the line and the normal to the plane, so the angle between the line and the plane will be the complement of this. Since this angle is not 90°, <em>the line and plane must intersect</em>.
acute angle = 90° -84.8° = 5.2°
_____
The attached graph shows the line and plane meet at a shallow angle, consistent with the above answer.
Let's say we use "x" of the 25% OJ... ok... well, how much juice is really in that "x" liters? well, 25% of it is OJ, the rest is water, how much is 25% of x? well, (25/100) * x, or 0.25x.
likewise, we'll use "y" of the 10% OJ, and it will end up with (10/100) *y or 0.10y of juice in it.
whatever "x" and "y" are, they must add up to 15 Liters, and the juice concentration on that mixture, must also be the sum of their sum concentration.
how much will be it of the 10% juice? well, y = 15 - x.
likewise, we'll use "y" of the 10% OJ, and it will end up with (10/100) *y or 0.10y of juice in it.
whatever "x" and "y" are, they must add up to 15 Liters, and the juice concentration on that mixture, must also be the sum of their sum concentration.
how much will be it of the 10% juice? well, y = 15 - x.