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2 answers:
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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.
Answer:
The solution is:
Step-by-step explanation:
The first step to solve this equation is placing everything with the logarithmicto one side of the equality, and everything without the exponential to the other side. So
It already is in the desired format.
Now, we have that, since e and ln are inverse operations
So, we apply the exponential to both sides of the equality
Answer:
C) 25%
Step-by-step explanation:
let salt be 's'
let water be 'w'
0.25 = 25%