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.
The algebraic expression would be 4 - n, I believe.
10x-61/12 is the difference of (7x-) - (-3x + ).
<h3>What is Expression?</h3>
An expression is combination of variables, numbers and operators.
The given expression is (7x-) - (-3x + )
7x-+3x-
7x-20/3+3x-19/4
Add the variable terms and constant terms.
10x-20/3-19/4
The LCM of 3 and 4 is 12/
10x-4-57/12
10x-61/12
Hence, 10x-61/12 is the difference of (7x-) - (-3x + ).
To learn more on Expressions click:
brainly.com/question/14083225
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Answer:
First lets find the solutions to each inequality.
-2x10 and -2x>10 (divide both sides by -2 to solve)
x-5 and x<-5
x-5 tell us that x could be -5 or less.
x<-5 tells us that x could be -6 or less.
The first one is less than or equal to which tells you that there is a possibility that the number is shows is could be an answer
Hope this helps ;)
2:3 is equivalent to 0.666 repeating
If you have any further questions feel free to ask.
Hope this helps.