Answer:
YES
Step-by-step explanation:
Most real numbers (points on the number-line) are irrational (not rational). The rational numbers are those which have repeating decimal expansions (for example 1/11=0.09090909..., and 1=1.000000...=0.999999...) . They are also those which have terminating continued fraction expansions.
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:
25 almost full boxes
Step-by-step explanation:
Answer:
27a
Step-by-step explanation:
-5(a-6)+2a
-5a+30+2a
-3a+30
27a