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.
Step-by-step explanation:
We are given:

We need to find (g.h)(n)
Finding (g.h)(n)

So,
Keywords: Composite Function
Learn more about Composite Function at:
#learnwithBrainly
Answer:
$32,400
Step-by-step explanation:
We can just replace 12 for x in the equation y = 2700x
y = 2700x
y = 2700(12)
y = 32,400
The money paid after 12 years is $32,400
-Chetan K