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 answer is 5.472
Step-by-step explanation:
-0.84 ÷ 2.1 = -0.4
-0.4 + 5.872 = <em>5.472</em>
-30m^3-3 here is your answer
Step-by-step explanation:
x and y are roughly in a linear relationship.
when x increases by 2 units, then also y increases by more or less 2 units.
when x increases by 3 units, then also y increases by more or less 3 units.
it is not precise, but a good approximation model.
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
- 4x + 3y = 12 ( add 4x to both sides )
3y = 4x + 12 ( divide the terms by 3 )
y = 
x + 4 ← in slope- intercept form
with slope m = and y- intercept c = 4
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Given
- 5x + 3y = - 9 ( add 5x to both sides )
3y = 5x - 9 ( divide the terms by 3 )
y = 
x - 3 ← in slope- intercept form
with slope m = and y- intercept c = - 3
