#4: STEM While resting, a human takes in about 5 liters of air In 30 seconds. At this rate, how many liters of air does he take
1 answer:
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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:
Part A) The area of the figure is
Part B) The perimeter of the figure is
Step-by-step explanation:
step 1
Find the area of the figure
we know that
The area of the figure is equal to the area of triangle ABD plus the area of triangle BCD
The area of triangle is equal to
<u>Area of triangle ABD</u>
Observing the graph
substitute
<u>Area of triangle BCD</u>
Observing the graph
substitute
The area of the figure is
step 2
Find the perimeter of the figure
we know that
The perimeter of the figure is equal to
we have
the formula to calculate the distance between two points is equal to
Find the distance AB
Find the distance BC
Find the distance CD
Find the distance AD
substitute the values