F (x) = 3x +2 fine the inverse of the function
1 answer:
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The solid shape is a cone and a half sphere. So the equation would be (cone volume) + (1/2 sphere volume):
If the volume of the cone is 270pi and the height of the cone is 10, then:
The radius of the object is 9 cm. Therefore, we can plug into the formula for the total volume:
The total volume is 513 pi cm^3
If the volume of the cone is 270pi and the height of the cone is 10, then:
The radius of the object is 9 cm. Therefore, we can plug into the formula for the total volume:
The total volume is 513 pi cm^3
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°
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The attached graph shows the line and plane meet at a shallow angle, consistent with the above answer.
