If answer is correct I will mark as brainliest.
1 answer:
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I am getting 7 as the value of b. I do not believe 4 is a correct answer!
Here's why:
General equation of a circle in the xy plane
with being the x,y coordinates of the center.
The center point can be determined from the two endpoints of the diameter because the line segment is horizontal, so we just find the center of the x coordinates of the two points:
and the radius r = diameter/2 = 8-(-2)/2 = 5
so we have
Given a point on the circle (0,b) with b>0:
Assuming you meant a "circular cross-section" of 201.06 in².
so, we know if we cut the sphere like a cantaloupe, in half, the circular inner-part of the cantaloupe will have an area of 201.6 in².
keeping in mind that, the radius of that circular section, is the same radius of the sphere, what is it anyway?
so, we know if we cut the sphere like a cantaloupe, in half, the circular inner-part of the cantaloupe will have an area of 201.6 in².
keeping in mind that, the radius of that circular section, is the same radius of the sphere, what is it anyway?
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.
