An electrical engineer has on hand two boxes of resistors, with five resistors in each box. The resistors in the first box are l
1 answer:
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Answer:
Intersection at (-1, 0, 1).
Angle 0.6 radians
Step-by-step explanation:
The helix r(t) = (cos(πt), sin(πt), t) intersects the paraboloid
z = x2 + y2 when the coordinates (x,y,z)=(cos(πt), sin(πt), t) of the helix satisfy the equation of the paraboloid. That is, when
But
so, the helix intersects the paraboloid when t=1. This is the point
(cos(π), sin(π), 1) = (-1, 0, 1)
The angle of intersection between the helix and the paraboloid is the angle between the tangent vector to the curve and the tangent plane to the paraboloid.
The <em>tangent vector</em> to the helix in t=1 is
r'(t) when t=1
r'(t) = (-πsin(πt), πcos(πt), 1), hence
r'(1) = (0, -π, 1)
A normal vector to the tangent plane of the surface
at the point (-1, 0, 1) is given by
where
since
so, a normal vector to the tangent plane is
(-2,0,-1)
Hence, <em>a vector in the same direction as the projection of the helix's tangent vector (0, -π, 1) onto the tangent plane </em>is given by
The angle between the tangent vector to the curve and the tangent plane to the paraboloid equals the angle between the tangent vector to the curve and the vector we just found.
But we now
where
= angle between the tangent vector and its projection onto the tangent plane. So
and
Answer:
3. What is the probability that an adult selected at random has both a landline and a cell phone?
A. 0.58
4. Given an adult has a cell phone, what is the probability he does not have a landline?
C. 0.3012
Step-by-step explanation:
We solve this problem building the Venn's diagram of these probabilities.
I am going to say that:
A is the probability that an adult has a landline at his residence.
B is the probability that an adult has a cell phone.
C is the probability that a mean is neither of those.
We have that:
In which a is the probability that an adult has a landline but not a cell phone and is the probability that an adult has both of these things.
By the same logic, we have that:
The sum of all the subsets is 1:
2% of adults have neither a cell phone nor a landline.
This means that .
73% of adults have a landline at their residence (event A); 83% have a cell phone (event B)
So .
What is the probability that an adult selected at random has both a landline and a cell phone?
This is .
We have that . So
By the same logic, we have that:
.
So
So the answer for question 3 is A.
4. Given an adult has a cell phone, what is the probability he does not have a landline?
83% of the adults have a cellphone.
We have that
25% of those do not have a landline.
So
The answer for question 4 is C.