Please help if you can, I'd really appreciate it.
2 answers:
Answer:
1) Circle 2) Parabola 3) A plane intersects only one nappe of a cone, and a plane is parallel to the generating line of the cone. 4) A degenerate Hyperbola is a pair of intersecting lines.
Step-by-step explanation:
1) A plane intersects one nappe of a double-napped cone such that it is perpendicular to the vertical axis of the cone. Which conic section is formed?
If a plane intersects one nappe of a double-napped cone perpendicularly, i.e. 90º then clearly the conic section is going to produce a circle.
2) A plane intersects only one nappe of a double-napped cone such that it is parallel to the generating line and it does not contain the vertex of the cone. Which conic section is formed?
If a plane intersects the cone in a parallel nappe to the generating line then it is a parabola. Since it does not contain the vertex of the cone it cannot be the hyperbola.
3) Which intersection forms a parabola?
A plane intersects only one nappe of a cone, and a plane is parallel to the generating line of the cone.
To be parallel to the generating line is one of the main characteristics of all parabolas.
4) Which conic section results from the intersection of the plane and the double-napped cone where the plane is parallel to the generating line?
It's a parabola due to be parallel to the generating line.
Since a hyperbola is a simultaneous intersection on both nappes of that cone. Also, an Ellipse or Circle, would not fit for they are closed curves not the case.
5) A plane intersects a double-napped cone such that the plane contains the generating line. Which terms describe the degenerate conic section that is formed?
A degenerate Hyperbola is a pair of intersecting lines.
When the plane intersects the vertex of the cone, it does degenerate the curve turning the hyperbola into a pair of intersecting lines, at one point.
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-5g - 3/h-3 + 7g +9/h-3 = -5g + 7g -3/h-3 + 9/h-3 = 2g + (9 - 3)/(h-3) =
= 2g + 6/(h-3) if we want it as one fraction it would be:
2g + 6/(h-3) = [2g(h-3) + 6]/(h-3) =
= 2g + 6/(h-3) if we want it as one fraction it would be:
2g + 6/(h-3) = [2g(h-3) + 6]/(h-3) =
1) 4.55
2) Short hit
Step-by-step explanation:
1)
The table containing the score and the relative probability of each score is:
Score 3 4 5 6 7
Probability 0.15 0.40 0.25 0.15 0.05
Here we call
X = Miguel's score on the Water Hole
The expected value of a certain variable X is given by:
where
are all the possible values that the variable X can take
is the probability that
Therefore in this problem, the expected value of MIguel's score is given by:
2)
In this problem, we call:
X = Miguel's score on the Water Hole
Here we have that:
- If the long hit is successfull, the expected value of X is
- Instead, if the long hit fails, the expected value of X is
Here we also know that the probability of a successfull long hit is
Which means that the probabilty of an unsuccessfull long hit is
Therefore, the expected value of X if Miguel chooses the long hit approach is:
In part 1) of the problem, we saw that the expected value for the short hit was instead
Since the expected value for X is lower (=better) for the short hit approach, we can say that the short hit approach is better.