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3 years ago

How to find the equation of a parabola given the vertex and one point?

1 answer:

3 0

First, write down y=a(x-the x coordinate of the vertex)^2+the y coordinate of the vertex)
second, plug the x coordinate and coordinate of the given point in the above equation to find out a
For example, vertex is (1,2), the point is (3,4)
y=a(x-1)^2+2
then plug in x=3, y=4 in the above equation to find out a
4=a(3-1)^2+2
4=4a+2
4a=2
a=1/2
the equation of the parabola with a vertex at (1,2) and passes through the point (3,4) is 0.5(x-1)^2+2

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3 years ago

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3 years ago

Suppose you pick two cards from a deck of 52 playing cards. What is the probability that they are both queens?

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Answer:

0.45% probability that they are both queens.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes

The combinations formula is important in this problem:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

Desired outcomes

You want 2 queens. Four cards are queens. I am going to call then A,B,C,D. A and B is the same outcome as B and A. That is, the order is not important, so this is why we use the combinations formula.

The number of desired outcomes is a combinations of 2 cards from a set of 4(queens). So

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Total outcomes

Combinations of 2 from a set of 52(number of playing cards). So

$T = C_{52,2} = \frac{52!}{2!(52-2)!} = 1326$

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0.45% probability that they are both queens.

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3 years ago

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3 years ago

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Answer:

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3 years ago