Derive the equation from the parabola with a focus at (0,1) and a directrix of y=-1

Mathematics

1 answer:

Lady bird [3.3K]3 years ago

3 0

Answer:

y = (x^2)/4

Step-by-step explanation:

The vertex of this parabola is halfway between the focus (0,1) and the directrix y = -1. Thus, the vertex is at (0,0). The variable p represents the distance between focus and vertex, which is 1.

Thus, adapting the general formula for the equation of a parabola, we have:

4(1)y=x^2, or 4y = x^2, or y = (x^2)/4.

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The two dot plots below compare the forearm lengths of two groups of schoolchildren:

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Answer:

Group A, because seven children have a forearm length longer than 10 inches

Step-by-step explanation:

Create the dot plots based on the given information (please see attached images).

Group A = blue dots

Group B = red dots

From inspection of the attached dot plots, we can see that Group A appears to have the longer average forearm length. This is because 7 children have a forearm length of longer than 10 inches.

To calculate the average forearm length, sum all data values and divide by the total number of data values.

$\textsf{Average of Group A}=\dfrac{ 3 \times 10 + 4 \times 11 + 3 \times 12}{10}=11$