3 years ago

What is the slope of a line that passes through (-4,-13) and (19,11)?

1 answer:

7 0

We can find the slope from the two given points using the standard formula:
$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$
$m=\frac{11-(-13)}{19-(-4)}$
$m=\frac{24}{23}$

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The cross section of a parabolic reflector has a vertical axis of symmetry with its vertex at (0,0) . The focus of the reflector

Paha777 [63]

Answer:

The depth of the reflector is 0.84 feet

Step-by-step explanation:

<em>(See the figure below)</em>

The equation of a parabola centered at the origin with an axis of symmetry on y-axis is:

$x^{2}=4py$ (1)

With p the distance from the origin to the focus using p=6, the equation (1) of the parabola becomes:

$x^{2}=4(6)y=24y$ (2)

Note that the point B is on the parabola, so this point should satisfy the parabola equation (2) that allow us to use the value x=4.5 to find the y value associated to it, that it is the depth (h) of the reflector:

$(4.5)^{2}=24y$ , solving for y