In a volcano, erupting lava flows continuously through a tube system about 24 kilometers to the sea. assume
a lava flow speed of 0.6 kilometers per hour and calculate how many hours it takes to reach the sea. use the
formula rate x time = distance.
show work

Distance = rate x time or d = rt...that means time t = d/r...and we have

t = 21 km / .5 km/hr = 42 hr

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

21/58.

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