A scientist is developing a parabolic object that is made up of mirrors and uses the sun's rays to focus heat on one particular location. To create a prototype of this object, she graphs a parabola on a coordinate plane that has a focus of (3,2)3,2 and a directrix of y=1y=1. This parabola can be represented by the equation (x−3)2=a(y−1.5)x-32=ay-1.5. Enter the value of a in the equation above.

x+5 and y=12

Step-by-step explanation:

its simple do the work

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!