The regular price is $24.50. Your discount is15% off. What is the sale price of your shirt?

s344n2d4d5 [400]

Well, this problem is best solved by setting up a system of two linear equations.

A linear equation can be defined
y=mx+b
where
b=initial value (when x=0), and
m=rate of increase or decrease.

In the given example, the x-axis represents hour, and the y-axis, number of cells.

Chemical #1
initial value = b = 12000 cells
rate = m = -4000 / hr
The equation is therefore
y1=-4000x+12000......................(1)

Similarly, for chemical #2
initial value = b = 6000 cells
rate = m = -3000 / hr
The equation is therefore
y2=-3000x+6000 .......................(2)

The time the two will have an equal sized colony would represent the solution of the system of equations (1) and (2), i.e. when y1=y2
which means
-4000x+12000 = -3000x+6000
transpose and solve for x
4000x-3000x = 12000-6000
1000x=6000
x=6 hours.

At 6 hours from the start,
y=-4000x+12000 = -4000*6+12000 = -24000+12000 = -12000 cells

So the solution is x=6, y=-12000, or (6,-12000)

Physical interpretation
Since cells cannot have a negative number, the two are actually equal before six hours, when they are both zero.
Case 1: y=0 when x=3
Case 2: y=0 when x=2

Therefore, after three hours, both trials will have zero cells.

You have to judge whether to give the mathematical solution (x=6,y=-12000) or the physical interpretation (x=3, y=0) as the answer.

6 0

2 years ago

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The focus of a parabola is (0, -3) and the directrix is y = 3. What is the equation of the parabola?

mart [117]

Focus has coordinates (0, a)
a = -3
Thus, 4a = 4(-3) = -12

Because a is negative, we know it will be a concave down or concave left parabola. Hence, A and D can be eliminated. And we know it has to be B because the directrix is the horizontal line y = 3. Hence, the equation of the parabola becomes:

$x^{2} = -12y$ or $y = -\frac{1}{12}x^{2}$