The vertex is at the point (0,0) and the focus at the point (0, 1/8). This is given to us. Both the vertex and focus are separated by a vertical distance in the positive direction.
This means that the parabola opens upward. The vertex form of the equation for a parabola that opens upward is:
y = a(x - h)^2 + k, where the point
(h, k) is the vertex of the parabola.
Plug the vertex given into the above equation.
y = a(x - 0)^2 + 0
y = ax^2 + 0
y = ax^2
What is a?
Note: a = 1/(4f), where f is the distance from the vertex to the focus or simply as given in the focus point above 1/8.
Let f = 1/8
a = 1/4(1/8)
a = 1/(1/2)
a = 2
The equation we want is
y = 2x^2.
f(x) = 2x^2
Choice A is the answer.
Answer:
- half-life: 95.3 days
- 60% life: 70.2 days
Step-by-step explanation:
a) The proportion remaining (p) after d days can be described by ...
p = (1 -0.73)^(d/180) = 0.27^(d/180)
Then p=1/2 when ...
0.50 = 0.27^(d/180)
log(0.50) = (d/180)log(0.27)
180(log(0.50)/log(0.27) = d ≈ 95.3
The half-life is about 95.3 days.
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b) For the proportion remaining to be 60/100, we can use the same solution process. In the end, 0.50 will be replaced by 0.60, and we have ...
d = 180(log(0.60)/log(0.27) ≈ 70.2 . . . days
60 mg will remain of a 100 mg sample after 70.2 days.
Answer:
Lower bound is 4340.5
Step-by-step explanation:
................
If you graph 4 separate triangles with the four different points, only (2,3) and (1,5) form a right triangle.
Answer:
V = 9.42
Step-by-step explanation:
A pillar candle resembles a cylinder.
Volume of cylinder.
V = πr²h
V = (3.14)(1)²(3)
V = (3.14)(3)
V = 9.42
