60 = a * (-30)^2
a = 1/15
So y = (1/15)x^2
abc)
The derivative of this function is 2x/15. This is the slope of a tangent at that point.
If Linda lets go at some point along the parabola with coordinates (t, t^2 / 15), then she will travel along a line that was TANGENT to the parabola at that point.
Since that line has slope 2t/15, we can determine equation of line using point-slope formula:
y = m(x-x0) + y0
y = 2t/15 * (x - t) + (1/15)t^2
Plug in the x-coordinate "t" that was given for any point.
d)
We are looking for some x-coordinate "t" of a point on the parabola that holds the tangent line that passes through the dock at point (30, 30).
So, use our equation for a general tangent picked at point (t, t^2 / 15):
y = 2t/15 * (x - t) + (1/15)t^2
And plug in the condition that it must satisfy x=30, y=30.
30 = 2t/15 * (30 - t) + (1/15)t^2
t = 30 ± 2√15 = 8.79 or 51.21
The larger solution does in fact work for a tangent that passes through the dock, but it's not important for us because she would have to travel in reverse to get to the dock from that point.
So the only solution is she needs to let go x = 8.79 m east and y = 5.15 m north of the vertex.
16,500
60 minutes in an hour / 12 minutes = 5
5 * 3,300 = 16,500
Answer: 54 mL
Step-by-step explanation: First, you need to find how many milliliters 10% is. To do this, divide 180 by 10, which equals 18. Then, since it needs to be thirty percent, times 18 by 3, which equals 54 mL. Hope this helps.
Answer:
36 gallons
Step-by-step explanation:
y = 4/5x
Let x = 45 minutes
y = 4/5 (45)
y = 36 gallons
Answer:
x=4
Step-by-step explanation:
22 = 18 + x
Subtract 18 from each side
22-18 = 18-18 + x
4 =x
