1,045 to the nearest thousands would be <u>1,000</u> because you must round down since there are no numbers close enough to round up.
7. honestly not 100% sure. i did 364 divided by 13 which was 28 so 28 flowers per table. and then 28 divided by 4. 7 flowers per vase.
Circumference is found with the formula
c = pi × d
d is diameter and we will use 3.14 for pi.
The diameter is the measure across the center of the circle. In the first problem, you are given the radius, so we have to multiply by 2 to get the diameter. Then we can use the formula.
12.4 in × 2 = 24.8 in (that's the diameter)
c = pi × D
c = 3.14 × 24.8
c = 77.872 inches
circumference is 77.872 inches.
Try the other problems on your own. They are just like this one. Just make sure they are giving you the diameter and not the radius. Post if you have problems.
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.
