Answer:
Step-by-step explanation:
The standard form of a parabola is
If we know the y intercept is (0, 400), that means that when x = 0, y = 400. That allows us to begin by finding c:
and c = 400.
Now to find a and b. Using the fact that the vertex is (1, 405), we know that h is 1 and k is 405. If
and h = 1, then
and
2a = -b so
b = -2a. Save that for a minute or two.
If
and k = 405, then
and
and
405 = 400 - 4a and
5 = -4a so
We will use that a value now to find the value of b. If b = -2a, then
and
Writing our parabolic equation now:
Finding the x-intercepts is just another way of saying "factor this quadratic" so we will begin that by setting the quadratic equal to 0:
and who hates all those fractions more than I do? Probably nobody, so we are going to get rid of them by multiplying everything by 4 to get
Assuming you can throw that into the quadratic formula to solve for the 2 values of x where y = 0, you'll find that the x-intercepts are
x = -16.91647287 and 18.91647287
Let the required point be (a,b)
The distance of (a,b) from (7,-2) is
=
But this distance needs to be betweem 50 & 60
So
Squaring all sides
2500 < (a-7)² + (b+2)² < 3600
Let a = 7
So we have
2500 < (b+2)² <3600
b+2 < 60 or b+2 > -60 => b <58 or b > -62
Also
b+2 >50 or b + 2 < -50 => b >48 or B < -52
Let us take one value of b < 58 say b = 50
So now we have the point as (7, 50)
The other point is (7,-2)
Distance between them
=
This is between 50 & 60
Hence one point which has a distance between 50 & 60 from the point (7,-2) is (7, 50)
Answer:
Step-by-step explanation:
sector area = angle/360 * pi * r^2
14.14 = angle/360 * 22/7 * 6^2
14.14 = angle/360 * 22/7 * 36
(360 * 14.14 * 7)/(22 * 36) = angle
angle = 44.99 = 45 degrees
It would be reflected. hope that helps