A radio telescope has an section (profile? not a native English speaker lol) that has shape of a parabola. This outline has the formula h = 0,1a^2 - a + 7
h is the height from the ground in metres and a is the distance from the leftside of the diameter.
diepte = depth | doorsnede telescoop = intersection of the telescope
1a. What would be the greatest height the telescope could reach above the ground?
1b. What is the diameter of the telescope?
1c. What is the depth of the telescope?
I don't understand this question at all and my English translation is crappy but hopefully you all can help me out!
+128631 1a. What would be the greatest height the telescope could reach above the ground?
The greatest height will be when a = 0 = 7 meters
1b. What is the diameter of the telescope?
We can find the a value where the hight of the telescope = 7 m on the right side
7 = a^2 - a + 7 subtract 7 from both sides
0 = a^2 - a
a^2 - a = 0 factor
a ( a - 1) = 0
Setting both factors to 0 and solving for a gives that
a = 0 (we know this) or a =1
So.....the diameter of the telescope is 1 meter
1c. What is the depth of the telescope?
The low point of the telescope will be where a = (1/2)
So....to find the height at that point, we have
(1/2)^2 - (1/2) + 7 = 1/4 - 1/2 + 7 = 7 - 1/4 = 6.75 m
So.....the depth of the telescope is 7 - 6.75 = .25m
