Let's have the first number, the larger number, be <em>x</em>. We'll have the second, smaller number be <em>y</em>.
We know that x = y + 6, since x is 6 greater than y.
We also know that 330 = x + y.
Because x = y + 6, 330 = y + 6 + y, which simplifies to 330 = 2y + 6.
Now all we need to do is simplify the equation. First, we subtract 6 from both sides:
330 - 6 = 324
2y + 6 - 6 = 2y.
So we have 324 = 2y. Then we divide both sides by 2 to get:
162 = y
Plug in y = 162 into the equation x = y + 6 to get:
x = 162 + 6
x = 168
Let's check to make sure our answer is right. 168 is 6 more than 162. 162 + 168 equals 330. So our two numbers are 168 and 162.
The angular resolution of telescope is roughly given by formula:
Where:
λ = wevelength of light
D = diameter of a telescope
First step in solving this question is to convert diameter given in inches into meters:
Telescope A:
6 * 0.0254 = 0.1524m
Telescope B:
10 * 0.0254 = 0.254m
Wavelength of visible light varies from 390nm to 700nm. We will take 500nm as a number for our calculation.
Telescope A:
Telescope B:
The results are given in radians. We need to transform this into degrees.
Telescope A:
Telescope B:
To find out which telescope can distinguish two stars we must convert given angle.
0.7'' is 0.7 arc seconds or 0.7 / 60 / 60 =0.0001944444444444 degrees
Telescope that has angles smaller than this can distinguish. In our case both telescopes have smaller angle and both can distinguish.
<span>None, because with triangles the sum of the two shorter side lengths (5 m + 5 m) needs to be equal to or greater than the length of the longest side (15 m). In this case, the sum of the two shorter sides is 10 m, which is less than 16 m, so a triangle cannot form.</span>