Divide ten by how much it cost 10/6.55=1.52
h^2 - 12h + 20 can be factored to:
(h-10)(h-2)
These cannot be zero so, h cannot be 10 or 2.
The square of a binomial is written like
![(x\pm a)^2 = x^2\pm 2ax + a^2](https://tex.z-dn.net/?f=%28x%5Cpm%20a%29%5E2%20%3D%20x%5E2%5Cpm%202ax%20%2B%20a%5E2)
In your case, you have
, which implies ![a=-4](https://tex.z-dn.net/?f=a%3D-4)
So, we want to write
![(x-4)^2 = x^2-8x+16](https://tex.z-dn.net/?f=%28x-4%29%5E2%20%3D%20x%5E2-8x%2B16)
But our left hand side is
![x^2-8x-10](https://tex.z-dn.net/?f=x%5E2-8x-10)
If we add 26 to both sides, we have
![x^2 - 8x - 10 +26 = 18+26 \iff x^2-8x+16=44 \iff (x-4)^2=44](https://tex.z-dn.net/?f=%20x%5E2%20-%208x%20-%2010%20%2B26%20%3D%2018%2B26%20%5Ciff%20x%5E2-8x%2B16%3D44%20%5Ciff%20%28x-4%29%5E2%3D44)
Add sin(x) to both sides
tan(x)sin(x)=sin(x)
Divide sin(x) from both sides
tan(x)=1
now you just have to figure out where tan(x)=1. you can figure this out from there by looking at the unit circle.
The first thing you should know is that by definition:
d = v * t
Where
d: distance
v: speed
t: time
We then have to clear the time:
t = (d) / (v)
Substituting the values:
t = (6000) / (200)
t = 30 minutes
Answer:
It will take a raindrop to travel 6000m about:
t = 30 minutes