Answer:
1/10 per sec
Step-by-step explanation:
When he's walked x feet in the eastward direction, the angle Θ that the search light makes has tangent
tanΘ = x/18
Taking the derivative with respect to time
sec²Θ dΘ/dt = 1/18 dx/dt.
He's walking at a rate of 18 ft/sec, so dx/dt = 18.
After 3seconds,
Speed = distance/time
18ft/sec =distance/3secs
x = 18 ft/sec (3 sec)
= 54ft. At this moment
tanΘ = 54/18
= 3
sec²Θ = 1 + tan²Θ
1 + 3² = 1+9
= 10
So at this moment
10 dΘ/dt = (1/18ft) 18 ft/sec = 1
10dΘ/dt = 1
dΘ/dt = 1/10 per sec
If the rate at which the temperature fell is 4/5 degree/hour then we can simply multiply 5 hours to get our answer.
4/5 * 5/1 = 20/5 = 4
So, it would change a total of 4 degrees.
I hope this helps. If something is confusing or this answer is wrong, don't be afraid to drop me a DM telling me what is wrong.
The answer is 80 because you divide 32 by 2/5
Compute the necessary values/derivatives of 
at 
:
Taylor's theorem then says we can "approximate" (in quotes because the Taylor polynomial for a polynomial is another, exact polynomial) at by
###
Another way of doing this would be to solve for the coefficients 
in
by expanding the right hand side and matching up terms with the same power of 
.
CosΘ < 0 ->2nd or 3rd quadrant
cotΘ > 0 -> 1/tanΘ > 0 -> tanΘ >0 -> 1st and 3rd quadrant.
So Θ lines in the 3rd quadrant
