Answer:
Angle A is 37 degrees, Angle B is 82 degrees, Angle C is 61 degrees
Step-by-step explanation:
Exterior angles are the supplement of interior angles, so subtract 143 from 180 to find Angle A.
180 - 143 = 37
All angles add up to 180.
37 + 61 = 98
180 - 98 = 82
Angle B is 82 degrees.
Hope this helped. :)
Use pythagoras
d = √(Δx² + Δy²)
d = √(12-2)² + (9-4)²
d = √(10² + 5²)
d = √(100 + 25)
d = √125
d = 5√5
d = 5 × 2.236
d = 11.18
The nearest tenth is 11.2, so the distance is near to 11.2
Answer:
a) 1/2
b) 250
Step-by-step explanation:
The start of the question doesn't matter entirely, although is interesting to read. What we are trying to do is find the value for 
such that 
is maximized. Once we have that , we can easily find the answer to part b.
Finding the value that maximizes is the same as finding the value that maximizes 
, just on a smaller scale. So, we really want to maximize . To do this, we will do a trick called completing the square.
.
Because there is a negative sign in front of the big squared term, combined with the fact that a square is always positive, means we need to find the value of such that the inner part of the square term is equal to 
.
.
So, the answer to part a is 
.
We can then plug 
into the equation for p to find the answer to part b.
.
So, the answer to part b is 
.
And we're done!
