Can sb answer this correctly plz not a lot so plz do fast thank u

So lets get to the problem

165°= 135° +30° 

To make it easier I'm going to write the same thing like this 
165°= 90° + 45°+30° 

Sin165° 
= Sin ( 90° + 45°+30° ) 
= Cos( 45°+30° )..... (∵ Sin(90 + θ)=cosθ 
= Cos45°Cos30° - Sin45°Sin30° 

Cos165° 
= Cos ( 90° + 45°+30° ) 
= -Sin( 45°+30° )..... (∵Cos(90 + θ)=-Sinθ 
= Sin45°Cos30° + Cos45°Sin30° 

Tan165° 
= Tan ( 90° + 45°+30° ) 
= -Cot( 45°+30° )..... (∵Cot(90 + θ)=-Tanθ 
= -1/tan(45°+30°) 
= -[1-tan45°.Tan30°]/[tan45°+Tan30°] 

Substitute the above values with the following... These should be memorized 
Sin 30° = 1/2 
Cos 30° =[Sqrt(3)]/2 
Tan 30° = 1/[Sqrt(3)] 
Sin45°=Cos45°=1/[Sqrt(2)] 
Tan 45° = 1

4 0

4 years ago

Suppose that p is the probability that a randomly selected person is left handed. The value (1-p) is the probability that the pe

solmaris [256]

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 $p$ such that $1000p(1-p)$ is maximized. Once we have that $p$ , we can easily find the answer to part b.

Finding the value that maximizes $1000p(1-p)$ is the same as finding the value that maximizes $p(1-p)$ , just on a smaller scale. So, we really want to maximize $p(1-p)$ . To do this, we will do a trick called completing the square.

$p(1-p)=p-p^2=-p^2+p=-(p^2-p)=-(p^2-p+1/4)-(-1/4)=-(p-1/2)^2+1/4$ .

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 $p$ such that the inner part of the square term is equal to $0$ .

$p-1/2=0\\p=1/2$ .

So, the answer to part a is $\boxed{1/2}$ .

We can then plug $1/2$ into the equation for p to find the answer to part b.

$1000(1/2)(1-1/2)=1000(1/2)(1/2)=1000*1/4=250$ .

So, the answer to part b is $\boxed{250}$ .

And we're done!

3 0

2 years ago