arism

You would want to find the zeros of this function. You could try factoring out a common multiple and try to factor, or use quadratic formula. 

We want csc x + cot x to get into terms of sin and cos, that means the first box that you drag in is 1/sinx + cosx/sinx as this is the first step that you could possibly take. They have the same base so we can combine it to be (1+cosx)/sinx. We then multiply the function by sinx/sinx which turns the denominator into sin^2x which is also (1-cos^2x), so right now the function is (sinx(cosx))/(1-cos^2x). We can then break the denominator into two pieces by difference of squares, so we have (sinx(1+cosx))/((1+cosx)(1-cosx)). the (1+cosx) in both the numerator and denominator cancel out and we are left with the identity.

a) Fill this in like a multiplication table:

b) There are a total of 9 possible scores that one can get. Two of them result in a 6, meaning that the possibility of getting a 6 is 2/9, or 1/3, or 33.3%.

c) Do the same thing like you did in b. There are a total of 9 possible scores. 5 of them being over 10, that means the possibility to get a score over 10 is 5/9, or 55.55%

Distribute the coefficients:

18x + 27 = 35x + 50

Isolate the variable by moving all the x's to one side and the numbers to the other

17x = -23

Divide by 17 on both sides

x= -23/17

So there is exactly one real solution

This solution and the one I posted are both plausible as the question is not specific enough to discern which one is the correct answer, but this question's distance gives reason that the altitude of the plane is well over 2,000,000, which is just impossible. This is correct mathematically, but reasonably this is impossible and incorrect

Let's set up a triangle for this equation

                          lines intersect here, this point is the plane

                          /\

                       65.22

 /                                               \

/59.38_________________55.4\

                  39 miles

Since the angle of the plane in relation to the two stations is 65.22, we can set up a law of wines.

\({39\over \sin(65.22)} = {x \over \sin 59.38}\)

x is the distance between the plane and station 2. We now cross multiply and we find the answer.

\(x = {39\sin(59.38)\over\sin(65.22)} \approx 17.4\)

The distance between station 2 and the plane is about 17.4 miles