7.42 as a fraction is 7420/1000. Now you need to simplify it. The easiest way to do this is to continuously divide the top and bottom by 2 as long as it is even. At this point it should be small enough to figure out the other factors, and finish simplifying it. This only simplifies to 371/50. While 371 is divisible by 7 and 53, 50 is not divisible by either of them, so the final solution is 371/30
Therefore 371/50 is 7.42 as a fraction.
Here are the answers:
1.D
2.D
3.C
4.A
5.C
Positive: 690
Negative: -30
Hi there!

We are given:
cos(7x)cos(4x) = -1 - sin(7x)sin(4x)
Begin by moving all terms with variables to one side:
cos(7x)cos(4x) + sin(7x)sin(4x) = -1
The corresponding trig identity is cos(A - B). Thus:
cos(7x - 4x) = cos(7x)cos(4x) + sin(7x)sin(4x) = -1
cos(3x) = -1
cos = -1 at π, so:
3x = π
x = π/3
We can also find another solution. Let 3π = -1:
3x = 3π
x = π
Thus, solutions on [0, 2π) are π/3 and π.