Solve each of the equations independently, then determine if the are continuous or discontinuous.
15≥-3x [start here]
-5≤x [divide both sides by (-3). *Dividing by a negative number means the direction of the sign changes!]
x≥-5 [just turned around for analysis]
Next equation:
2/3x≥-2 [start here]
x≥-2(3/2) [multiply both sides of the equation by the reciprocal, 3/2)
x≥-3
So, (according to the first equation) all values of x must be greater than, or equal to -5.
(According to the second equation) all values of x must be greater than, or equal to -3.
So, when graphed on a number line, both equations graph in the same direction, so they are continuous.
I believe the answer is 14
So there is an identity we'll need to use to solve this:
cos(x+y) = cosxcosy - sinxsiny
replace the numerator with the right hand side of that identity and we get:
(cosxcosy - sinxsiny)/cosxsiny
Separate the numerator into 2 fractions and we get:
cosxcosycosxsiny- sinxsiny/cosxsiny
the cosx's cancel on the left fraction, the siny's cancel on the right fraction and we're left with:
cosy/siny - sinx/cosx
which simplifies to:
coty - tanx
If x=2, the line is just a straight, vertical line intersecting the x-axis at 2.
