Answer:
x = π/6, π/2, 5π/6, 3π/2
Step-by-step explanation:
cos x = sin(2x)
Use double angle formula.
cos x = 2 sin x cos x
Move everything to one side and factor.
cos x − 2 sin x cos x = 0
cos x (1 − 2 sin x) = 0
Set each factor to 0 and solve.
cos x = 0
x = π/2, 3π/2
1 − 2 sin x = 0
sin x = 1/2
x = π/6, 5π/6
The total solution is:
x = π/6, π/2, 5π/6, 3π/2
Answer: 2 solutions.
The given equation breaks down into these two equations
3x+12 = 18 and 3x+12 = -18
Basically 3x+12 equal to plus 18 and minus 18. This is due to the fact that something like |x| = 7 means x = 7 or x = -7, ie those x values are exactly seven units away from zero on the number line.
If you want to solve each equation, then
3x+12 = 18
3x = 18-12
3x = 6
x = 6/3
x = 2 is one solution
and
3x+12 = -18
3x = -18-12
3x = -30
x = -30/3
x = -10 is the other solution
a. 
is a joint density function if its integral over the given support is 1:
so the answer is yes.
b. We should first find the density of the marginal distribution, 
:
Then
or about 0.2019.
For the other probability, we can use the joint PDF directly:
which is about 0.7326.
c. We already know the PDF for 
, so we just integrate:
![E[Y]=\displaystyle\int_{-\infty}^\infty y\,f_Y(y)\,\mathrm dy=\frac15\int_0^\infty ye^{-y/5}\,\mathrm dy=\boxed5](https://tex.z-dn.net/?f=E%5BY%5D%3D%5Cdisplaystyle%5Cint_%7B-%5Cinfty%7D%5E%5Cinfty%20y%5C%2Cf_Y%28y%29%5C%2C%5Cmathrm%20dy%3D%5Cfrac15%5Cint_0%5E%5Cinfty%20ye%5E%7B-y%2F5%7D%5C%2C%5Cmathrm%20dy%3D%5Cboxed5)
If 10% was added to the total (100%), then subtract 10% from 17.85.
17.85 * 0.1 = 1.785
17.85 - 1.785 = 16.065
$16.07
Answer:
The answer is 173.2
Step-by-step explanation:
