1. B
2. D I'm not sure about this one
3. A
4. C
5. C
6. B
7. -9
8. 1
9. -2
10. 5
Hope this helps! I'm sure about all except for number 2!
Step-by-step explanation:
Let y1 and y2 be (e^x)/2, and (xe^x)/2 respectively.
The Wronskian of them functions be
W = (y1y2' - y1'y2)
y1 = (e^x)/2 = y1'
y2 = (xe^x)/2
y2' = (1/2)(x + 1)e^x
W = (1/4)(x + 1)e^(2x) - (1/4)xe^(2x)
= (1/4)(x + 1 - x)e^(2x)
W = (1/4)e^(2x)
Since the Wronskian ≠ 0, we conclude that functions are linearly independent, and hence, form a set of fundamental solutions.
Answer:
θ = 36.94°
Step-by-step explanation:
Brewster's law for polarization states that; tan(θ_p) = n2/n1
Where ;
θ_p is the polarizing angle
n1 is the index of refraction of first material
n2 is the index of refraction of second material
Now, our first material here is air while second material is water.
Index of refraction of water = 1.33 while index of refraction of air is 1
Thus,
tan(θ_p) = n2/n1 = 1.33/1
tan(θ_p) = 1.33
(θ_p) = tan^(-1)1.33
(θ_p) = 53.06°
Now, polarizing angle is the angle of incidence for which all the reflected light is polarized and it's above the vertical. Thus to get the angle to the horizontal, it will be;
θ = 90° - (θ_p) = 90° - 53.06° = 36.94°
Answer:
z/3 = 3/2 so 2z = 9 z = 4.5 cuz triangles are proportional
