Answer:
(3/8) + (1/8)cos 4x - (1/2)cos 2x
Step-by-step explanation:
sin^(4) x = (sin² x ) (sin² x) ------ (1)
Recall double angle identity: cos 2x = 1 - 2 sin² x
or sin² x = (1/2) (1 - cos 2x)
substituting this into (1)
sin^(4) x = (sin² x ) (sin² x) = [ (1/2)(1-cos 2x) ]²
= (1/4) ( 1 - 2 cos 2x + cos²2x) ------(2)
Also recall double angle identiy : cos 2x = 2 cos² x - 1
or cos² x = (1/2) ( 1+ cos 2x)
or cos² 2x = (1/2) ( 1+ cos 4x)
substituting this into (2)
(1/4) ( 1 - 2 cos 2x + cos²2x)
= (1/4) [ 1 - 2 cos 2x + (1/2)(1 + cos 4x) ] (expand and reduce)
= (3/8) + (1/8)cos 4x - (1/2)cos 2x
G(x) can be obtained from F(x) by shifting F(x) 4 units to the right and 1 unit upwards.
Shift towards right can be obtained by subtracting 4 from the x in the function and the upward shift can be obtained by adding 1 to the function.
So,
G(x) = F(x-4) + 1
Thus,
G(x) = (x-4)² + 1
So, the correct answer to this question is option B
0.5 is the same thing as saying 5/10. When you reduce your answer, you get 1/2. To reduce, divide the numerator by 5 and the denominator by 5. :-)
Answer:
x = 20 but see below.
Step-by-step explanation:
Remark.
This is not well enough marked to know whether D = A or whether you have to do some algebra to find the relationship between A and D. So I will assume A = D and then I'll solve it so you have to manipulate A and D.
A = D
3x - 10 = 2x + 10 Add 10 to both sides
3x - 10 + 10 = 2x + 10 + 10 Cancel
3x = 2x + 20 Subtract 2x from both sides
3x-2x=2x-2x + 20
x = 20
A = E
If A = E then to find x you have to add 3 angles together.
E + D + 45 = 180 Add the three angles of the triangle
E + D = 180 - 45 Subtract 45 from both sides
E + D = 135 Substitute for D and E
3x - 10 + 2x + 10 = 135 Combine like terms
5x = 135 Divide by 5
x = 135 / 5
x = 27
Answer
I'd go with the first one.