Answer:
060.28
Step-by-step explanation:
3 can't go into 1, but it goes into 18 six times with 0 left over. 3 goes into 0 zero times. 3 goes into 5 one time with 2 left over. 3 goes into 26 (because you pull the 6 down) 8 times with 2 left over.
It looks like the given equation is
sin(2x) - sin(2x) cos(2x) = sin(4x)
Recall the double angle identity for sine:
sin(2x) = 2 sin(x) cos(x)
which lets us rewrite the equation as
sin(2x) - sin(2x) cos(2x) = 2 sin(2x) cos(2x)
Move everything over to one side and factorize:
sin(2x) - sin(2x) cos(2x) - 2 sin(2x) cos(2x) = 0
sin(2x) - 3 sin(2x) cos(2x) = 0
sin(2x) (1 - 3 cos(2x)) = 0
Then we have two families of solutions,
sin(2x) = 0 or 1 - 3 cos(2x) = 0
sin(2x) = 0 or cos(2x) = 1/3
[2x = arcsin(0) + 2nπ or 2x = π - arcsin(0) + 2nπ]
… … … or [2x = arccos(1/3) + 2nπ or 2x = -arccos(1/3) + 2nπ]
(where n is any integer)
[2x = 2nπ or 2x = π + 2nπ]
… … … or [2x = arccos(1/3) + 2nπ or 2x = -arccos(1/3) + 2nπ]
[x = nπ or x = π/2 + nπ]
… … … or [x = 1/2 arccos(1/3) + nπ or x = -1/2 arccos(1/3) + nπ]
Answer:
1 7/12
Step-by-step explanation:
6
5
+
4
3
2 Find the Least Common Denominator (LCD) of \frac{5}{6},\frac{3}{4}
6
5
,
4
3
. In other words, find the Least Common Multiple (LCM) of 6,46,4.
LCD = 1212
3 Make the denominators the same as the LCD.
\frac{5\times 2}{6\times 2}+\frac{3\times 3}{4\times 3}
6×2
5×2
+
4×3
3×3
4 Simplify. Denominators are now the same.
\frac{10}{12}+\frac{9}{12}
12
10
+
12
9
5 Join the denominators.
\frac{10+9}{12}
12
10+9
6 Simplify.
\frac{19}{12}
12
19
7 Convert to mixed fraction.
1\frac{7}{12}1
12
7
