x= -4 and x=8
f(x) =6║x-2║+3
39= 6║x-2║+3
36=6║x-2║
6=║x-2║
-(x-2)=6
-x+2=6
x=-4
x-2=6
x=8
Rearrange the equation as
cos(x) - √(1 - 3 cos²x) = 0
cos(x) = √(1 - 3 cos²x)
Note that both sides have to be positive, since the square root function is non-negative. If we end up with any solutions that make cos(x) < 0, we must throw them out.
Take the square of both sides.
(cos(x))² = (√(1 - 3 cos²(x))²
cos²(x) = 1 - 3 cos²(x)
4 cos²(x) = 1
cos²(x) = 1/4
cos(x) = ± √(1/4)
cos(x) = ± 1/2
We throw out the negative case and we're left with
cos(x) = 1/2
This has general solution
x = arccos(1/2) + 360° n or x = -arccos(1/2) + 360° n
(where n is any integer)
x = 60° + 360° n or x = -60° + 360° n
Now just pick out the solutions that fall in the interval 0° ≤ x < 360°.
• From the first solution set, we have x = 60° when n = 0.
• From the second set, we have x = 300° when n = 1.
So the answer is D.
Answer:
Mistake in Line 2
Step-by-step explanation:
Line 1
7(6) ÷ 5 + 42
Line 2
7(6) ÷ 5 + 16
Line 3
42 ÷ 5 + 16
Line 4
42 ÷ 21
Line 5
2
To simplify any expression we use order of operation
Line 1 is 7(6) ÷ 5 + 42
Order of operation is PEMDAS
First we start with parenthesis
so we multiply 7(6) in line 2
7*6- 42
So Line 2 is 42 ÷ 5 + 42
Hence there is a mistake in Line 2
Answer:
don't understand
but mean = <u>summation x</u>
total number
15=<u>7+4+5+2x+11</u>
5
15=<u>27+2x</u>
5
multiply both sides by 5
15×5=<u>2</u><u>6</u><u>+</u><u>2</u><u>x</u> ×5
5
75=26+2x
75-26=2x
<u>49</u>=<u>2x</u>
2. 2
x= 24.5