cos (2x) = cos x
2 cos^2 x -1 = cos x using the double angle formula
2 cos ^2 x -cos x -1 =0
factor
(2 cos x+1) ( cos x -1) = 0
using the zero product property
2 cos x+1 =0 cos x -1 =0
2 cos x = -1 cos x =1
cos x = -1/2 cos x=1
taking the arccos of each side
arccos cos x = arccos (-1/2) arccos cos x = arccos 1
x = 120 degrees x=-120 degrees x=0
remember you get 2 values ( 2nd and 3rd quadrant)
these are the principal values
now we need to add 360
x = 120+ 360n x=-120+ 360n x = 0 + 360n where n is an integer
<span>First, calculate the difference between 15 and 12. The operation, subtraction, will give us the answer of 3. Then, divide the calculated value by 12 since this it the theoretical length of the nail. Multiply the quotient by 100% to arrive to the final answer. That is (3/12)(100%). The final answer to this item is 25% which is the last choice. </span>
Explanation is in the file
tinyurl.com/wpazsebu
Answer:
f(2) = -40
Step-by-step explanation:
Just substitute x=2 into the function:
f(x) = 2x³ - 3x² - 18x - 8
f(2) = 2(2)³ - 3(2)² - 18(2) - 8
f(2) = 2(8) - 3(4) - 36 - 8
f(2) = 16 - 12 - 44
f(2) = 4 - 44
f(2) = -40
You can always draw a right-angled triangle where the sloped side c is the line between the two points of interest, and a and b are the sizes of the horizontal and vertical lines.
Then apply c = √(a²+b²)
