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
Answer:
20 gallons
Step-by-step explanation:
First start off by dividing 48 by 12 to see how many times 12 goes into 48.
48 / 12 = 4
now that you know that 12 goes into 48 4 times, multiply 4 by 5 to see how many gallons the leaky faucet will fill in 48 hours.
4 x 5 = 20
therefore the answer is 20 gallons
I hope this helps ^^
Answer:
this is question is wrong it you typed it wrong
how come the triangle named XYZ and the angle wxz and if there 2 triangles one must be a failure because there is no triangle which all his angels equals more than 180°
look again and if possible take a picture of the question
To determine if the triangle is a right triangle, we use the Pythagorean theorem to test or see if the data agrees. We do as follows:
c² = a² + b²
10² = (5√3)² + 5²
100 = 75 + 25
100 = 100
Therefore, the triangle with the given measurements is a right triangle. The angle that would have a right angle is angle BAC. Hope this answers the question. Have a nice day. Feel free to ask more questions.
