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:
x^7 + x^6 - 3x^4 + 4x^3 + 6x - 3.
Step-by-step explanation:
(x3 + 2x - 1) (x4 - x3 + 3)
= x^7 - x^6 + 3x^3 + 2x^6 - 2x^4 + 6x - x^4 + x^3 - 3
= x^7 + x^6 - 3x^4 + 4x^3 + 6x - 3.
The answer is: "2.5 years" .
___________________________________________________
Note: I = P * r * t ; { " Interest = Principal * rate * time "} ;
→ Solve for "t" {"time", in years} ;
Divide each side of the equation by "{P * r}" ;
to isolate "t" on one side of the equation ;
→ I / (P * r) = {P * r * t) / (P * r} ;
to get: " I / (P * r) = t " ;
↔ t = I / (P * r) ;
Given: I = $450 ;
<span>P = $2400 ;
r = 7.5% = 7.5/100 = 0.075 ;
Plug in these values into the formula to solve for the time, "t" :
</span>→ t = I / (P * r ) ;
= $450 / (<span>$2400 * 0.075) ;
= </span>$450 / ($2400 * 0.075) ;
= $450 / $180 ;
= $45 / $18 ;
= ($45 ÷ 9) / ($18 ÷ 9)
= $5 / $2 ;
= 2.5 ;
→ t = 2.5 years.
_______________________________________________________
The answer is: "2.5 years" .
_______________________________________________________
3/2 because the proper solution is rise over run, in this case it rises 3 & runs to the right 2
Answer:
20 red and 100 blue
Step-by-step explanation:
give me brainliest please
