Hello :
<span>5cosθ = 3cosθ - 1.
</span><span>5cosθ - 3cosθ = 1.
2cos</span>θ =1
cosθ =1/2
all solutions :
cosθ =cos<span>π<span>/3
</span></span>all solutions :
θ =π/3 +2kπ or θ = - π/3 +2kπ ....k in Z
Let 
. Then differentiating, we get
We approximate 
at 
with the tangent line,
The 
-intercept for this approximation will be our next approximation for the root,
Repeat this process. Approximate at 
.
Then
Once more. Approximate at 
.
Then
Compare this to the actual root of , which is approximately <u>1.76929</u>2354, matching up to the first 5 digits after the decimal place.
Step-by-step explanation:
F(x) = ∫ₐˣ t⁷ dt
F(x) is the area under f(t) between t=a and t=x. When x=a, the width of the interval is 0, so the area is zero.
F(6) = 0, so a = 6.
F(x) = ∫₆ˣ t⁷ dt
F(6) = ∫₆⁶ t⁷ dt
F(6) = 0
The population ten years ago was 6,000.
Because the population doubled you divide 12,000 by 2
12,000 / 2 = 6,000
