Arc tan ( 1/√3 ) = arc tan ( √3/3 ) = 30°
180° = π ( in radians )
30° = 180°/6 = π/6
F(x)=x⁴-1
f'(x)=4x³
Newton’s Method: x[n+1]=x[n]-f(x[n])/f'(x[n]); x[n+1]=x[n]-(x[n]⁴-1)/4x[n]³
x₁=3.00390625
x₂=2.26215...
x₃=1.7182...
X'=X-(X⁴-1)/4X³=X-X/4+1/4X³ is a symbolic way of writing the recursive formula, where X' represents the next iteration.
When X'≈X, -X/4+1/4X³≈0; so X/4≈1/4X³; X≈1/X³, so X⁴≈1 and X⁴-1≈0. But this is f(x)≈0. Hence Newton’s Method converges to a solution.
The rate of change is x[n+1]-x[n]=-(x[n]⁴-1)/4x[n]³=x[n]/4-1/4x[n]³ or symbolically -X/4+1/4X³.
Note that the method converges to one solution. A different x₀ will possibly converge to the solution x=-1.
Answer:
D
Step-by-step explanation:
CD is an angle bisector and divides the opposite side into segments which are proportional to the other 2 sides, that is
= 
, substitute values
= 
( cross- multiply )
3x = 9 ( divide both sides by 3 )
x = 3 → D
Answer:
13.20 min
Step-by-step explanation:
Rate of the reaction is a measure of the rate of decomposition of the compound.
Rate (R) = Concentration (C) ÷ time (t)
C1/t1 = C2/t2
C1 = 52.3% = 0.523
t1 = 8.6 min
C2 = 80.3% = 0.803
t2 = C2t1/C1 = 0.803×8.6/0.523 = 13.20 min (to 2 decimal places)
