Mathematics, 18.12.2019 03:31 j215495

25 points
approximate the solution to the equation above using three iterations of successive approximation. use the graph below as a starting point.

25 points approximate the solution to the equation above using three iterations of successive

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Answer from: mungerjennifer

$x_{5}=0.85$

Step-by-step explanation:

We can use Newton's method to solve this kind of problems.

It is a method of computing fixed points of iterated functions, the equation is given by:

$x_{n+1}=x_{n}-\frac{f(x_{n})}{f'(x_{n})}$

So, first of all we need to identify the function.

We know that our equation is: $-2x+6=-(2/3)^{x}+5$

Let's simplify and rewrite this equation using the natural log.

ln(2x-1)=xln(2/3) and if we put all these terms on the left side we will get the function.

f(x)=ln(2x-1)-x*ln(2/3)

f'(x) is the first derivative of the function, Let's take the derivative.

$f'(x)=\frac{2}{2x-1}-ln(2/3)$

Now, using the graph we choose x₁ = 0.6 as a starting point. Let's recall we need to find the intersection point, so we must choose a value of x as close as possible to the intersect point.

$x_{1}=0.6$

$x_{2}=x_{1}-\frac{f(x_{1})}{f'(x_{1})}$

$x_{2}=x_{1}-\frac{ln(2*x_{1}-1)-x_{1}*ln(2/3)}{2/(2*x_{1}-1)-ln(2/3)}$

$x_{2}=0.6-\frac{ln(2*0.6-1)-0.6*ln(2/3)}{2/(2*0.6-1)-ln(2/3)}$

$x_{2}=0.73$

We need to put x₂ in the equation again and find x₃

$x_{3}=0.73-\frac{ln(2*0.73-1)-0.73*ln(2/3)}{2/(2*0.73-1)-ln(2/3)}$

$x_{3}=0.83$

$x_{4}=0.83-\frac{ln(2*0.83-1)-0.83*ln(2/3)}{2/(2*0.83-1)-ln(2/3)}$

$x_{4}=0.85$

$x_{5}=0.85-\frac{ln(2*0.85-1)-0.85*ln(2/3)}{2/(2*0.85)-ln(2/3)}$

$x_{5}=0.85$

Therefore the approximate solution is 0.85.

I hope it helps you!

Answer from: Quest

points are handed out whenever you post answers.

brainliest answers are handed out by the person asking the question, so whether your answer is picked depends entirely on whether the asker bothers to pick

if you're asking about your rank, it depends on having a certain number of points and a certain number of brainliest answers. for example, at the time of this writing, i have 44338 points out of 15000 needed for the next (nearly triple the requirement! ) but i only have 24 out of 50 required brainliest answers. this number decays, meaning after a certain amount of time (i think about a month), the total number of brainliest answers you've earned doesn't count toward this total. (i've been stuck at the same rank for a long

the lesson to learn here is that you shouldn't worry about points or rank. chances are, no matter how good an answer you may provide, your efforts will go mostly unnoticed unless you focus on the newest/most active questions that get posted.

Answer from: Quest

answer: haha (: i’ll go see what it is

step-by-step explanation: