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Newton's numerical method to estimate the square root of N uses the iterative relation
x₀ = initial guess
We want to estimate the square root of 15, so N = 15.
We know that √{16) = 4, therefore let x₀ = 4 for the initial guess.
Calculate relative error after n iterations as
When the relative error is less than 0.01, we shall accept the approxmate answer.
Iteration #1:
x₁ = 0.5(x₀ + N/x₀) = 0.5(4 + 15/4) = 3.875
e₁ = |1 - 4/3.875| = 0.032
Iteration #2:
x₂ = 0.5(3.875 + 15/3.875) = 3.873
e₂ = |1 - 3.875/3.873| = 5.2 x 10⁻⁴
This is good enough.
Therefore the approximate value for √(15) is 3.873.
On a number line, the progression to find the square root is shown below.
Answer: 3.873
x₀ = initial guess
We want to estimate the square root of 15, so N = 15.
We know that √{16) = 4, therefore let x₀ = 4 for the initial guess.
Calculate relative error after n iterations as
When the relative error is less than 0.01, we shall accept the approxmate answer.
Iteration #1:
x₁ = 0.5(x₀ + N/x₀) = 0.5(4 + 15/4) = 3.875
e₁ = |1 - 4/3.875| = 0.032
Iteration #2:
x₂ = 0.5(3.875 + 15/3.875) = 3.873
e₂ = |1 - 3.875/3.873| = 5.2 x 10⁻⁴
This is good enough.
Therefore the approximate value for √(15) is 3.873.
On a number line, the progression to find the square root is shown below.
Answer: 3.873
Answer:
The y-intercept of AB is <u>(4/3)</u> and the equation of BC is y = <u>(-1/6)</u> x + <u>(4/3)</u>
If the y-coordinate of point C is 13, its x-coordinate is <u>4</u>.
=====================================
Step-by-step explanation:
AB and BC form a right angle at their point of intersection, B.
So, AB ⊥ BC
A = (14 , -1) , B = (2,1)
<u>Part A: Find the y-intercept of AB.</u>
The general equation of the line y = mx + c
Where: m is the slope and c is constant represents y-intercept.
m = (y₂ - y₁)/(x₂ - x₁)
m =
y = (-1/6) x + c
Substitute with the point (2,1) to find c
1 = (-1/6) * 2 + c
c = 1 + 2 *(1/6) = 4/3
y = (-1/6) x + 4/3
So, <u>the y-intercept of AB is 4/3</u>
=======================================
<u>Part B: Find the equation of BC.</u>
BC ⊥ AB at point B
if m is the slope of AB, the slope of BC = (-1/m)
m = (-1/6)
So, the slope of BC = (-1/m) = 6
The equation of the line BC ⇒ y = 6x + c
Substitute with the point (2,1) to find c
1 = 6 * 2 + c
c = 1 - 12 = -11
y = 6x - 11
=========================================
<u>Part C: Find x-coordinate of C if y-coordinate of point C is 13.</u>
The equation of the BC is y = 6x - 11
Substitute with the y-coordinate of point C = 13
13 = 6x - 11
6x = 13 + 11 = 24
x = 24/6 = 4
