You have 5 gallons of water. You use of the
2 answers:
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Answer:
Solution: x = 3, y = 2, or (3, 2)
Step-by-step explanation:
Given the systems of linear equations with two variables:
The <u>process of elimination</u> will be used to solve for the solution to the given problem.
<h3><u /></h3><h3><u>Step 1:</u></h3>First, we must multiply Equation 1 by 2:
(2)[4x - 2y] = 8(2)
8x - 4y = 16
<h3><u>Step 2:</u></h3>Add the revised Equation 1 (from the previous step) to Equation 2:
Next, divide both sides by 11 to solve for x:
x = 3
<h3><u>Step 4:</u></h3>Substitute the value of x = 3 into Equation 1 to solve for y:
4x - 2y = 8
4(3) - 2y = 8
12 - 2y = 8
<h3><u>Step 5</u>: </h3>Subtract 12 from both sides:
12 - 12 - 2y = 8 - 12
- 2y = -4
<h3><u>Step 6</u>: </h3>Divide both sides by -2 to solve for y:
y = 2
<h2><u>Double-check:</u></h2>
In order to verify whether we have the correct values for the solution, substitute x = 3, and y = 2 into both equations:
Equation 1: 4x - 2y = 8
4(3) - 2(2) = 8
12 - 4 = 8
8 = 8 (True statement).
Equation 2: 3x + 4y = 17
3(3) + 4(2) = 17
9 + 8 = 17
17 = 17 (True statement).
Therefore, the solution to the given system is x = 3, y = 2, or (3, 2).
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