Roxanne is using successive approximation to solve this equation. 6x + 2 = VI + 2 – 3 She started from a graph, where she found the solution to be between -1 and 0. Using the lower and upper bounds from the graph, Roxanne started the first iteration of successive approximation. Rewrite the equation so it equals zero. 6x + 2 = VI + 2 – 3 Step 1 (6x + 2) – (VE + 2 – 3) = 0 Evaluate the rewritten equation at the lower and upper bounds. Since the solution to the equation represents a zero, one bound should yield a negative value and the other should produce a positive value. Step 2 (6(–1) + 2) – (S–1) + 2 – 3) = (6(0) + 2) – (V0) + 2 – 3) z 3.5858 = -2 Take the average of the lower and upper bounds from the graph. Step 3 -1 + 0 %3D Evaluate the rewritten equation at * = Step 4 ((-4) + 2) – (/(-) + 2 – 3) 2 0.7753 Since this value is positive, replace the previous lower bound so Step 5 the bounds are now * = and r = 0. Where did Roxanne make a mistake, and what was the error? O A. Roxanne made a mistake at step 5. She should have used = - as the new upper bound. O B. Roxanne made a mistake in Step 2. The actual evaluation of the rewritten equation at r = -1 is -3. OC. Roxanne made a mistake in Step 3. The average of the two bounds is = O D. Roxanne made a mistake in step 4. The actual evaluation of the rewritten equation is approximately -0.7753
Roxanne is using successive approximation to solve this equation. 6x + 2 = VI + 2 – 3 She started from a graph, where she found the solution to be between -1 and 0. Using the lower and upper bounds from the graph, Roxanne started the first iteration of successive approximation. Rewrite the equation so it equals zero. 6x + 2 = VI + 2 – 3 Step 1 (6x + 2) – (VE + 2 – 3) = 0 Evaluate the rewritten equation at the lower and upper bounds. Since the solution to the equation represents a zero, one bound should yield a negative value and the other should produce a positive value. Step 2 (6(–1) + 2) – (S–1) + 2 – 3) = (6(0) + 2) – (V0) + 2 – 3) z 3.5858 = -2 Take the average of the lower and upper bounds from the graph. Step 3 -1 + 0 %3D Evaluate the rewritten equation at * = Step 4 ((-4) + 2) – (/(-) + 2 – 3) 2 0.7753 Since this value is positive, replace the previous lower bound so Step 5 the bounds are now * = and r = 0. Where did Roxanne make a mistake, and what was the error? O A. Roxanne made a mistake at step 5. She should have used = - as the new upper bound. O B. Roxanne made a mistake in Step 2. The actual evaluation of the rewritten equation at r = -1 is -3. OC. Roxanne made a mistake in Step 3. The average of the two bounds is = O D. Roxanne made a mistake in step 4. The actual evaluation of the rewritten equation is approximately -0.7753
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter7: Applying Fractions
Section7.8: Work Problems
Problem 23P
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Transcribed Image Text:Select the correct answer.
Roxanne is using successive approximation to solve this equation.
6x + 2 = VI + 2 – 3
She started from a graph, where she found the solution to be between -1 and 0. Using the lower and upper bounds from the graph,
Roxanne started the first iteration of successive approximation.
Rewrite the equation so it equals zero.
6x + 2 = VI + 2 – 3
Step 1
(6x + 2) – (VI + 2 – 3) = 0
Evaluate the rewritten equation at the lower and upper bounds.
Since the solution to the equation represents a zero, one bound
should yield a negative value and the other should produce a
positive value.
Step 2
(6(–1) + 2) – (V=1) + 2 – 3) = -2
(6(0) + 2) – (/0) + 2 – 3) = 3.5858
Take the average of the lower and upper bounds from the
graph.
Step 3
-1 + 0
Evaluate the rewritten equation at * =
Step 4
(6(-1) + 2) – (/) +
+ 2 –
2 0.7753
Since this value is positive, replace the previous lower bound so
Step 5
the bounds are now * =
-i and I = 0.
Where did Roxanne make a mistake, and what was the error?
O A.
Roxanne made a mistake at Step 5. She should have used r =
as the new upper bound.
O B. Roxanne made a mistake in step 2. The actual evaluation of the rewritten equation at r = -1 is –3.
OC.
Roxanne made a mistake in Step 3. The average of the two bounds is r =
O D.
Roxanne made a mistake in step 4. The actual evaluation of the rewritten equation is approximately -0.7753-
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