008A Sample Final A, Question 5 - Revision history

MathAdmin at 19:22, 2 June 2015

2015-06-02T19:22:18Z

MathAdmin at 06:52, 26 May 2015

2015-05-26T06:52:06Z

MathAdmin at 06:13, 23 May 2015

2015-05-23T06:13:40Z

MathAdmin at 06:13, 23 May 2015

2015-05-23T06:13:25Z

MathAdmin at 21:45, 28 April 2015

2015-04-28T21:45:09Z

MathAdmin at 21:44, 28 April 2015

2015-04-28T21:44:48Z

MathAdmin: Created page with "'''Question: '''Graph the system of inequalities $y < \vert x\vert +1$ $x^2 + y^2 \le 9$ {| class="mw-collapsible mw..."

2015-04-28T21:07:56Z

Created page with "'''Question: '''Graph the system of inequalities <math>y < \vert x\vert +1 </math> <math>x^2 + y^2 \le 9</math> {| class="mw-collapsible mw..."

New page

'''Question: '''Graph the system of inequalities <math>y < \vert x\vert +1 </math>           <math>x^2 + y^2 \le 9</math>

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Foundations
|-
|1) What do the graphs of <math>y=\vert x\vert + 1</math>, and <math>x^2 + y^2 = 9</math> look like?
|-
|2) Each graph splits the plane into two regions. Which one do you want to shade?
|-
|Answer:
|-
|1) The first graph looks like a V with the vertex at (0, 1), the latter is a circle centered at the origin with radius 3.
|-
|2) Since the Y-value must be less than <math>\vert x\vert + 1</math>, shade below the V. For the circle shde the inside.
|}

Solution:

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 1:
|-
|First we replace the inequalities with equality. So <math>y = \vert x\vert + 1</math>, and <math>x^2 + y^2 = 9</math>.
|-
|Now we graph both functions.
|}

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 2:
|-
|Now that we have graphed both functions we need to know which region to shade with respect to each graph.
|-
|To do this we pick a point an equation and a point not on the graph of that equation. We then check if the
|-
|point satisfies the inequality or not. For both equations we will pick the origin.
|-
|<math>y < \vert x\vert + 1:</math> Plugging in the origin we get, <math>0 < \vert 0\vert + 1 = 1</math>. Since the inequality is satisfied shade the side of
|-
|<math>y < \vert x\vert + 1</math> that includes the origin. We make the graph of <math>y < \vert x\vert + 1</math>, since the inequality is strict.
|-
|<math>x^2 + y^2 \le 9:</math> <math>(0)^2 +(0)^2 = 0 \le 9</math>. Once again the inequality is satisfied. So we shade the inside of the circle.
|-
|We also shade the boundary of the circle since the inequality is <math>\le</math>
|}

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 3:
|-
|The final solution is the portion of the graph that below <math>y = \vert x\vert + 1</math> and inside <math> x^2 + y^2 = 9</math>
|}

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Final Answer:
|-
|The final solution is the portion of the graph that below <math>y = \vert x\vert + 1</math> and inside <math> x^2 + y^2 = 9</math>
|}

[[008A Sample Final A|<u>'''Return to Sample Exam</u>''']]

@@ Line 49: / Line 49: @@
 |-
 |The region we are referring to is shaded both blue and red.
 |[[File:8A_Final_5.png]]
 |}
 [[008A Sample Final A|<u>'''Return to Sample Exam</u>''']]

@@ Line 12: / Line 12: @@
 |1) The first graph looks like a V with the vertex at (0, 1), the latter is a circle centered at the origin with radius 3.
 |-
-|2) Since the Y-value must be less than <math>\vert x\vert + 1</math>, shade below the V. For the circle shde the inside.
+|2) Since the Y-value must be less than <math>\vert x\vert + 1</math>, shade below the V. For the circle shade the inside.
 |}

@@ Line 2: / Line 2: @@
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-! Foundations
+! Foundations: &nbsp;
 |-
 |1) What do the graphs of <math>y=\vert x\vert + 1</math>, and <math>x^2 + y^2 = 9</math> look like?
@@ Line 18: / Line 18: @@
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-! Step 1:
+! Step 1: &nbsp;
 |-
 |First we replace the inequalities with equality. So <math>y = \vert x\vert + 1</math>, and <math>x^2 + y^2 = 9</math>.
@@ Line 26: / Line 26: @@
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-! Step 2:
+! Step 2: &nbsp;
 |-
 |Now that we have graphed both functions we need to know which region to shade with respect to each graph.
@@ Line 44: / Line 44: @@
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-! Final Answer:
+! Final Answer: &nbsp;
 |-
 |The final solution is the portion of the graph that below <math>y = \vert x\vert + 1</math> and inside <math> x^2 + y^2 = 9</math>

008A Sample Final A, Question 5 - Revision history

MathAdmin at 19:22, 2 June 2015

MathAdmin at 06:52, 26 May 2015

MathAdmin at 06:13, 23 May 2015

MathAdmin at 06:13, 23 May 2015

MathAdmin at 21:45, 28 April 2015

MathAdmin at 21:44, 28 April 2015

MathAdmin: Created page with "'''Question: '''Graph the system of inequalities y < \vert x\vert +1 x^2 + y^2 \le 9 {| class="mw-collapsible mw..."

MathAdmin: Created page with "'''Question: '''Graph the system of inequalities $y < \vert x\vert +1$ $x^2 + y^2 \le 9$ {| class="mw-collapsible mw..."