Difference between revisions of "8A F11 Q5"

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(Created page with "'''Question: '''Graph the system of inequalities <math>y < \vert x\vert +1 </math>           <math>x^2 + y^2 \le 9</math>")
 
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'''Question: '''Graph the system of inequalities <math>y < \vert x\vert +1 </math> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; <math>x^2 + y^2 \le 9</math>
 
'''Question: '''Graph the system of inequalities <math>y < \vert x\vert +1 </math> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; <math>x^2 + y^2 \le 9</math>
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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
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! Foundations
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|1) What do the graphs of <math>y=\vert x\vert + 1</math>, and <math>x^2 + y^2 = 9</math> look like?
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|2) Each graph splits the plane into two regions. Which one do you want to shade?
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|-
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|Answer:
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|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.
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|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.
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|}
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Solution:
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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
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! Step 1:
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|-
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|The zeros of the left hand side are <math>-\frac{1}{2}</math>, 1, and 4
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|}

Revision as of 15:52, 22 March 2015

Question: Graph the system of inequalities           Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x^2 + y^2 \le 9}

Foundations
1) What do the graphs of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y=\vert x\vert + 1} , and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x^2 + y^2 = 9} 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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vert x\vert + 1} , shade below the V. For the circle shde the inside.

Solution:

Step 1:
The zeros of the left hand side are Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -\frac{1}{2}} , 1, and 4
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