c3cd3027-6cfc-4ea7-92ee-55dfdb95fb6d.html

<h4>Activity</h4>
<p>In your group, work through your assigned problem. Then be ready to share.</p>
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    <p><strong>Group 1.</strong> When Raoul runs on the treadmill at the gym, the number of calories, \( c \), he burns varies directly with the number of minutes, \( m \), he uses the treadmill. He burned 315 calories when he used the treadmill for 18 minutes. Write the equation that relates \( c \) and \( m \).&nbsp;</p>
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    <p>Enter your answer here:</p>
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    <p>Compare your answer:</p>
    <p>\(c=17.5m\)</p>
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    <p><strong>Group 2.</strong> The number of calories, \( c \), burned varies directly with the amount of time, \( t \), spent exercising. Arnold burned 312 calories in 65 minutes exercising. Write the equation that relates \( c \) and \( t \).</p>
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    <p>Enter your answer here:</p>
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    <p>Compare your answer:</p>
    <p>\(c = 4.8 m\)</p>
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    <p><strong>Group 3.</strong> The distance a moving body travels, \( d \), varies directly with time, \( t \), it moves. A train travels 100 miles in 2 hours. Write the equation that relates \( d \) and \( t \).</p>
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    <p>Enter your answer here:</p>
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    <p>Compare your answer:</p>
    <p>\(d=50t\)</p>
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<h4>What is Direct Variation?</h4>
<p>All of these are examples of direct variation.</p>
<p>Two variables vary directly if one is the product of a constant and the other.</p>
<p>For any two variables \(x\) and \( y \), \( y \) varies directly with \( x \) if&nbsp;</p>
<p>\( y=kx \), where \( k&ne;0 \).</p>
<p> The constant \(k\) is called the constant of variation.</p>
<p>Look back at the problem you solved. Use the direct variation equation to solve it again using these steps:<br>
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  <p><strong>Step 1</strong> - Write the equation for direct variation.</p>
  <p><strong>Step 2</strong> - Substitute the given values for the variables.</p>
  <p><strong>Step 3</strong> - Solve for the constant of variation.</p>
  <p><strong>Step 4 </strong>- Write the equation that relates x and y using the constant of variation.</p>
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<p>Let&rsquo;s look at example 3 again and solve it with the direct variation equation.</p>
<p>The distance a moving body travels, \( d \), varies directly with time, \( t \), it moves. A train travels 100 miles in 2 hours. Write the equation that relates \( d \) and \( t \).</p>
<p><strong>Step 1 </strong>- Write the equation for direct variation.<br>
  \( y = kx \)</p>
<p><strong>Step 2</strong> - Substitute the given values for the variables.<br>
  \( 100 = k(2) \)</p>
<p><strong>Step 3</strong> - Solve for the constant of variation.<br>
  \( k=50 \)</p>
<p><strong>Step 4</strong> - Write the equation that relates x and y using the constant of variation.<br>
  \( y =50x \)</p>
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