Let 
, so that differentiating both sides wrt 
gives
If 
and 
, the above reduces to
This is the slope of the tangent line, which has equation
<em>The answer is 25.12 exactly</em>
Et x = the volume of the 3.5% solution
<span>Let y = the volume 6% solution </span>
<span>(3.5%)x + (6%)y = (4.5%)(200) </span>
<span>0.035)x + 0.06y = 0.045(200) </span>
<span>0.035x + 0.06y = 9 ( Equation 1 )</span>
<span>x + y = 200 ( Equation 2 )</span>
<span>x = 200 - y </span>
<span>Substitute x = 200 - y into equation 1: </span>
<span>0.035x + 0.06y = 9 </span>
<span>0.035(200 - y) + 0.06y = 9 </span>
<span>7 - 0.035y + 0.06y = 9 </span>
<span>0.06y - 0.035y = 9 - 7 </span>
<span>0.025y = 2 </span>
<span>y = 2/(0.025) </span>
<span>y = 80 mL (the volume of 6% solution.)</span>
<span>Substitute y = 80 into equation 2: </span>
<span>x + y = 200 </span>
<span>x + 80 = 200 </span>
<span>x = 200 - 80 </span>
<span>x = 120 mL (the volume of the 3.5% solution.)</span>
<span>Therefore, Mr. Larson should combine 120 mL of the 3.5% solution </span>
<span>and 80 mL of the 6% solution to make 200 mL of 4.5% solution. </span>
<span>Answer is 120 mL of the 3.5% solution & 80 mL of the 6% solution
Hope I helped :)</span>
Answer:
10
Step-by-step explanation:
12/2=6+4=10
