SOLUTION: Please help me solve this word problem of variation. The volume rate of flow R of blood through an artery varies directly as the fourth power of the radius r of the artery and inve

Question 623150: Please help me solve this word problem of variation. The volume rate of flow R of blood through an artery varies directly as the fourth power of the radius r of the artery and inversly as the distance d along the artery. If an operation is successful in effectively increasing the radius of an artery by 25% and decreasing its length by 2%, by how much is the volume rate of flow increased?
Found 2 solutions by Alan3354, ankor@dixie-net.com:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
The volume rate of flow R of blood through an artery varies directly as the fourth power of the radius r of the artery and inversly as the distance d along the artery. If an operation is successful in effectively increasing the radius of an artery by 25% and decreasing its length by 2%, by how much is the volume rate of flow increased?
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Use F1 for flow, F2 for flow after surgery, r for radius & L for length
F1 = k*r^4*L
--> F2 = k*(1.25r)^4/(0.98L)
F2 =~ k*2.4414/0.98r^4*L
F2/F1 =~ 2.4912
Increase = F2/F - 1
= 1.4912
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It's 2.49 times the original
Increased 1.49 times the original, a 149% increase.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Write a proportion equation for each statement
:
"The volume rate of flow R of blood through an artery varies directly as the fourth power of the radius r of the artery and inversely as the distance d along the artery."
R =
:
"If an operation is successful in effectively increasing the radius of an artery by 25% and decreasing its length by 2%, by how much is the volume rate of flow increased?
:
Assuming the radius and the dist were both 1, we have
R = =
R = 2.49 * 100 = 249% increase in blood flow

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