Power Law Equation Help: Solving for v with x=0.02 | Homework Equations

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SUMMARY

The discussion centers on solving the equation v(x) = 47.8 ⋅ (0.451/x)^(5.39) for v when x is given as 0.02. Participants clarify that to find v(0.02), one simply substitutes 0.02 into the equation without needing to manipulate it further. The confusion arises from the misunderstanding of the term "solve for v," which in this case does not require additional steps since v is already isolated. Logarithmic methods are suggested for solving for x, not for v.

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Adam_9333
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Homework Statement


need to solve for v? I also know the value of x=0.02

Homework Equations


v(x)= 47.8 ⋅ (0.451/x)^(5.39)

The Attempt at a Solution


how do I take the log of both sides, is that the right approach to solve for v?
 
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Apply the product rule then the power rule.
 
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But, if you already know x, you don't have anything to solve. Just put .02 in for x and evaluate.
 
I am little confused, my calculus skills stayed in first year. Do put 0.02 in the x term on the left side of the equation also, and just solve for V?
 
Adam_9333 said:
I am little confused, my calculus skills stayed in first year. Do put 0.02 in the x term on the left side of the equation also, and just solve for V?
You didn't state the problem accurately, but if it's asking you to determine v(0.02), then all you have to do is to replace the x on the right by 0.02 and perform the computations. To "solve for v" would be to find an equivalent equation with v alone on one side, but the equation is already of that form, so what you need to do to solve for v is nothing at all.

Adam_9333 said:
how do I take the log of both sides, is that the right approach to solve for v?
That would be a good approach if you wanted to solve for x.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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