Plese i in this exam,its a challenge.

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The discussion revolves around a request for help with calculating the curvature of the curve defined by the parametric equation r(t) = ti + t^(3/2) j for t > 0. The user expresses urgency due to an upcoming exam and indicates difficulty in finding a solution. A response encourages the user to recall the formula for curvature based on the given parametrization. The conversation highlights the importance of understanding the underlying equations for effective problem-solving in calculus. The focus remains on providing guidance for the curvature calculation.
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Homework Statement



i need help in solving this,coz i have an exam tomorrow,please help me,i search everywhere and i didnt know how to do it

Homework Equations


find the curvature of the fowloing curve
r(t)= t i +t^3/2 j , t>0


The Attempt at a Solution

 
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Welcome to PF shishi.
I assume that you have learned how to calculate the curvature of a curve. If you are given a parametrization r(t), then what is the formula for the curvature?
 
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Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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