Finding t for Parametric Equations

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To evaluate the line integral of the function along the specified line segment, the parametric equations x = 4t, y = 3 + 2t, and z = 5 + 2t are established. The value of t can be determined by substituting the coordinates of the starting point (0, 3, 5) into the equations, leading to t = 0. This allows for the evaluation of the integral over the defined path. The discussion highlights the importance of understanding how to derive t from the parametric equations to solve the integral correctly. The problem is resolved once the correct value of t is identified.
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Evaluate the line integral \int x^5*z*ds where C is the line segment from (0,3,5) to (4,5,7)

so first thing i did was found the parametric equations
the parametric equations are:
x= 4t
y= 3+2t
z= 5+2t

how do i find out what t is? i totally forgot how to do that and i can't seem to find it in the book because it's so easy they don't bother to explain it. i can solve the problem if i know what t is, so help me if you can. thanks in advance
 
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Surely you can figure out what t is when, say, (x, y, z) = (0, 3, 5)?
 
lol ah thanks alot, i got it
 
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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