Find the arc length function for the curve y = 2x^3/2 with starting point p0(36, 432).

Step-by-step explanation:

When considering a curve defined by a function f(x) and its respective derivative f'(x) that are continuous in an interval [a, b], the length s of the arc delimited by a and b is given by the equation:

First, let's find the derivate of y(x):

Replacing the derivate in the previous equation:

Substitute u=1+9x and du=9x, so:

The antiderivative of is:

u=1+9x, so:

Evaluating the antiderivative at the limits:

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step-by-step explanation:

we have the parent function given by,

1. the function is translated 5 units to the left.

so, we get,   becomes

2. the function is translated 5 units to the right.

so, we get,   becomes

3. the function is translated 5 units upwards.

so, we get,   becomes

4. the function is translated 5 units downwards.

so, we get,   becomes

5. the function is reflected across x-axis.

so, we get,   becomes

6. the function is reflected across y-axis.

so, we get,   becomes .

step-by-step explanation:

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