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:

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1

step-by-step explanation:

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