(a) If the particle's position (measured with some unit) at time <em>t</em> is given by <em>s(t)</em>, where

then the velocity at time <em>t</em>, <em>v(t)</em>, is given by the derivative of <em>s(t)</em>,

(b) The velocity after 3 seconds is

(c) The particle is at rest when its velocity is zero:

(d) The particle is moving in the positive direction when its position is increasing, or equivalently when its velocity is positive:

In interval notation, this happens for <em>t</em> in the interval (0, √11) or approximately (0, 3.317) s.
(e) The total distance traveled is given by the definite integral,

By definition of absolute value, we have

In part (d), we've shown that <em>v(t)</em> > 0 when -√11 < <em>t</em> < √11, so we split up the integral at <em>t</em> = √11 as

and by the fundamental theorem of calculus, since we know <em>v(t)</em> is the derivative of <em>s(t)</em>, this reduces to

Answer: 9
Explanation: you would use PEMDAS to solve the algebraic expression first by doing parentheses so subtract 8 and 7 which leaves you with 4 + 1 times 6-1. You would then multiply 1 into 6 which would leave you with 4 + 6 - 1 which you would then sum up 4 and 6 which leaves you with 10-1 which would give you the answer of 9
So the answer would be 9
Hope this helps!
Just square the top and bottom. z^2 over 25
2+1=3 is not an identity property. The rest are because the value equals itself after dividing, subtracting, and multiplying.