Let b be a rigid body rotating about the z-axis. the rotation can be described by the vector w = ωk, where ω is the angular speed of b, that is, the tangential speed of any point p in b divided by the distance d from the axis of rotation. let r = x, y, z be the position vector of p.

Which statement explains how you could use coordinate geometry to prove the opposite sides of a quadrilateral are congruent? a. use the slope formula to prove the slopes of the opposite sides are the same. b. use the slope formula to prove the slopes of the opposite sides are opposite reciprocals. c. use the distance formula to prove the lengths of the opposite sides are the same. d. use the distance formula to prove the midpoints of the opposite sides are the same.

Can someone plz me understand how to do these. plz, show work. in exercises 1-4, rewrite the expression in rational exponent form.[tex]\sqrt[4]{625} \sqrt[3]{512} (\sqrt[5]{4} )³ (\sqrt[4]{15} )^{7}\\ (\sqrt[3]{27} )^{2}[/tex]

If johnny ate 5 cans of sugar, but in the kitchen they only had 3. what did johnny eat? (he found a secret stash btw.)