Suppose we want to choose 3 colors, without replacement, from the 4 colors red, blue, green, and purple.

(a) How many ways can this be done, if the order of the choices matters?

(b) How many ways can this be done, if the order of the choices does not matter?

Find the arc length parameter along the given curve from the point where tequals=0 by evaluating the integral s(t)equals=integral from 0 to t startabsolutevalue bold v left parenthesis tau right parenthesis endabsolutevalue d tau∫0tv(τ) dτ. then find the length of the indicated portion of the curve r(t)equals=1010cosine tcost iplus+1010sine tsint jplus+88t k, where 0less than or equals≤tless than or equals≤startfraction pi over 3 endfraction π 3.

Pat listed all the numbers that have 15 as a multiple write the numbers in pats list

Solve the following simultaneous equation by using an algebraic method (either substitution or elimination) 2x + 3y=-4 4x-y=11