1) average velocity = (v(8) - v(0))/(8 - 0) = (10 - 18)/8 = -1m/s

2) v(5) = 5^2 - 9(5) + 18 = 25 - 45 + 18 = -2m/s

3) set v(t) = 0

t^2 - 9t + 18 = 0

(t - 6)(t - 3) = 0

t = 6 t = 3

when 0
4) find the acceleration function

a(t) = 2t - 9

2t - 9 = 0

2t = 9

t = 9/2

when 0
5) int(t^2 -9t + 18) = (t^3)/3 - (9t^2)/2 + 18t + c

s(0) = 1

s(t) = (t^3)/3 - (9t^2)/2 + 18t + 1

now we use the 3 intervals in part 3 to find the total distance

s(3) - s(0) = (9 - 81/2 + 54 + 1) - 1 = 45/2
s(6) - s(3) = ( 72 -162 + 108 + 1) - 47/2 = -9/2
s(8) - s(6) = (512/3 - 288 + 144 + 1) - 19 = 26/3

all distances are scalar quantities so they are positive

45/2 + 9/2 + 26/3 = 107/3 meters

is this correct?

Abanner is made of a square and a semicircle. the square has side lengths of 24 inches. one side of the square is also the diameter of the semicircle. what is the total area of the banner? use 3.14 for π.

F(x)=x/2-2 and g(x)=2x^2+x-3 find (f+g)(x)

Apsychology student wishes to investigate differences in political opinions between business majors and political science majors at her college. she randomly selects 100 students from the 260 business majors and 100 students from the 180 political science majors. does this sampling plan result in a simple random sample? why or why not? no, because each group of 200 students in the sample does not have the same chance of being selected. yes, because each group of 200 students in the sample has the same chance of being selected. no, because each individual student does not have an equal chance of being selected. yes, because each individual student has the same chance of being selected.