A particle moves along a line so that its velocity at time t is v(t) = t2 − t − 20
(measured in meters per second).
(a) Find the displacement of the particle during
3 ≤ t ≤ 10.

(b) Find the distance traveled during this time period.

step-by-step explanation:

b. 153 students do not participate in sports and seventy-five 12th graders were surveyed

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b