Following problems are from chapter 45 1 Locate three points

Following problems are from chapter 4.5.

1. Locate three points that are red labeled on the graph and find the quadratic equation.
Hint: One point can be obtained with the hint given in the problem as “lowest point is 15 feet above the roadway”. Other two points can be obtained using the symmetry feature.
Take the roadway as x-axis and having x-axis the axis of symmetry find the other points as labeled on the figure.

2. The annual rainfall R, in inches, in a particular region in year t since the start of the last century can be modeled by the formula R (t) = -0.03t2 + 1.9t + 45. Find the total rainfall from 1900 (when t = 0) through 2000 in that region. Hint: Be careful, t starts from 0.

Solution

first question doesnot have figure givenn

2)given annual  rainfall modeled by the formula R (t) = -0.03t² + 1.9t + 45

t =0 in 1900year

t =2000-1900=100 in 2000year

the total rainfall from 1900 (when t = 0) through 2000 in that region =_{[0 to 100]}R(t) dt

total rainfall=_{[0 to 100]} -0.03t² + 1.9t + 45 dt

total rainfall=_{[0 to 100]} (-0.03/3)t³ + (1.9/2)t² + 45t

total rainfall=_{[0 to 100]} (-0.01)t³ + (1.9/2)t² + 45t

total rainfall=(-0.01)100³ + (1.9/2)100² + 45*100 -0

total rainfall=4000 inches