The rate of a country's per capita sales of bottled water for the period 2007–2014 could be approximated by s(t) = 0.29t2 − t + 25 gallons per year (0 ≤ t ≤ 7), where t is time in years since the start of 2007. Use a Riemann sum with n = 5 to estimate the total country's per capita sales of bottled water from the start of 2008 to the start of 2012. (Use a left Riemann sum to find your answer. Round your answer to the nearest gallon.) HINT [See Example 2.]

Step-by-step explanation:

Then, Riemann sum with n = 5 for the function described in the statement is:

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is