Bottled Water Sales (Compare Exercise 46 in Section 6.3.) The rate of U.S. per capita sales of bottled water for the period 2007–2014 can be approximated by s ( t ) = 0.25 t 2 − t + 29 gallons per year ( 0 ≤ t ≤ 7 ) , where t is time in years since the start of 2007. Use a definite integral to estimate the total U.S. per capita sales of bottled water from the start of 2008 to the start of 2012. (Round your answer to the nearest gallon.)
Bottled Water Sales (Compare Exercise 46 in Section 6.3.) The rate of U.S. per capita sales of bottled water for the period 2007–2014 can be approximated by s ( t ) = 0.25 t 2 − t + 29 gallons per year ( 0 ≤ t ≤ 7 ) , where t is time in years since the start of 2007. Use a definite integral to estimate the total U.S. per capita sales of bottled water from the start of 2008 to the start of 2012. (Round your answer to the nearest gallon.)
Solution Summary: The author calculates the total sales of bottled water per capita between 2008 and 2012 based on the Fundamental Theorem of Calculus.
Bottled Water Sales (Compare Exercise 46 in Section 6.3.) The rate of U.S. per capita sales of bottled water for the period 2007–2014 can be approximated by
s
(
t
)
=
0.25
t
2
−
t
+
29
gallons per year
(
0
≤
t
≤
7
)
,
where t is time in years since the start of 2007. Use a definite integral to estimate the total U.S. per capita sales of bottled water from the start of 2008 to the start of 2012. (Round your answer to the nearest gallon.)
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
2. Find a matrix A with the following qualities
a. A is 3 x 3.
b. The matrix A is not lower triangular and is not upper triangular.
c. At least one value in each row is not a 1, 2,-1, -2, or 0
d. A is invertible.
Find the exact area inside r=2sin(2\theta ) and outside r=\sqrt(3)
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