Calculus: Single And Multivariable
7th Edition
ISBN: 9781119444190
Author: Hughes-Hallett, Deborah; Mccallum, William G.; Gleason, Andrew M.; Connally, Eric; Kalaycioglu, Selin; Flath, Daniel E.; Lahme, Brigitte; Lomen, David O.; Lock, Patti Frazer; Lovelock, David; Morris, Jerry; Lozano, Guadalupe I.; Mumford, David; Quinney, D
Publisher: WILEY
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Chapter 5.1, Problem 1E
Figure 5.11 shows the velocity of a car for 0 ≤ t ≤ 12 and the rectangles used to estimate the distance traveled.
- (a) Do the rectangles represent a left or a right sum?
- (b) Do the rectangles lead to an upper or a lower estimate?
- (c) What is the value of n?
- (d) What is the value of Δt?
- (e) Give an approximate value for the estimate.
Figure 5.11
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Consider the region below f(x) = (11-x), above the x-axis, and between x = 0 and x = 11. Let x; be the midpoint of the ith subinterval. Complete parts a. and b. below.
a. Approximate the area of the region using eleven rectangles. Use the midpoints of each subinterval for the heights of the rectangles.
The area is approximately square units. (Type an integer or decimal.)
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The power station has three different hydroelectric turbines, each with a known (and unique)
power function that gives the amount of electric power generated as a function of the water
flow arriving at the turbine. The incoming water can be apportioned in different volumes to
each turbine, so the goal of this project is to determine how to distribute water among the
turbines to give the maximum total energy production for any rate of flow.
Using experimental evidence and Bernoulli's equation, the following quadratic models were
determined for the power output of each turbine, along with the allowable flows of operation:
6
KW₁ = (-18.89 +0.1277Q1-4.08.10 Q) (170 - 1.6 · 10¯*Q)
KW2 = (-24.51 +0.1358Q2-4.69-10 Q¹²) (170 — 1.6 · 10¯*Q)
KW3 = (-27.02 +0.1380Q3 -3.84-10-5Q) (170 - 1.6-10-ºQ)
where
250 Q1 <1110, 250 Q2 <1110, 250 <3 < 1225
Qi = flow through turbine i in cubic feet per second
KW
=
power generated by turbine i in kilowatts
Hello! Please solve this practice problem step by step thanks!
Chapter 5 Solutions
Calculus: Single And Multivariable
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