a) To find the width of triangle at depth y is f ( y ) = y 2 .

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Answer 1

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Chapter 9.3, Problem 5E

To determine

a)

To find the width of triangle at depth $y$ is $f (y) = \frac{y}{2} .$

To determine

b)

To find out the thin strip of thickness $Δ y$ at depth $y$ .Explain why the fluid force on a side of this strip is approximation equal to $ρ g \frac{1}{2} y^{2} Δ y$

To determine

c)

To find out an approximation for the total fluid force $F$ on a side of the plate as a Riemann sum and indicate the integral to which it converges.

To determine

d)

To calculate $F$ .

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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.)

Rama/Shutterstock.com Romaset/Shutterstock.com 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

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Answer 2

Question

Chapter 9.3, Problem 5E

To determine

a)

To find the width of triangle at depth $y$ is $f (y) = \frac{y}{2} .$

To determine

b)

To find out the thin strip of thickness $Δ y$ at depth $y$ .Explain why the fluid force on a side of this strip is approximation equal to $ρ g \frac{1}{2} y^{2} Δ y$

To determine

c)

To find out an approximation for the total fluid force $F$ on a side of the plate as a Riemann sum and indicate the integral to which it converges.

To determine

d)

To calculate $F$ .

Expert Solution & Answer

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Answer 3

Question

Chapter 9.3, Problem 5E

To determine

a)

To find the width of triangle at depth $y$ is $f (y) = \frac{y}{2} .$

To determine

b)

To find out the thin strip of thickness $Δ y$ at depth $y$ .Explain why the fluid force on a side of this strip is approximation equal to $ρ g \frac{1}{2} y^{2} Δ y$

To determine

c)

To find out an approximation for the total fluid force $F$ on a side of the plate as a Riemann sum and indicate the integral to which it converges.

To determine

d)

To calculate $F$ .

Expert Solution & Answer

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See solution

Answer 4

Question

Chapter 9.3, Problem 5E

To determine

a)

To find the width of triangle at depth $y$ is $f (y) = \frac{y}{2} .$

To determine

b)

To find out the thin strip of thickness $Δ y$ at depth $y$ .Explain why the fluid force on a side of this strip is approximation equal to $ρ g \frac{1}{2} y^{2} Δ y$

To determine

c)

To find out an approximation for the total fluid force $F$ on a side of the plate as a Riemann sum and indicate the integral to which it converges.

To determine

d)

To calculate $F$ .

Expert Solution & Answer

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See solution

Answer 5

Chapter 9.3, Problem 5E

To determine

a)

To find the width of triangle at depth $y$ is $f (y) = \frac{y}{2} .$

To determine

b)

To find out the thin strip of thickness $Δ y$ at depth $y$ .Explain why the fluid force on a side of this strip is approximation equal to $ρ g \frac{1}{2} y^{2} Δ y$

To determine

c)

To find out an approximation for the total fluid force $F$ on a side of the plate as a Riemann sum and indicate the integral to which it converges.

To determine

d)

To calculate $F$ .

Answer 6

Chapter 9.3, Problem 5E

To determine

a)

To find the width of triangle at depth $y$ is $f (y) = \frac{y}{2} .$

Answer 7

Chapter 9.3, Problem 5E

To determine

a)

To find the width of triangle at depth $y$ is $f (y) = \frac{y}{2} .$

Answer 8

To determine

b)

To find out the thin strip of thickness $Δ y$ at depth $y$ .Explain why the fluid force on a side of this strip is approximation equal to $ρ g \frac{1}{2} y^{2} Δ y$

Answer 9

To determine

b)

To find out the thin strip of thickness $Δ y$ at depth $y$ .Explain why the fluid force on a side of this strip is approximation equal to $ρ g \frac{1}{2} y^{2} Δ y$

Answer 10

To determine

c)

To find out an approximation for the total fluid force $F$ on a side of the plate as a Riemann sum and indicate the integral to which it converges.

Answer 11

To determine

c)

To find out an approximation for the total fluid force $F$ on a side of the plate as a Riemann sum and indicate the integral to which it converges.

Answer 12

To determine

d)

To calculate $F$ .

Answer 13

To determine

d)

To calculate $F$ .

Answer 14

Expert Solution & Answer

Answer 15

Expert Solution & Answer

Answer 16

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Answer 17

Ch. 9.1 - Prob. 1PQ Ch. 9.1 - Prob. 2PQ Ch. 9.1 - Prob. 3PQ Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E

a) To find the width of triangle at depth y is f ( y ) = y 2 .

Solution Summary: The author explains how the solution obtained for y is f (y) = Y 2 and the approximation for the total fluid force F on a side of the plate.

Videos

a)

To find the width of triangle at depth $y$ is $f (y) = \frac{y}{2} .$

b)

To find out the thin strip of thickness $Δ y$ at depth $y$ .Explain why the fluid force on a side of this strip is approximation equal to $ρ g \frac{1}{2} y^{2} Δ y$

c)

To find out an approximation for the total fluid force $F$ on a side of the plate as a Riemann sum and indicate the integral to which it converges.

d)

To calculate $F$ .

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Chapter 9 Solutions

a) To find the width of triangle at depth y is f ( y ) = y 2 .

Solution Summary: The author explains how the solution obtained for y is f (y) = Y 2 and the approximation for the total fluid force F on a side of the plate.

Videos