a. Answer The velocity of blood flow when t = 0.4 is 4440 cm/sec and t = 0.4 is 1665 cm/sec . Explanation Given: The particular equation is, v ( t ) = 18500 ( 0.25 − r 2 ) on the interval 0 ≤ r ≤ 0.5 Calculation: Plug t = 0.1 in v ( t ) = 18500 ( 0.25 − r 2 ) v ( 0.1 ) = 18500 ( 0.25 − ( 0.1 ) 2 ) v ( 0.1 ) = 4440 cm/sec Plug t = 0.4 in v ( t ) = 18500 ( 0.25 − r 2 ) v ( 0.4 ) = 18500 ( 0.25 − ( 0.4 ) 2 ) v ( 0.4 ) = 1665 cm/sec Thus, the velocity of blood flow when t = 0.4 is 4440 cm/sec and t = 0.4 is 1665 cm/sec . b. To determine To explain the blood moves through a vein or an artery for the answers found in part a. Answer The blood moves through a vein or an artery of radius 0.1 cm at velocity of 4440 cm/sec while it moves through a vein or an artery of radius 0.4 cm at velocity of 1665 cm/sec . Explanation It means that the blood moves through a vein or an artery of radius 0.1 cm at velocity of 4440 cm/sec while it moves through a vein or an artery of radius 0.4 cm at velocity of 1665 cm/sec . c. To determine To determine the values of blood flow velocities for different values of r . Answer The values of v ( t ) = 18500 ( 0.25 − r 2 ) for r = 0 , 0.1 , 0.2 , 0.3 , 0.4 , 0.5 is shown in table as shown below: r cm v ( t ) cm / sec 0 4625 0.1 4440 0.2 3885 0.3 2960 0.4 1665 0.5 0 Explanation Given: v ( t ) = 18500 ( 0.25 − r 2 ) on the interval 0 ≤ r ≤ 0.5 Calculation: Plug r = 0 in v ( t ) = 18500 ( 0.25 − r 2 ) then, v ( 0 ) = 18500 ( 0.25 − 0 2 ) = 18500 ( 0.25 ) = 4625 Plug r = 0.1 in v ( t ) = 18500 ( 0.25 − r 2 ) then, v ( 0.1 ) = 18500 ( 0.25 − 0.1 2 ) = 18500 ( 0.25 − 0.01 ) = 18500 ( 0.24 ) = 4440 Plug r = 0.2 in v ( t ) = 18500 ( 0.25 − r 2 ) then, v ( 0.2 ) = 18500 ( 0.25 − 0.2 2 ) = 18500 ( 0.25 − 0.04 ) = 18500 ( 0.21 ) = 3885 Plug r = 0.3 in v ( t ) = 18500 ( 0.25 − r 2 ) then, v ( 0.3 ) = 18500 ( 0.25 − 0.3 2 ) = 18500 ( 0.25 − 0.09 ) = 18500 ( 0.16 ) = 2960 Plug r = 0.4 in v ( t ) = 18500 ( 0.25 − r 2 ) then, v ( 0.4 ) = 18500 ( 0.25 − 0.4 2 ) = 18500 ( 0.25 − 0.16 ) = 18500 ( 0.09 ) = 1665 Plug r = 0.5 in v ( t ) = 18500 ( 0.25 − r 2 ) then, v ( 0.5 ) = 18500 ( 0.25 − 0.5 2 ) = 18500 ( 0.25 − 0.25 ) = 18500 ( 0 ) = 0 The values of v ( t ) = 18500 ( 0.25 − r 2 ) for r = 0 , 0.1 , 0.2 , 0.3 , 0.4 , 0.5 is shown in table as shown below: r cm v ( t ) cm / sec 0 4625 0.1 4440 0.2 3885 0.3 2960 0.4 1665 0.5 0

6th Edition

ISBN: 9781133715047

Author: Watson

Publisher: YUZU

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Differential Equations

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Question

Chapter 2.1, Problem 73E

To determine

To find the velocity of blood flow using the equation : v(t)=18500(0.25−r2) on the interval 0≤r≤0.5

Expert Solution

Answer to Problem 73E

The velocity of blood flow when t=0.4 is 4440cm/sec and t=0.4 is 1665cm/sec .

Explanation of Solution

Given: The particular equation is,

v(t)=18500(0.25−r2) on the interval 0≤r≤0.5

Calculation:

Plug t=0.1 in v(t)=18500(0.25−r2)

v(0.1)=18500(0.25−(0.1)2)v(0.1)=4440cm/sec

Plug t=0.4 in v(t)=18500(0.25−r2)

v(0.4)=18500(0.25−(0.4)2)v(0.4)=1665cm/sec

Thus, the velocity of blood flow when t=0.4 is 4440cm/sec and t=0.4 is 1665cm/sec .

To determine

To explain the blood moves through a vein or an artery for the answers found in part a.

Expert Solution

Answer to Problem 73E

The blood moves through a vein or an artery of radius 0.1cm at velocity of 4440cm/sec while it moves through a vein or an artery of radius 0.4cm at velocity of 1665cm/sec .

Explanation of Solution

It means that the blood moves through a vein or an artery of radius 0.1cm at velocity of 4440cm/sec while it moves through a vein or an artery of radius 0.4cm at velocity of 1665cm/sec .

To determine

To determine the values of blood flow velocities for different values of r .

Expert Solution

Answer to Problem 73E

The values of v(t)=18500(0.25−r2) for r=0,0.1,0.2,0.3,0.4,0.5 is shown in table as shown below:

r cmv(t)cm/sec046250.144400.238850.329600.416650.50

Explanation of Solution

Given:

v(t)=18500(0.25−r2) on the interval 0≤r≤0.5

Calculation:

Plug r=0 in v(t)=18500(0.25−r2) then,

v(0)=18500(0.25−02)=18500(0.25)=4625

Plug r=0.1 in v(t)=18500(0.25−r2) then,

v(0.1)=18500(0.25−0.12)=18500(0.25−0.01)=18500(0.24)=4440

Plug r=0.2 in v(t)=18500(0.25−r2) then,

v(0.2)=18500(0.25−0.22)=18500(0.25−0.04)=18500(0.21)=3885

Plug r=0.3 in v(t)=18500(0.25−r2) then,

v(0.3)=18500(0.25−0.32)=18500(0.25−0.09)=18500(0.16)=2960

Plug r=0.4 in v(t)=18500(0.25−r2) then,

v(0.4)=18500(0.25−0.42)=18500(0.25−0.16)=18500(0.09)=1665

Plug r=0.5 in v(t)=18500(0.25−r2) then,

v(0.5)=18500(0.25−0.52)=18500(0.25−0.25)=18500(0)=0

The values of v(t)=18500(0.25−r2) for r=0,0.1,0.2,0.3,0.4,0.5 is shown in table as shown below:

r cmv(t)cm/sec046250.144400.238850.329600.416650.50

Chapter 2.1, Problem 72E

Chapter 2.1, Problem 74E

Chapter 2 Solutions

EBK PRECALCULUS: MATHEMATICS FOR CALCUL

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Prob. 87E Ch. 2.5 - Prob. 88E Ch. 2.5 - Prob. 89E Ch. 2.5 - Prob. 90E Ch. 2.5 - Prob. 91E Ch. 2.5 - Prob. 92E Ch. 2.5 - Prob. 93E Ch. 2.6 - From the graphs of f and g in the figure, we find...Ch. 2.6 - By definition, (f g)(x) = _____. So if g(2) = 5...Ch. 2.6 - If the rule of the function f is add one and the...Ch. 2.6 - We can express the functions in Exercise 3...Ch. 2.6 - Prob. 5E Ch. 2.6 - Prob. 6E Ch. 2.6 - Prob. 7E Ch. 2.6 - Prob. 8E Ch. 2.6 - Prob. 9E Ch. 2.6 - Prob. 10E Ch. 2.6 - Prob. 11E Ch. 2.6 - Prob. 12E Ch. 2.6 - Prob. 13E Ch. 2.6 - Prob. 14E Ch. 2.6 - Prob. 15E Ch. 2.6 - Prob. 16E Ch. 2.6 - Prob. 17E Ch. 2.6 - Prob. 18E Ch. 2.6 - Prob. 19E Ch. 2.6 - Prob. 20E Ch. 2.6 - Prob. 21E Ch. 2.6 - Prob. 22E Ch. 2.6 - Prob. 23E Ch. 2.6 - Prob. 24E Ch. 2.6 - Prob. 25E Ch. 2.6 - Prob. 26E Ch. 2.6 - Prob. 27E Ch. 2.6 - Prob. 28E Ch. 2.6 - Prob. 29E Ch. 2.6 - Prob. 30E Ch. 2.6 - Prob. 31E Ch. 2.6 - Prob. 32E Ch. 2.6 - Prob. 33E Ch. 2.6 - Prob. 34E Ch. 2.6 - Prob. 35E Ch. 2.6 - Prob. 36E Ch. 2.6 - Prob. 37E Ch. 2.6 - Prob. 38E Ch. 2.6 - Prob. 39E Ch. 2.6 - Prob. 40E Ch. 2.6 - Prob. 41E Ch. 2.6 - Prob. 42E Ch. 2.6 - Prob. 43E Ch. 2.6 - Prob. 44E Ch. 2.6 - Prob. 45E Ch. 2.6 - Prob. 46E Ch. 2.6 - Prob. 47E Ch. 2.6 - Prob. 48E Ch. 2.6 - Prob. 49E Ch. 2.6 - Prob. 50E Ch. 2.6 - Prob. 51E Ch. 2.6 - Prob. 52E Ch. 2.6 - Prob. 53E Ch. 2.6 - Prob. 54E Ch. 2.6 - Prob. 55E Ch. 2.6 - Prob. 56E Ch. 2.6 - Prob. 57E Ch. 2.6 - Prob. 58E Ch. 2.6 - Prob. 59E Ch. 2.6 - Revenue, Cost, and Profit A print shop makes...Ch. 2.6 - Area of a Ripple A stone is dropped in a lake,...Ch. 2.6 - Inflating a Balloon A spherical balloon is being...Ch. 2.6 - Area of a Balloon A spherical weather balloon is...Ch. 2.6 - Multiple Discounts You have a 50 coupon from the...Ch. 2.6 - Multiple Discounts An appliance dealer advertises...Ch. 2.6 - Airplane Trajectory An airplane is flying at a...Ch. 2.6 - Prob. 67E Ch. 2.6 - Prob. 68E Ch. 2.6 - Prob. 69E Ch. 2.6 - Prob. 70E Ch. 2.7 - A function f is one-to-one if different inputs...Ch. 2.7 - (a) For a function to have an inverse, it must be...Ch. 2.7 - A function f has the following verbal description:...Ch. 2.7 - True or false? (a) If f has an inverse, then f1(x)...Ch. 2.7 - Prob. 5E Ch. 2.7 - Prob. 6E Ch. 2.7 - Prob. 7E Ch. 2.7 - Prob. 8E Ch. 2.7 - Prob. 9E Ch. 2.7 - Prob. 10E Ch. 2.7 - Prob. 11E Ch. 2.7 - Prob. 12E Ch. 2.7 - Prob. 13E Ch. 2.7 - Prob. 14E Ch. 2.7 - Prob. 15E Ch. 2.7 - Prob. 16E Ch. 2.7 - Prob. 17E Ch. 2.7 - Prob. 18E Ch. 2.7 - Prob. 19E Ch. 2.7 - Prob. 20E Ch. 2.7 - Prob. 21E Ch. 2.7 - Prob. 22E Ch. 2.7 - Prob. 23E Ch. 2.7 - Prob. 24E Ch. 2.7 - Prob. 25E Ch. 2.7 - Prob. 26E Ch. 2.7 - Prob. 27E Ch. 2.7 - Prob. 28E Ch. 2.7 - Prob. 29E Ch. 2.7 - Prob. 30E Ch. 2.7 - Prob. 31E Ch. 2.7 - Prob. 32E Ch. 2.7 - Prob. 33E Ch. 2.7 - Prob. 34E Ch. 2.7 - Prob. 35E Ch. 2.7 - Prob. 36E Ch. 2.7 - Prob. 37E Ch. 2.7 - Prob. 38E Ch. 2.7 - Prob. 39E Ch. 2.7 - Prob. 40E Ch. 2.7 - Prob. 41E Ch. 2.7 - Prob. 42E Ch. 2.7 - Prob. 43E Ch. 2.7 - Prob. 44E Ch. 2.7 - Prob. 45E Ch. 2.7 - Prob. 46E Ch. 2.7 - Prob. 47E Ch. 2.7 - Prob. 48E Ch. 2.7 - Prob. 49E Ch. 2.7 - Prob. 50E Ch. 2.7 - Prob. 51E Ch. 2.7 - Prob. 52E Ch. 2.7 - Prob. 53E Ch. 2.7 - Prob. 54E Ch. 2.7 - Prob. 55E Ch. 2.7 - Prob. 56E Ch. 2.7 - Prob. 57E Ch. 2.7 - Prob. 58E Ch. 2.7 - Prob. 59E Ch. 2.7 - Prob. 60E Ch. 2.7 - Prob. 61E Ch. 2.7 - Prob. 62E Ch. 2.7 - Prob. 63E Ch. 2.7 - Prob. 64E Ch. 2.7 - Prob. 65E Ch. 2.7 - Prob. 66E Ch. 2.7 - Prob. 67E Ch. 2.7 - Prob. 68E Ch. 2.7 - Prob. 69E Ch. 2.7 - Prob. 70E Ch. 2.7 - Prob. 71E Ch. 2.7 - Prob. 72E Ch. 2.7 - Prob. 73E Ch. 2.7 - Prob. 74E Ch. 2.7 - Prob. 75E Ch. 2.7 - Prob. 76E Ch. 2.7 - Prob. 77E Ch. 2.7 - Prob. 78E Ch. 2.7 - Prob. 79E Ch. 2.7 - Prob. 80E Ch. 2.7 - Fee for Service For his services, a private...Ch. 2.7 - Prob. 82E Ch. 2.7 - Prob. 83E Ch. 2.7 - Prob. 84E Ch. 2.7 - Prob. 85E Ch. 2.7 - Prob. 86E Ch. 2.7 - Income Tax In a certain country the tax on incomes...Ch. 2.7 - Prob. 88E Ch. 2.7 - Prob. 89E Ch. 2.7 - Prob. 90E Ch. 2.7 - Prob. 91E Ch. 2.7 - Prob. 92E Ch. 2.7 - Prob. 93E Ch. 2 - Prob. 1RCC Ch. 2 - Prob. 2RCC Ch. 2 - Prob. 3RCC Ch. 2 - Prob. 4RCC Ch. 2 - Prob. 5RCC Ch. 2 - Prob. 6RCC Ch. 2 - Prob. 7RCC Ch. 2 - Prob. 8RCC Ch. 2 - Prob. 9RCC Ch. 2 - Prob. 10RCC Ch. 2 - Prob. 11RCC Ch. 2 - Prob. 12RCC Ch. 2 - Prob. 1RE Ch. 2 - Prob. 2RE Ch. 2 - Prob. 3RE Ch. 2 - Prob. 4RE Ch. 2 - Prob. 5RE Ch. 2 - Prob. 6RE Ch. 2 - Prob. 7RE Ch. 2 - Prob. 8RE Ch. 2 - Prob. 9RE Ch. 2 - Prob. 10RE Ch. 2 - Prob. 11RE Ch. 2 - Prob. 12RE Ch. 2 - Prob. 13RE Ch. 2 - Prob. 14RE Ch. 2 - Prob. 15RE Ch. 2 - Prob. 16RE Ch. 2 - Prob. 17RE Ch. 2 - Prob. 18RE Ch. 2 - Prob. 19RE Ch. 2 - Prob. 20RE Ch. 2 - Prob. 21RE Ch. 2 - Prob. 22RE Ch. 2 - Prob. 23RE Ch. 2 - Prob. 24RE Ch. 2 - Prob. 25RE Ch. 2 - Prob. 26RE Ch. 2 - Prob. 27RE Ch. 2 - Prob. 28RE Ch. 2 - Prob. 29RE Ch. 2 - Prob. 30RE Ch. 2 - Prob. 31RE Ch. 2 - Prob. 32RE Ch. 2 - Prob. 33RE Ch. 2 - Prob. 34RE Ch. 2 - Prob. 35RE Ch. 2 - Prob. 36RE Ch. 2 - Prob. 37RE Ch. 2 - Prob. 38RE Ch. 2 - Prob. 39RE Ch. 2 - Prob. 40RE Ch. 2 - Prob. 41RE Ch. 2 - Prob. 42RE Ch. 2 - Prob. 43RE Ch. 2 - Prob. 44RE Ch. 2 - Prob. 45RE Ch. 2 - Prob. 46RE Ch. 2 - Prob. 47RE Ch. 2 - Prob. 48RE Ch. 2 - Prob. 49RE Ch. 2 - Prob. 50RE Ch. 2 - Prob. 51RE Ch. 2 - Prob. 52RE Ch. 2 - Prob. 53RE Ch. 2 - Prob. 54RE Ch. 2 - Prob. 55RE Ch. 2 - Prob. 56RE Ch. 2 - Prob. 57RE Ch. 2 - Prob. 58RE Ch. 2 - Prob. 59RE Ch. 2 - Prob. 60RE Ch. 2 - Prob. 61RE Ch. 2 - Prob. 62RE Ch. 2 - Prob. 63RE Ch. 2 - Prob. 64RE Ch. 2 - Prob. 65RE Ch. 2 - Prob. 66RE Ch. 2 - Prob. 67RE Ch. 2 - Prob. 68RE Ch. 2 - Prob. 69RE Ch. 2 - Prob. 70RE Ch. 2 - Prob. 71RE Ch. 2 - Prob. 72RE Ch. 2 - Prob. 73RE Ch. 2 - Prob. 74RE Ch. 2 - Prob. 75RE Ch. 2 - Prob. 76RE Ch. 2 - Prob. 77RE Ch. 2 - Prob. 78RE Ch. 2 - Prob. 79RE Ch. 2 - Prob. 80RE Ch. 2 - Prob. 81RE Ch. 2 - Prob. 82RE Ch. 2 - Prob. 83RE Ch. 2 - Prob. 84RE Ch. 2 - Prob. 85RE Ch. 2 - Prob. 86RE Ch. 2 - Prob. 87RE Ch. 2 - Prob. 88RE Ch. 2 - Prob. 89RE Ch. 2 - Prob. 90RE Ch. 2 - Prob. 91RE Ch. 2 - Prob. 92RE Ch. 2 - Prob. 1T Ch. 2 - Prob. 2T Ch. 2 - A function f has the following verbal description:...Ch. 2 - A school fund-raising group sells chocolate bars...Ch. 2 - Prob. 5T Ch. 2 - Prob. 6T Ch. 2 - Prob. 7T Ch. 2 - Prob. 8T Ch. 2 - Prob. 9T Ch. 2 - Prob. 10T Ch. 2 - Prob. 11T Ch. 2 - Prob. 12T Ch. 2 - Prob. 1P Ch. 2 - Prob. 2P Ch. 2 - Prob. 3P Ch. 2 - Prob. 4P Ch. 2 - Prob. 5P Ch. 2 - Prob. 6P Ch. 2 - Prob. 7P Ch. 2 - Prob. 8P Ch. 2 - Prob. 9P Ch. 2 - Prob. 10P Ch. 2 - Prob. 11P Ch. 2 - Length A woman 5 ft tall is standing near a street...Ch. 2 - Distance Two ships leave port at the same time....Ch. 2 - Prob. 14P Ch. 2 - Area An isosceles triangle has a perimeter of 8...Ch. 2 - Prob. 16P Ch. 2 - Area A rectangle is inscribed in a semicircle of...Ch. 2 - Height The volume of a cone is 100 in3. Find a...Ch. 2 - Prob. 19P Ch. 2 - Minimizing a Sum Find two positive numbers whose...Ch. 2 - Prob. 21P Ch. 2 - Dividing a Pen A rancher with 750 ft of fencing...Ch. 2 - Fencing a Garden Plot A property owner wants to...Ch. 2 - Maximizing Area A wire 10 cm long is cut into two...Ch. 2 - Light from a Window A Norman window has the shape...Ch. 2 - Volume of a Box A box with an open top is to be...Ch. 2 - Area of a Box An open box with a square base is to...Ch. 2 - Inscribed Rectangle Find the dimensions that give...Ch. 2 - Minimizing Costs A rancher wants to build a...Ch. 2 - Minimizing Time A man stands at a point A on the...Ch. 2 - Bird Flight A bird is released from point A on an...Ch. 2 - Area of a Kite A kite frame is to be made from six...

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