Consider the solid obtained by rotating the region bounded by the given curves about the specified line. y=√√x-1, y = 0, x = 6; about the x-axis Set up an integral that can be used to determine the volume V of the solid. V= Find the volume of the solid. V = Sketch the region. y 7 6 5 4 3 2 dx y 가 199 6 6 5 5 3 2 X 2 3 5 6 7 10 1 Sketch the solid and a typical disk or washer. Graph Graph Description -7-6-5-4-3-2 122 3 O 2 3 4 5 6 7 X ⑪O 4 3 2 X 1 2 3 4 5 6 7 Graph Graph Description -7-6-5-4-3-2-1 O @O y 7- 9 5- 3 2 X 1 2 3 4 5 6 7 Graph Graph Description -7-6-5-4-3-2 6 3 2 O O Graph Graph Description 33 -7-6-5-4-3-2-1 122 The rate of growth of a fish population was modeled by the equation 90,000e-0.6t G(t) = = (1 + 5e-0.6r)², where t is measured in years since 2000 and G in kilograms per year. Write an integral to find the change in the population predicted between 2000 and 2020. 90,000e-0.6t 20 0 1 + 5e-0.6t Se-0.6t) 2 dt Find a substitution and apply it to rewrite the integrand in the form 1+5e-12 -30000 ✓ ) (+2) ()()~ 1 du 1 du. 2 6 If the biomass was 30,000 kg in the year 2000, what is the predicted biomass (in kg) for the year 2020? (Round your answer to the nearest whole number.) × kg 549999
Consider the solid obtained by rotating the region bounded by the given curves about the specified line. y=√√x-1, y = 0, x = 6; about the x-axis Set up an integral that can be used to determine the volume V of the solid. V= Find the volume of the solid. V = Sketch the region. y 7 6 5 4 3 2 dx y 가 199 6 6 5 5 3 2 X 2 3 5 6 7 10 1 Sketch the solid and a typical disk or washer. Graph Graph Description -7-6-5-4-3-2 122 3 O 2 3 4 5 6 7 X ⑪O 4 3 2 X 1 2 3 4 5 6 7 Graph Graph Description -7-6-5-4-3-2-1 O @O y 7- 9 5- 3 2 X 1 2 3 4 5 6 7 Graph Graph Description -7-6-5-4-3-2 6 3 2 O O Graph Graph Description 33 -7-6-5-4-3-2-1 122 The rate of growth of a fish population was modeled by the equation 90,000e-0.6t G(t) = = (1 + 5e-0.6r)², where t is measured in years since 2000 and G in kilograms per year. Write an integral to find the change in the population predicted between 2000 and 2020. 90,000e-0.6t 20 0 1 + 5e-0.6t Se-0.6t) 2 dt Find a substitution and apply it to rewrite the integrand in the form 1+5e-12 -30000 ✓ ) (+2) ()()~ 1 du 1 du. 2 6 If the biomass was 30,000 kg in the year 2000, what is the predicted biomass (in kg) for the year 2020? (Round your answer to the nearest whole number.) × kg 549999
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.3: Cylinders And Cones
Problem 26E
Related questions
Question
Transcribed Image Text:Consider the solid obtained by rotating the region bounded by the given curves about the specified line.
y=√√x-1, y = 0, x = 6; about the x-axis
Set up an integral that can be used to determine the volume V of the solid.
V=
Find the volume of the solid.
V =
Sketch the region.
y
7
6
5
4
3
2
dx
y
가
199
6
6
5
5
3
2
X
2
3
5
6 7
10
1
Sketch the solid and a typical disk or washer.
Graph
Graph Description
-7-6-5-4-3-2
122 3
O
2
3
4
5 6 7
X
⑪O
4
3
2
X
1
2
3
4
5
6
7
Graph
Graph Description
-7-6-5-4-3-2-1
O
@O
y
7-
9
5-
3
2
X
1
2
3 4 5 6
7
Graph
Graph Description
-7-6-5-4-3-2
6
3
2
O
O
Graph
Graph Description
33
-7-6-5-4-3-2-1
122
Transcribed Image Text:The rate of growth of a fish population was modeled by the equation
90,000e-0.6t
G(t) =
=
(1 + 5e-0.6r)²,
where t is measured in years since 2000 and G in kilograms per year.
Write an integral to find the change in the population predicted between 2000 and 2020.
90,000e-0.6t
20
0
1 + 5e-0.6t
Se-0.6t) 2
dt
Find a substitution and apply it to rewrite the integrand in the form
1+5e-12
-30000
✓ ) (+2)
()()~
1
du
1
du.
2
6
If the biomass was 30,000 kg in the year 2000, what is the predicted biomass (in kg) for the year 2020? (Round your answer to the nearest whole number.)
× kg
549999
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