Let R be the region in the first quadrant bounded by the graph of y=sqrt{x-2} and the line y=2.(a). Find the volume of the solid generated when R is revolved about the x-axis.
(b). Find the volume of the solid generated when R is revolved about the line y=-2.
Answers
Volume of the solid generated when R is revolved about the x-axis is 10π and the volume of the solid generated when R is revolved about the line y = -2 is 40π/3.
What is Graph?
Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The volume of the solid generated when R is revolved about the x-axis,
where a and b are the x-coordinates of the points of intersection of the curve y = √(x-2) and the line y = 2.
Solving y = √(x-2) and y = 2 for x, we get:
x = 6 and x = 2
Limits of integration are a = 2 and b = 6. Substituting y = √(x-2) into the formula for the volume, we get:
V =
V= π [(6²/2 - 2(6)) - (2²/2 - 2(2))]
=10π
Volume of the solid generated when R is revolved about the x-axis is 10π.
b. The volume of the solid generated when R is revolved about the line y = -2
Substituting y = √(x-2) into the formula for the volume, we get:
We can simplify this by using the identity:
V =40π/3
Therefore, the volume of the solid generated when R is revolved about the line y = -2 is 40π/3.
Hence, Volume of the solid generated when R is revolved about the x-axis is 10π and the volume of the solid generated when R is revolved about the line y = -2 is 40π/3.
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Y=3x 2x+y=15 Can you please help with this? It's confusing. It's soling systems of equations by substitution
Answers
Answer:
The solution to the inequality is;
x > -7/3
Step-by-step explanation:
We want to find the solution to the inequality;
-3x + 8 < 15
We can have this as;
-3x < 15-8
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Answer:
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Answers
large cylinder: 950.02 m3
B.
small cylinder: 972.14 m3
large cylinder: 12,924.24 m3
C.
small cylinder: 851.22 m3
large cylinder: 13,300.25 m3
D.
small cylinder: 682.95 m3
large cylinder: 13,539.68 m3
Answers
r1 : r 2 = 3 : 1.2
r2 = 1.2 · r1 / 3
r 2 = 0.4 · r1
If the two cylinders are similar than also: h 2 = 0.4 · h 2
V 1 = r1² · π · h1
V 2 = ( 0.4 r1)² π · 0.4 · h1 = 0.064 r1² · π · h1
V 2 ( small cylinder )= 0.064 · V 1 ( large cylinder )
851.22 m³= 13.300.25 m³ · 0.064
Answer: C )
Answer: out of all the available options the one that shows the correct volumes for each cylinder is answer choice C) small cylinder: 851.22 m³ & large cylinder: 13,300.25 m³.
I hope it helps, Regards.
Answers
The number of bacteria that exist in the culture after 8 hours will be 1024.
What is an exponent?
Consider the function:
y = a (1 ± r) ˣ
Where x is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.
If there is a plus sign, then there is exponential growth happening by r fraction or 100r %
If there is a minus sign, then there is exponential decay happening by r fraction or 100r %
A bacteria culture begins with 4 bacteria which double in size every hour.
Then the equation will be
y = 4 (2)ⁿ
Where n is the number of hours.
Then the number of the bacteria that exist in the culture after 8 hours will be
y = 4 (2)⁸
y = 4 x 256
y = 1024
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After 1 hour= 4 x 2= 8
2 hours= 8 x 2= 16
3 hours= 16 x 2= 32
4 hours= 32 x 2= 64
5 hours= 64 x 2=128
6 hours= 128 x 2=256
7 hours= 256 x 2= 512
8 hours= 512 x 2= 1024
Answer: 1024
Answers
y>=5x-9
3x+y<=15
Answers
y ≥ 5x - 9
3x + y ≤ 15
3(-3) + (5x - 9) ≤ 15
-9 + (5x - 9) ≤ 15
(-9 - 9) + 5x ≤ 15
-18 + 5x ≤ 15
+ 18 + 18
5x ≤ 33
5 5
x ≤ 6.6
y ≤ 5(6.6) - 9
y ≤ 33 - 9
y ≤ 24
(x, y) ≤ (6.6, 24)