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12345 [234]
1 year ago
6

Find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x2, y =

4x; about the y-axis v = incorrect: your answer is incorrect.
Physics
1 answer:
Simora [160]1 year ago
4 0

The correct answer for  the volume v of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x2, y = 4x is 128/3 * π.

Volume of Solid of Revolution by Shell method is given by

V = 2π * integrate x(height) dx Here, height = 4x-x2

(1)& x-varies from x = 0 to x = 4 then from eqn(1)  V = 2π * integrate x(4x - x ^ 2) dx from x = 0 to 4 = 2π * integrate (4x ^ 2 - x ^ 3) dx from x = 0 to 4

Basic Rule(1) ∫ x^n dx =x^ n+1/ n+1

V=2 π [4((x ^ 3)/3) - (x ^ 4)/4] 0 ^ 4 =2 π[ 4/3 x^ 3 - x^ 4/4 ] 0 ^ 4

V = 2π [4/3 * 4 ^ 3 - (4 ^ 4)/4} - 0]

V = 128/3 * π.

Learn more about area under curve here :-

brainly.com/question/15122151

#SPJ4

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suppose you got up this morning and the lightbulb in your room wouldn't come on. Use the of the scientific method to explain how
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Answer:TEP 1: State the Problem

A problem is a question to be thought about and either solved or answered. Problems surround all of us. Each day we are faced with more problems than we realize and we use the scientific method to solve them without even thinking about it.

EXAMPLE: The lamp does not come on when you flip the switch.

Your problem may be something that you observe around you or it can be determined by researching a topic and attempting to repeat an experiment of another scientist based on what you are working with.

STEP 2: Make Observations

An observation is the act of recognizing and recording something that is happening. Observing often involves the use of measurements and instruments to take measurements with.

EXAMPLE: (1) There is a light bulb. (2) The switch is in the on position.

(3)Other lights in the house are on. (4) The electrical cord is plugged in.

You make these observations based on the things you see, hear, and in other ways notice going on around you. You may also base your observations on information you found from researching the topic. Maybe you found the manual for the lamp and read about how it is supposed to work. You might have searched for information about Thomas Edison and his invention of the light bulb. These works of others are called background research.

 

STEP 3: Form a Hypothesis

A hypothesis is an educated guess meaning an explanation for something that happens based on facts that can then be tested to try and find logical answers.

EXAMPLE: The light bulb is burned out.

Your hypothesis should answer your question of why the lamp does not come on. You can come to this conclusion based on your own knowledge or from researching how a lamp works. We assume that if the lamp is plugged in and turned on that it should light. We also know that if other lights in the house are on, some electricity is running through the house. Your hypothesis does not have to be proven correct by your experiment, it just needs to be testable.

Having more than one hypothesis is fine. There could be a number of reasons why the lamp is not lit and testing them all might be the only way to find an answer. Before beginning to experiment, use logical reason to determine if any of your hypotheses can be eliminated. Maybe the fuse is blown or the outlet is bad. The switch could be wired wrong or broken. These are all testable hypotheses that could be looked into if the light bulb is not the problem.

 

STEP 4: Experiment

An experiment is a step-by-step procedure that is carried out under controlled conditions to attempt to prove a hypothesis, discover and unknown effect or law, or to illustrate a known law.

EXAMPLE: First remove the light bulb and screw it back in tightly to make sure that it was not loose. If that does not work, take the bulb from a lamp you know is working and place it in the broken lamp. If that lights, try another bulb to be sure.

Your experimental set-up should include a control and a variable. You may include more than one variable, but this will increase the size of your experiment. It is also very important to replicate in your experimetal procedure to avoid error. This means that you should try it at least three times. From your experiment you will need to gather data. Data can be organized in charts and or graphs and numerical data should be measured using the metric system.

The Metric System

How To Organize a Data Table

How To Graph

 

STEP 5: Draw a Conclusion

A conclusion is a reasonable judgment based on the examination of data from an experiment. The result or outcome of an act or process.

EXAMPLE: The lamp lit after the bulb was changed, therefore the light bulb must have been burned out.

You might also know from experience that if the filament is broken in a light bulb, it will make a rattling sound when you shake the bulb. To confirm your results, you could shake the bul

Explanation:

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