Using implicit differentiation, and considering that the inflation rate is of 200 cubic feet per minute and the radius is of 5 feet, it is found that:
The radius is increasing at a rate of 0.6366 feet per minute.The surface area is changing at a rate of 80 feet squared per minute.The volume of an sphere of radius r is given by:
[tex]V = \frac{4\pi r^3}{3}[/tex]
Applying implicit differentiation, the rate of change is given by:
[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]
For this problem:
Inflation rate of 200 cubic feet per minute, hence [tex]\frac{dV}{dt} = 200[/tex]Radius is of 5 feet, hence [tex]r = 5[/tex]Then:
[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]
[tex]200 = 4\pi (5)^2\frac{dr}{dt}[/tex]
[tex]\frac{dr}{dt} = \frac{200}{100\pi}[/tex]
[tex]\frac{dr}{dt} = 0.6366[/tex]
The radius is increasing at a rate of 0.6366 feet per minute.
The surface area is:
[tex]S = 4\pi r^2[/tex]
Hence, the rate of change is:
[tex]\frac{dS}{dt} = 8\pi r\frac{dr}{dt}[/tex]
Hence:
[tex]\frac{dS}{dt} = 8\pi (5)(0.6366) = 80[/tex]
The surface area is changing at a rate of 80 feet squared per minute.
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Which provides evidence of universe expansion that supports the big bang theory.
Answer:
Hubble's discovery in the 1920s of a relationship between a galaxy's distance from Earth and its speed
The link between a galaxy's speed and distance from Earth was discovered by Hubble in the 1920s.
What is Big Bang theory?Big Bang theory is defined as the physical theory that explains how the universe expanded from an initial state of high density and temperature. The early evolution of the universe is explained by the Big Bang theory. In accordance with this idea, the Universe began in a very small, very hot, and very dense state. It has since grown, gotten less dense, and gotten cooler.
The Big Bang theory is backed up by two significant scientific discoveries: the link between a galaxy's speed and distance from Earth, discovered by Hubble in the 1920s. In the 1960s, the cosmic microwave background radiation was discovered.
Thus, the link between a galaxy's speed and distance from Earth was discovered by Hubble in the 1920s.
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Evaluate the surface integral. S y2 ds s is the part of the sphere x2 + y2 + z2 = 36 that lies inside the cylinder x2 + y2 = 9 and above the xy-plane.
Parameterize S in cylindrical coordinates by the vector function
r(u, v) = (x(u, v), y(u, v), z(u, v))
with
x(u, v) = u cos(v)
y(u, v) = u sin(v)
z(u, v) = 36 - u²
with 0 ≤ u ≤ 3 and 0 ≤ v ≤ 2π. Take the normal vector to S to be
[tex]\vec n = \dfrac{\partial r}{\partial u} \times \dfrac{\partial r}{\partial v} = (2u^2\cos(v),2u^2\sin(v),u)[/tex]
so that the surface element is
[tex]dS = \|\vec n\| \, du\,dv = u \sqrt{1+4u^2}\, du\, dv[/tex]
Then the surface integral is
[tex]\displaystyle \iint_S y^2\,ds = \int_0^{2\pi} \int_0^3 u\sqrt{1+4u^2} \, du\, dv[/tex]
[tex]\displaystyle \iint_S y^2\,ds = 2\pi \int_0^3 u\sqrt{1+4u^2} \, du[/tex]
[tex]\displaystyle \iint_S y^2\,ds = \frac{2\pi}8 \int_0^3 8u\sqrt{1+4u^2} \, du[/tex]
[tex]\displaystyle \iint_S y^2\,ds = \frac\pi4 \int_0^3 \sqrt{1+4u^2} \, d(1+4u^2)[/tex]
[tex]\displaystyle \iint_S y^2\,ds = \frac\pi4 \cdot \frac23(1+4u^2)^{\frac32} \bigg|_0^3 = \boxed{\frac\pi6 \left(37^{\frac32}-1\right)}[/tex]
How can buddhism affect change on powerful countries that use war.
Buddhism is a religion that seeks to avoid conflict and harm, so other countries can learn from this.
During his party in chapter 3 which is an example of the gossip about gatsby.
Answer: During his party in chapter 3, one of the gossip about Gatsby is that he killed a man once
Explanation:
Answer:
that he attended oxford
Explanation:
Choose the solution(s) of the following system of equations: x2 + y2 = 6 x2 – y = 6 no solution mr001-1. Jpg mr001-2. Jpg mr001-3. Jpg infinitely many solutions mr001-4. Jpg mr001-5. Jpg mr001-6. Jpg.
The solution to the system of equations are -1 and ±√5
Given the systems of equations;
[tex]x^2 + y^2 = 6\\ x^2 - y = 6[/tex]
From equation 2;
[tex]x^2 = 6 + y[/tex]..................................... 3
Substitute equation 3 into 1 to have:
[tex]6+y+y^2=6y^2+y=6-6\\y^2+y=0\\y^2=-y\\y = -1[/tex]
Substitute y = -1 into equation 3
[tex]x^2 = 6 + y\\x^2 = 6 + (-1)\\x^2 = 6 -1\\x^2=5\\x=\pm \sqrt{5}[/tex]
Hence the solution to the system of equations are -1 and ±√5
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Answer:
its a,b,c, and f on edge which is -1/2,1/2,-i squareroot2, i square root 2
Explanation:
Identify the outlier for the given data: 23, 34, 27, 7, 30, 26, 28, 31, 34.
Answer:
The outlier is 7.
Explanation:
Hope this helps you!
Promoters and enhancers are dna sequences both bound directly by ____________.
Answer:
Transcription factors
A wheel rotates with a constant angular acceleration of 3. 50 rad/s2.
Answer:
is this a true or false question?
Explanation:
are there other universes?
Answer:
no
Explanation:
The discussion of the ""greatest of poets and philosophers"" in the third paragraph suggests that the author believes the audience of the speech will.
There a lot of great poets and philosophers in the world today. The author believes the audience of the speech will recognize an implicit reference to Shakespeare and agree about his importance.
There have been a lot of English literature. One of the greatest poet of all time is William Shakespeare.
He was known for his famous quote where He said that All the world, is a stage, and all the men and women merely players.
The author recognize the importance of Shakespeare and his impressive work of literature.
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Which President's domestic policy included putting down the Whiskey Rebellion? Question 7 options: Andrew Jackson George Washington James Madison John Adams
Answer:
George Washington
Explanation:
Which of the following statements about hybridization are true?.
A cell accumulated damage to the majority of its nucleic acids. Is in unlikely to.
Answer:
Normally if a cell has accumulated DNA damage, it is unlikely to pass the G2 check point.
Explanation:
The cell cycle is regulated at three checkpoints to ensure that the cells are ready to proceed through the process of division. At each of these checkpoints, the cell waits to receive signals on whether or not it has carried out the function that should have been completed at the previous stage. The three key check points of the cell cycle are: the cell restriction or growth check point, the DNA synthesis checkpoint and the mitosis or the metaphase checkpoint.
Quis:
*Indonesian assignment*
Find the meanings of the following words using the Indonesian Dictionary
1. Effectiveness
2. Instrument
3. Generator
4. Distribution
5. Consumption
Work in a notebook or lat
pls help me bro :-)
those who are lazy must report :) Ok ^_^
Which comparison between events in the passage would best support a claim that a significant theme of the passage is fulfillment?.
The comparison that illustrates the theme is Theodora's isolation from her family and her reading of the publisher's response regarding her manuscript.
The theme of a story simply means the central idea that's conveyed in a story. It illustrates what the author wants the readers to know in the story.
The comparison between events in the passage support a claim that a significant theme of the passage is fulfillment. This was illustrated as Theodora's isolation from her family and her reading of the publisher's response regarding her manuscript.
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Which statement is accurate about Native Americans and the American Revolutionary War?.
Answer:
regardless of which side they chose, native americans would lose land due to the outcome of the war
Explanation:
k12 yes? good luck, hope this helps
Which law would you use to simplify the expression mc006-1. Jpg? quotient of powers power of a quotient product of powers power of a product.
Answer:
Law of transparency
Explanation:
The law that will be used in simplifying the option is a3¹⁰/3⁴ is the quotient of powers. The correct option is a.
What is the quotient of powers?According to the Quotient of Powers Property, exponents are subtracted from powers when they are divided by the same base, provided the base is not equal to 0. Using variables, nanb=n(ab) n a n b = n (a b) is defined.
It is quicker and simpler to subtract the bases than to write down the multiplications and cancel. The denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator, is how the Quotient Rule defines the derivative of a quotient.
[tex]\dfrac{x^a}{x^b} = x^{( a - b)}[/tex]
[tex]\dfrac{3^{10}}{3^4} = 3 ^ {( 10 - 4)}\\\\\dfrac{3^{10}}{3^4} = 3^6[/tex]
Therefore, the correct option is a, the quotient of powers.
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The question is incomplete. Your most probably complete question is given below:
The equation is:
3^10/3^4
After earning $50 million in net income, monroe millwork distributed $15 million in dividends to its stockholders. Monroe’s board of directors decided to invest the remaining $35 million back into the business. This $35 million reinvestment of profits represents.
Based on the information given, it can be deduced that the reinvestment of profit which is $35 million is known as the retained earnings.
Retained earnings simply refer to part of the cumulative profit that is earned by a company which is saved for future use.
Retained earnings are typically earned from the net income at the end of a particular period. In this case, the company had a net income of $50 million and distributed $15 million as a dividend.
Therefore, the remaining $35 million is the retained earnings.
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Write and answer the following in your answer sheet.
A taxi service charges a flat fee of $1. 25 and $0. 75 per mile. If Henri has $14. 00, which of the following shows the number of miles he can afford to ride in the taxi? m less-than-or-equal-to 17 m greater-than-or-equal-to 17 m less-than-or-equal-to 20. 3 m greater-than-or-equal-to 20. 3.
Answer:
Its less than or equal to 17
Explanation:
Mason bought 6 loaves of bread and 3 packages of cheese for a total of $27. The cost of a package of cheese is $1. 50 more than the cost of a one loaf of bread. What is the combined cost of one loaf of bread and one package of cheese?.
Answer:
Bitlog
Explanation:
iklog
You get lost in extremely cold weather. You are unable to start a fire. Which of the following is the best way to survive?.
Answer:
go back in time and dont go anywhere cold
Explanation:
For the lunch special at a high school cafeteria, students can get either salad or french fries as a side order. The following table shows the number of each side order for the lunch specials purchased on one day, classified by the grade of the student.
The probability that the student that's selected will be in grade 10 given that the student ordered French fries as the side will be 71/248.
From the information given, the number of students that are in grade 10 is 105. Out of all the students, 34 had salad and 71 had French fries. The total students in the school that are French fries was 248.
Therefore, the probability that the student that's selected will be in grade 10 given that the student ordered French fries as the side will be calculated thus:
= Number of students who French fries in grade 10 / Total number of people that had French fries
= 71/248
In conclusion, the correct option is 71/248.
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An angle measures 4. 3 radians. To the nearest degree, what is the measure of the angle? degrees.
Marianna is working on improving her communication skills. To be a good listener, she should.
Answer:
I don't know the answer choices, however if one wants to be a good listener they should 1. Have a clear head space, 2. Always be focused on the one speaking, 3. ask questions.
Explanation:
How did she get from the stage to the balcony crossword.
Answer:
she used stairs
Explanation:
It should be noted that the word that fits the scenario is stairs.
A crossword clue simply means a hint that is given to a player of a crossword puzzle where the person has to find the missing pieces of the game.
The question is simply about how she got from the stage to the balcony crossword. Therefore, the correct option will be stairs which is six letters.
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Which of the following best describes why ddt is classified as a persistent organic pollutant.
The reasons why DDT is classified as a persistent organic pollutant are;
DDT can be used to control diseases, such as malaria and typhus, that are spread by insects.DDT is detected in food worldwide and the general human population is most commonly exposed to the toxin through food.Persistent Organic Pollutants can be regarded as toxic substances which are made up of organic chemical compounds.
These are industrial chemicals such as;
PCBs pesticides like DDT.DDT is classified as a persistent organic pollutant because of it's usefulness in control diseases and it is been found in food stuff across the globe.
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The square root of a number is between 8 and 9 which of these could be that number.
9
9 is a square root because when u multiply 3×3=9
The distribution of number of hours worked by volunteers last year at a large hospital is approximately normal with mean 80 and standard deviation 7. Volunteers in the top 20 percent of hours worked will receive a certificate of merit. If a volunteer from last year is selected at random, which of the following is closest to the probability that the volunteer selected will receive a certificate of merit given that the number of hours the volunteer worked is less than 90 ?.
Explanation:
Using the normal distribution, it is found that the probability that the volunteer selected will receive a certificate of merit given that the number of hours the volunteer worked is less than 90 is closest to:
B 0.123
In a normal distribution with mean \muμ and standard deviation \sigmaσ , the z-score of a measure X is given by:
Z = \frac{X - \mu}{\sigma}Z=σX−μ
It measures how many standard deviations the measure is from the mean.
After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
In this problem:
The mean is of 80, hence \mu = 80μ=80 .
The standard deviation is of 7, hence \sigma = 7σ=7 .
The minimum value is the 80th percentile, which means that it is X_mXm when Z has a p-value of 0.8.
The probability that the volunteer selected will receive a certificate of merit given that the number of hours the volunteer worked is less than 90 is P(X_m < X < 90)P(Xm<X<90) , which is the p-value of Z when X = 90 subtracted by the p-value of Z when X = X_mX=Xm , hence the p-value of Z when X = 90 subtracted by 0.8.
Z = \frac{X - \mu}{\sigma}Z=σX−μ
Z = \frac{90 - 80}{7}Z=790−80
Z = 1.43Z=1.43
Z = 1.43Z=1.43 has a p-value of 0.9236.
0.9236 - 0.8 = 0.1236, hence closest to 0.123, option B.
Using the normal distribution, it is found that the probability that the volunteer selected will receive a certificate of merit given that the number of hours the volunteer worked is less than 90 is closest to:
Letter B
In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}\\Z=\sigma X - \mu[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X. In this problem:
The mean is of 80, hence [tex]\mu = 80[/tex]. The standard deviation is of 7, hence [tex]\sigma = 7[/tex]. The minimum value is the 80th percentile, which means that it is [tex]X_m[/tex] when Z has a p-value of 0.8.The probability that the volunteer selected will receive a certificate of merit given that the number of hours the volunteer worked is less than 90, which is the p-value of Z when X = 90 subtracted by the p-value of Z when X = X_mX=Xm , hence the p-value of Z when X = 90 subtracted by 0.8.
[tex]Z = \frac{X - \mu}{\sigma}\\Z=\sigma X - \mu\\Z = \frac{90 - 80}{7}\\Z=790 - 80\\Z = 1.43Z=1.43[/tex]
Has a p-value of 0.9236.
[tex]0.9236 - 0.8 = 0.1236[/tex]
Hence closest to 0.123.
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What is the acceleration of a 32 kg object if a 6. 75 n force is applied to it? 0. 21 m/s2 4. 74 m/s2 21. 09 m/s2 216. 00 m/s2.
The acceleration of the object is 4.74 m/s²
From the question given above, the following data were obtained:
Mass (m) = 32 Kg
Force (F) = 6.75 N
Acceleration (a) =?The acceleration of the object can be obtained as follow:
[tex]a = \frac{f}{m} \\ \\ a \: = \frac{32}{6.75} \\ \\ [/tex]
a = 4.74 m/s²Therefore, the acceleration of the object is 4.74 m/s²
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