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1. Find the volume of the solid that results when the region enclosed by the given curves = ^(−2), = 0, = 0, and = 1 is revolved about the x-axis.
2. Find the volume of the solid that results when the region enclosed by the given curves = ^(−2), = 0, = 0, and = 1 is revolved about the y-axis.
Answers
The volume of the solid that results when the region enclosed by the given curves y = e⁻²ˣ, y = 0, x = 0, and x = 1 is revolved around the x-axis and the y-axis is 0.77 and 0.7135.
What is the revolution of the curve?Revolving the region bordered by y = f(x) and the x-axis on the interval [a, b] around the x-axis generates the volume (V) of a solid.
The volume is given as
\(\rm Volume = \int _a^b \pi y^2 \ dx\)
The volume of the solid that results when the region enclosed by the given curves y = e⁻²ˣ, y = 0, x = 0, and x = 1 is revolved around the x-axis.
\(\rm Volume = \int _0^1 \pi (e^{-2x})^2 \ dx\\\\\\Volume = \int _0^1 \pi (e^{-4x}) dx\\\\\\Volume = \pi [\dfrac{e^{-4x}}{-4}]_0^1\\\\\\Volume = - \dfrac{\pi}{4} [e^{-4} - e^0]\\\\\\Volume = -\dfrac{\pi}{4} [-0.98168]\\\\\\Volume = 0.77\)
The volume of the solid that results when the region enclosed by the given curves y = e⁻²ˣ, y = 0, x = 0, and x = 1 is revolved around the y-axis.
\(\rm Volume = \pi \left [\int_{0}^{0.135} dy + \int_{0.135}^{1}\left ( \dfrac{\ln x}{-2} \right )^{2}dy \right ]\\\\Volume =0.71375\)
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Related Questions
47.5% of children say that chocolate chip cookie is their favorite kind of cookie. If you randomly select 12 children find the probability that: a) at least 10 of them say that chocolate chip cookie is their favorite cookie. B) four of them say that chocolate chip cookie is their favorite cookie. C) Find the mean and standard deviation for this sample.
Answers
Answer: a) 0.0125 b) 0.1454 c) Mean = 5.7, standard deviation = 1.73
Step-by-step explanation:
Let x = Number of children say that chocolate chip cookie is their favorite kind of cookie.
x follows binomial distribution.
Binomila distribution formula:
\(P(X=x)=\ ^nC_xp^x(1-p)^{n-x}\) , where p = probability in each trial, n = sample size, x= number of successes
Sample size : n= 12, p=0.475
a)
\(P(x\geg10)= P(x=10)+P(x=11)+P(x=12)\\\\=\ ^{12}C_{10}(0.475)^{10}(1-0.475)^{2}+^{12}C_{11}(0.475)^{11}(1-0.475)^{1}+^{12}C_{12}(0.475)^{12}(1-0.475)^{0}\\\\=\dfrac{12!}{2!10!}(0.475)^{10}(0.525)^{2}+(12)(0.475)^{11}(0.525)^{1}+(1)(0.475)^{12}\\\\\approx0.0125\)
b)
\(P(x=4)= ^{12}C_{4}(0.475)^4(0.525)^{8}\\\\=\dfrac{12!}{4!8!}(0.000293798)\\\\=0.1454\)
c) Mean = np
= (12)(0.475) =5.7
Standard deviation = \(\sqrt{np(1-p)}\)
\(=\sqrt{12\times0.475\times0.525}\\\\=\sqrt{2.9925}\approx1.73\)
45 +2.50m = 3.75m
what is the answer
Answers
m = 36
Work
45 + 2.50m = 3.75m
-3.75m -3.75m
45 - 1.25m = 0
- 45 - 45
-1.25m = -45
-1.25 -1.25
m = 36
the sum of -3 and it's opposite
Answers
Answer:
it equals 0
Step-by-step explanation:
3 + -3=0
Which of the following is an example of cluster sampling? Combining all food workers from the 67 Guilford County elementary schools and randomly choosing 150 at random to interview Randomly choosing 3 food workers from each of the 67 schools and interviewing the ones choosen Randomly choosing 8 elementary schools from the 67 in Guilford county and interviewiing all food workers at each of these schools
Answers
Cluster sampling is a method of sampling used in statistics, where the population is divided into several groups called clusters, and some of the clusters are chosen randomly to be included in the sample.
In cluster sampling, all the individuals in a selected cluster are included in the sample. Cluster sampling is useful when the population is too large to be sampled entirely or when the population is geographically dispersed. Randomly choosing 8 elementary schools from the 67 in Guilford county and interviewing all food workers at each of these schools is an example of cluster sampling. This is because the 67 elementary schools are divided into clusters of 8 schools, and a random selection of these clusters is made. Then, all the food workers in the selected clusters are included in the sample, and there is no need to sample food workers from the other schools. In this example, cluster sampling is an effective way of obtaining a representative sample of the food workers in the Guilford County elementary schools.
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if x^2 = a and a > 0. what is x?
Answers
\(\\ \sf\longmapsto x^2=a\)
\(\\ \sf\longmapsto x=\sqrt{a}\)
Now if a be 1,2,3,4....
\(\\ \sf\longmapsto x=\sqrt{1}=1\)
\(\\ \sf\longmapsto x=\sqrt{2}\)
\(\\ \sf\longmapsto x=\sqrt{3}\)
\(\\ \sf\longmapsto x=\sqrt{4}=2\)
And so on
Counting jails and prisons, approximately how many citizens are incarcerated? a. 1 million b. 2.3 million c. 3 million d. 4.3 million.
Answers
In September 2021, the approximate number of citizens incarcerated in jails and prisons is around 2.3 million.
It is important to note that this figure can vary over time due to changes in policies, criminal justice reforms, and other factors. The incarcerated population includes individuals who have been convicted of crimes and are serving their sentences, as well as those who are awaiting trial or have been sentenced but not yet transferred to a correctional facility.
These numbers can vary between different countries and jurisdictions. To obtain the most accurate and up-to-date information on current incarceration rates, it is advisable to refer to official sources such as the U.S. Bureau of Justice Statistics or relevant governmental organizations in your country.
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In simple graphical method a graph is plotted from the available data, between water usage and population. 2) Pressure in a distribution system must be high enough to permit the fire department adequate hydrant flows. 3) Distribution system is used to describe collectively the facilities used to supply water from its source to the point of usage. 4) Brackish water or briny water is water that has more salinity than fresh water, and more than seawater salinity. 5) The effect of monthly variation influences the design of storage reservoirs. 6) Jordan is not considered a "Water Scarce" country. 7) If a fire breaks out, a small quantity of water is required to be supplied during long duration, necessitating the need for a maximum rate of hourly supply. 8) The Manning equation is commonly used to design and evaluate the performance of sanitary sewers. 9) If d is less than 200 mm then the pipe final diameter D is 200 mm. 10) The diameter for lateral pipe is larger than the diameter of interceptor pipe.
Answers
The given statements are correct or incorrect is given below:
1) Correct.
2) Correct.
3) Correct.
4) Correct.
5) Correct.
6) Incorrect.
7) Correct.
8) Correct.
9) Correct.
10) Incorrect.
Here, we have,
1) Correct. In a simple graphical method, a graph is plotted to show the relationship between water usage and population.
2) Correct. The pressure in a distribution system needs to be sufficient to allow for adequate hydrant flows in case of a fire.
3) Correct. The term "distribution system" refers to the infrastructure and facilities used to supply water from its source to the point of usage.
4) Correct. Brackish water is water that has a higher salinity level than fresh water and even higher than seawater.
5) Correct. Monthly variation in water usage can impact the design and capacity requirements of storage reservoirs.
6) Incorrect. Jordan is considered a "Water Scarce" country, as it faces significant challenges in terms of water availability and scarcity.
7) Correct. During a fire, a significant quantity of water needs to be supplied over an extended period, necessitating a high rate of hourly supply.
8) Correct. The Manning equation is commonly used in the design and evaluation of sanitary sewers.
9) Correct. If the diameter (d) is less than 200 mm, the pipe's final diameter (D) is set at 200 mm.
10) Incorrect. The diameter of the interceptor pipe is typically larger than the diameter of the lateral pipe. The interceptor pipe carries wastewater from multiple lateral pipes.
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How do you graph y=2/3x-4
Answers
━━━━━━━☆☆━━━━━━━
▹ Answer
You can use a graphing calculator.
▹ Step-by-Step Explanation
Attached is a screenshot.
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Answer:
See explanation and picture attached
Step-by-step explanation:
We can break down this expression into it's core components:
Since the constant here is -4, the y intercept is -4.
Since the value we are multiplying x by is \(\frac{2}{3}\), the slope is \(\frac{2}{3}\). This means for every time we go horizontal 3 units, the line increases by 2.
The graph is attached.
Hope this helped!
3. A leaking tap drips water at 0,5 ml/sec. Convert this rate to l/h.
Answers
Answer: 1.8 L/h
Step-by-step explanation:
To convert the rate of water dripping from a tap from millilitres per second (ml/sec) to litres per hour (L/h), we need to use conversion factors.
Step 1:
First, let's convert the rate from millilitres per second to litres per second.
There are 1000 millilitres in a litre, so we can divide the rate in millilitres per second by 1000 to get the rate in litres per second:
\(\LARGE \boxed{\textsf{0.5 ml/sec $\div$ 1000 = 0.0005 L/sec}}\)
Step 2:
We can convert the rate from litres per second to litres per hour. There are 3600 seconds in an hour, so we can multiply the rate in litres per second by 3600 to get the rate in litres per hour:
\(\LARGE \boxed{\textsf{0.0005 L/sec $\times$ 3600 = 1.8 L/h}}\)
Therefore, the rate of water dripping from the tap is 1.8 L/h.
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will mark brainles if answered fast There are 72 items on Ginny bookshelf 1/3 of items are hardcover books. 4/9 of the items are softcover books The many DVDs are on Ginny's shelf?
Answers
3/9+4/9=7/9
2/9 is DVDS
72/9=8
8x2=16
which of the following statements is true about a rational function of the form where g and h are polynomial functions?
Answers
The true statement about the function is that (c) the domain of f(x) consists of all values of x such that g(x) does not equal 0 and h(x) does not equal 0.
How to determine the true statement of the function f(x)?The complete question is added at the end of this solution
From the complete question, we have the following equation
f(x) = g(x)/h(x)
The above equation means that
The function f(x) is the quotient of the functions g(x) and h(x)
For the function f(x) to have real values, the function h(x) must not equal 0
i.e. h(x) ≠ 0
This is so because
A number or an expression divided by 0 is not a real number
Hence, the true statement is that the domain of f(x) consists of all values of x where h(x) does not equal 0.
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Complete question
which of the following statements is true about a rational function of the form where g and h are polynomial functions?
A. If the rational function has a removable discontinuity, then it cannot have a vertical asymptote. g(x)
B. The rational function f(x) h(x) will have a removable discontinuity at x = a if g(a) = 0. g(x)
C. The domain of f(x) consists of all values of x such that g(x) does not equal 0 and h(x) does not equal 0.
D. If the rational function has a removable discontinuity, then it cannot have a horizontal asymptote.
a family buys 6 tickets to show. they also pay a $3 parking fee. they spend $27 ti see the show.
what does x represent?
Answers
X represents the cost of each ticket which is $4.50
Ex: 6* 4.50 =27 +3 parking fee =30
in regression analysis, the independent variable is typically plotted on the _____.
Answers
In regression analysis, the independent variable is typically plotted on the x-axis.
The x-axis represents the independent variable or predictor variable, which is the variable that is believed to influence or have an impact on the dependent variable. This variable is typically plotted horizontally on the graph.
For example, let's say we are studying the relationship between the amount of study time and exam scores. In this case, the independent variable would be the amount of study time, which could be measured in hours.
By plotting the amount of study time on the x-axis, we can visually analyze how it relates to the dependent variable, which is the exam scores, typically plotted on the y-axis. This helps us understand the nature and strength of the relationship between the two variables.
So, in summary, the independent variable is plotted on the x-axis in regression analysis.
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Find the Perimeter of the figure below , composed of a rectangle and a semicircle Round to the nearest tenths place.
Answers
The perimeter of the figure is 53.7.
What is perimeter?Perimeter can be defined as the total distance around a object.
To calculate the perimeter of the the figure below, we use the formula below.
Formula:
P = 2l+w+πw/2.......... Equation 1From the diagram,
Given:
l = 14w = 10π = 22Substitute these values into equation 1
P = (2×14)+10+(3.14×10/2)P = 28+10+15.7P = 53.7Hence, the perimeter of the figure is 53.7
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If there are 48 oranges then how many apples are there?
Answers
The graph of the equation y =2x² -2 is shown which equation will shift the graph up 3 units
Answers
somebody please solve this and tell me, show how you got the answer pleaser. i’ll give lots of points and brainliest
Answers
Line a & b are parallel
Line c is perpendicular to both lines a & b
Step-by-step explanation:
Let's solve for y in all the lines, starting with line a
-3x - 12y = 36
Add 3x to both sides
-3x - 12y = 36
+ 3x + 3x
-12y = 3x + 36
Divide both sides by -12
-12y/-12 = (3x + 36)/-12
y = -x/4 - 3
Now for line b
x + 4y = 2
- x - x
4y = -x + 2
4y/4 = (-x + 2)/4
y = -x/4 + .5
Since line a and b have the same slop, they are parallel
Notice how their slops are opposite and flipped of line c, 4x, making them perpendicular to line c.
Green = line a
Blue = line b
Purple = line c
Find two numbers that round to 387.4 when rounded to the nearest tenth.
Answers
1. 387.43 (.43 is closest to .4, not .5)
2. 387.41 (.41 is closest to .4, not .5)
hope this helps!
What is wrong with this argument? Check all that apply.
Suppose x = 2
2x = 4
2x + 1 = 5
- Nothing.
- Punctuation is missing. Each sentence needs to be terminated with a period (.).
- The logical glue is missing. Lines 2 is a consequence of line 1, and line 3 is a consequence of line 2. Words and phrases like "Thus", "Therefore", "It follows", etc. need to be used to make it clear that we are drawing conclusions.
- The assumption that x is an integer was not stated. Line 1 should have been "Suppose x is an integer and x = 2".
Answers
The logical glue is missing, that is the wrong thing in the argument.
What is wrong with this argument?The argument is:
Suppose that x = 2
Then:
2x = 4 → This is true, if we take the original equation and we multiply both sides by 2, we will get 2x = 4
Then:
2x + 1 = 5 → This is also true, we just added 1 in both sides.
Then there is nothing wrong here, but, as you can see the "connectors" between the statemnts aren't in the argument
So the correct option is the third one, the logical glue is missing.
And we don't need to assume that x is an integer, if it is not defined, then the standard is that we assume that all the numbers are real. And the argument is still true if x is real.
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Use polar coordinates to find the volume of the given solid.
Below the paraboloid z = 18 − 2x² − 2y² and above the xy-plane
Answers
V = π [(3(\(\sqrt{18/2}\))³/1) - (2(\(\sqrt{18/2}\))⁵/15)] - π [0]
Simplifying this expression will give us the final volume of the solid.
, we need to evaluate the triple integral:
V = ∫₀²π ∫₀ᵣ ∫(18 - 2r²) r dz dr dθ
Integrating with respect to z first, we have:
V = ∫₀²π ∫₀ᵣ (18 - 2r²) r dr dθ
Integrating the volume with respect to r, we get:
V = ∫₀²π [(9r² - 2/3r⁴)]ᵣ₀ dθ
Simplifying the expression inside the brackets and evaluating the integral, we have:
V = ∫₀²π (9r² - 2/3r⁴) dθ
V = π [(9/3)r³ - (2/15)r⁵]ᵣ₀
V = π [(3r³/1) - (2r⁵/15)]ᵣ₀
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3) -7y + 9 = 3y + 49
Answers
Answer:
y = -4
Step-by-step explanation:
first add 7y to both sides
9 = 10y + 49
second subtract 49 from both sides
-40 = 10y
flip it
10y = -40
now divide both sides by 10
y = -4
that is your answer
Answer: 7y+9=3y+49
We move all terms to the left:
-7y+9-(3y+49)=0
We get rid of parentheses
-7y-3y-49+9=0
We add all the numbers together, and all the variables
-10y-40=0
We move all terms containing y to the left, all other terms to the right
-10y=40
y=40/-10
y=-4
if force 1 = 258 newton with 45 mm length of vector, force2 = ?, length of vector = 28mm. what is force 2 equal to?
Answers
Force 2 has a magnitude of approximately 160.8 Newton.
To find the value of force2, we can use the concept of vector equivalence. If force1 has a magnitude of 258 Newton and a length of vector equal to 45 mm, and force2 has a length of vector equal to 28 mm, we can set up the following proportion:
|force1| / length of vector for force1 = |force2| / length of vector for force2
Substituting the given values:
258 / 45 = |force2| / 28
To solve for |force2|, we can cross-multiply and solve for it:
258 * 28 = 45 * |force2|
|force2| = (258 * 28) / 45
Calculating this expression gives us:
|force2| ≈ 160.8 Newton
Therefore, force2 has a magnitude of approximately 160.8 Newton.
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Complete the congruence statement
Answers
Answer: That would be line XY.
Solve for x:
X =
3x + 5
————-
2
=5x-4
Answers
Answer:
1) x= -2.5
2) x= -0.4
Step-by-step explanation:
1)
x=3x+5
-5. -5
x-5=3x
-x. -x
-5=2x
/2. /2
-2.5=x
2)
2=5x+4
-4. -4
-2=5x
/5. /5
-0.4=x
Hopes this helps please mark brainliest
Answer:
1) x = -5/2
2) x = 6/5
Step-by-step explanation:
Part 1:x = 3x + 5
Subtract x from both sides
0 = 3x - x + 5
0 = 2x + 5
Subtract 5 from both sides
-5 = 2x
Divide 2 to both sides
-5/2 = x
x = -5/2Part 2:2 = 5x - 4
Add 4 to both sides
2 + 4 = 5x
6 = 5x
Divide 5 to both sides
6/5 = x
x = 6/5\(\rule[225]{225}{2}\)
there are (36)2⋅ 30 candies in a store. what is the total number of candies in the store? (5 points) group of answer choices 312 33 38 34 next
Answers
The total number of candies in the store is 312. It is obtained by using the concept of exponent and power on the given problem.
What is an Exponent?
The number of times a quantity is multiplied by itself is referred to as an exponent or power of the given quantity. For eg: 25, where 5 is an exponent or power of 2 and 2 is called the base of exponent 5. Any quantity raised to the power 0 always returns 1 as result.
Calculation of the total number of candies in the store
(36)2 * 30
Using the properties of an exponent, we have
A number with an exponent of 0 always gives 1
(36)2 * 1
(3)6×2 * 1
312 * 1
312
Thus, the total number of candies in the store is 312.
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Daisy filled a bucket with 7/6 gallon of rain.water.
later she poured out 1/6 of gallon of of the water. how much water is left in the bucket?
I'll mark you brilliantest
Answers
The statistical approach involved in generalizing from a sample of 25 patients to an entire population of the hundreds of patients in a particular hospital is known as?
Answers
Answer:
Decision making
Step-by-step explanation:
The statistical approach involved in generalizing from a sample of 25 patients to an entire population of the hundreds of patients in a particular hospital is known as decision making .
Decision making is the process of making choices by identifying a decision, gathering information, and assessing alternative resolutions. Using a step-by-step decision-making process can help you make more deliberate, thoughtful decisions by organizing relevant information and defining alternatives.
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A student takes an exam containing 17 true or false questions. At least 11 correct answers are required to pass. If the student guesses, what is the probability that he will fail
Answers
The probability that the student will fail, given that he guesses the answers, is 0.227.
Since there are only two possible outcomes for each question (true or false),
the probability of guessing a correct answer is 1/2 = 0.5.
Likewise, the probability of guessing a wrong answer is also 1/2 = 0.5.
To find the probability of failing the exam,
we need to find the probability of answering less than 11 questions correctly.
Using the binomial probability formula,
the probability of getting k successes (correct answers) in n trials (questions) is given by:
P(k) = (n C k) * p^k * q^(n-k)
where p is the probability of success (getting a correct answer),
q is the probability of failure (getting a wrong answer), and (n C k) is the number of combinations of n things taken k at a time.
In this case,
n = 17, p = 0.5, and
q = 0.5.
The number of ways to get less than 11 correct answers is:
P(X < 11) = P(X = 0) + P(X = 1) + ... + P(X = 10)P(X = k) = (n C k) * p^k * q^(n-k)
Substituting the values:
P(X < 11) = P(X = 0) + P(X = 1) + ... + P(X = 10)
P(X = 0) = (17 C 0) * (0.5)^0 * (0.5)^17 = 0.0015
P(X = 1) = (17 C 1) * (0.5)^1 * (0.5)^16 = 0.0146
P(X = 2) = (17 C 2) * (0.5)^2 * (0.5)^15 = 0.0586
P(X = 3) = (17 C 3) * (0.5)^3 * (0.5)^14 = 0.1558
P(X = 4) = (17 C 4) * (0.5)^4 * (0.5)^13 = 0.268
P(X = 5) = (17 C 5) * (0.5)^5 * (0.5)^12 = 0.327
P(X = 6) = (17 C 6) * (0.5)^6 * (0.5)^11 = 0.2732
P(X = 7) = (17 C 7) * (0.5)^7 * (0.5)^10 = 0.1537
P(X = 8) = (17 C 8) * (0.5)^8 * (0.5)^9 = 0.0573
P(X = 9) = (17 C 9) * (0.5)^9 * (0.5)^8 = 0.013
P(X = 10) = (17 C 10) * (0.5)^10 * (0.5)^7 = 0.0015
Therefore, P(X < 11) = 0.0015 + 0.0146 + 0.0586 + 0.1558 + 0.268 + 0.327 + 0.2732 + 0.1537 + 0.0573 + 0.013 + 0.0015P(X < 11) = 0.8857
Thus, the probability of failing is: P(fail) = P(X < 11) = 0.8857
The probability that the student will fail, given that he guesses the answers, is 0.227 (rounded to three decimal places).
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The cost, in dollars, for a video game developer to code g games can be represented by the function v(g) . The number of games produced in w weeks is given by the function g(w) = 4w.
Answers
After w weeks, the expression for the total cost of games is 250 + 4000w.
What is Expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
An algebraic expression known as a linear expression has terms that are either constants or variables raised to the first power. Alternatively put, none of the exponents can be greater than 1.
As an illustration, while x is a variable raised to the first power, x2 is a variable raised to the second power. An illustration of a constant is 5.
Linear expressions are what the two expressions are. One variable raised to the power of one makes up a linear expression.
250 + 1000g.
Where: g(w) = 4w.
250 + 1000(4w).
250 + 4000w.
Therefore, number of games produced in w weeks is 250 + 4000w.
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Solve the x 2/3x +5 1/2 = -10
Answers
Answer:
x = 2/3x + 5 1/2 = -10 = x = -93/4
Step-by-step explanation: