The true statements are (c) When using disk method, we cut region into small slices perpendicular to x-axis.
(d) Volume of solid of revolution can be interpreted as the limit of Riemann sums.
(e) When using shell method, we cut region into small slices parallel to x-axis.
In the question ,
seven statements are given about a solid of revolution obtained by rotating a region R around the x-axis.
we have to find statement which are true .
Option (a)
Thickness of the slide is dx for disk method and
dy for the shell method while rotating about x - axis ,
So , statement of option(a) is false .
Option(b)
In shell method , elementary cylinders are drawn with axis of symmetry same as axis of rotation ,
thus the cylinder elements will be parallel to x axis rather than being perpendicular to the x axis ,
So , statement of option (b) is false .
Option(c)
In disk method , the slices are cut perpendicular to the axis of rotation , since we are rotating the region about x axis ,
Thus , slices are cut perpendicular to the x axis .
statement of option (c) is True .
Option (d)
As in 2D , the bounded area can be interpreted as a limit of Riemann sums , Similarly in 3D , the volume formed by rotating the bounded region about the x axis can be interpreted as a limit of Riemann sums .
So , statement of option(d) is True .
Option(e)
When using shell method, we cut region into small slices perpendicular to the x-axis .
So , statement of option(e) is False .
Option(f)
There can be both the kinds of cases , like in some cases disk method is easier than shell method and
in other cases shell method can be easier than disk method .
So , statement of option(f) is False .
Option(g)
When using disk method, we cut region into small slices perpendicular to x-axis .
So , statement of option (g) is False .
Therefore , The true statements are (c) When using disk method, we cut region into small slices perpendicular to x-axis.
(d) Volume of solid of revolution can be interpreted as the limit of Riemann sums.
(e) When using shell method, we cut region into small slices parallel to x-axis.
The given question is incomplete , the complete question is
Consider a solid of revolution obtained by rotating a region R around the x-axis. Select all the True statements below:
(a) The thickness of the slices will be dx for both methods.
(b) When using the shell method, we cut the region into small slices perpendicular to the x-axis.
(c) When using the disk method, we cut the region into small slices perpendicular to the x-axis.
(d) The volume of the solid of revolution can be interpreted as the limit of Riemann sums.
(e) When using the shell method, we cut the region into small slices parallel to the x-axis.
(f) The shell method will always result in a less complicated integral.
(g) When using the disk method, we cut the region into small slices parallel to the z-axis.
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5x + 3x + 7 which expressions are equal to it 15x +7 , 8x+ 7 ,15x , 5x+ 10
Answer:
8x + 7
Step-by-step explanation:
5x + 3x = 8x
Etimate each product. Then write whether the etimate i greater than or le than the actual product. There are 325 row of 9 chair in the theater. There are 102 chair in the balcony. About how many chair are there?
There are total 3027 chairs in the balcony and whole theater.
According to the Question,
There are total 325 rows, each rows have 09 chairs.
The number of chairs contains in theater are:
total number of rows × total chairs in rows
= 325 × 9 = 2925.
Again, there are additional 102 chairs in the balcony.
∴ 2925 + 102 = 3027
∴ There are total 3027 chairs in the whole theater.
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Iterative formula please help me thank you!!
The value of x₃ , starting with x₁ = 8 is 4.578
Given in the question ,
The iterative formula for the sequence is
=> xₙ₊₁ = 5 - 2 / xₙ
Also , x₁ = 8
Putting n = 2 in iterative formula
x₂ = 5 - 2 / x₁
Substituting the value of x₁
=> x₂ = 5 - 2 / 8
=> x₂ = 5 - 1 / 4
=> x₂ = (20 - 1)/4
=> x₂ = 19/4
=> x₂ = 4.75
Now , putting n = 3
x₃ = 5 - 2 / x₂
Substituting the value of x₂
=> x₃ = 5 - 2 / x₂
=> x₃ = 5 - 2 / 4.75
=> x₃ = 5 - 0.421
=> x₃ = 4.578
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If a triangle is equiangular, then the triangle is a(n) _ triangle
Equilateral
O Isosceles
Scalene
O Right
If the triangle is equiangular, then the triangle is an equilateral triangle.
What is equiangular triangle?
A triangle with three equal interior angles is called an equiangular triangle. In an equiangular triangle, the measure of each of its interior angles is 60
What is equilateral triangle?
an equilateral triangle is a triangle that has all its sides equal in length. Also, the three angles of the equilateral triangle are congruent and equal to 60 degrees. The sum of all three angles of an equilateral triangle is equal to 180 degrees. 60° + 60° + 60° = 180°.
As we can see, that in equilateral triangle, all the angles are of 60, as same as of equiangular triangle.
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drew thinks the answer to the question 3/7 ÷ -2/3 is -6/21. Is drew correct.
No drew is incorrect and the right answer to this question is - 9/14 which can be calculated by using BODMAS rule.
What is BODMAS rule?
It stands for Bracket Of Division Multiplication Addition Subtraction which is a simple rule for solving calculation. It means first we solve brackets of a statement and so on.
Main Body:
Given :
⇒3/7÷ 2/3
This can be solved by changing the division to multiplication and taking reciprocal of the term behind it.
⇒3/7×-3/2
⇒-9/14
Hence the correct answer to the statement is -9/14.
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explain how a number line can be used to compare two negative integers.
On a number line, plot the negative integers. The number that is further to the left will be less than the other.
What is the number?A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.
We have to explain how a number line can be used to compare two negative integers.
Integers are whole numbers they can be negative whole numbers or positive whole numbers for example 2, 4, 1, -8, 0, etc.
Plot the negative integers on a number line. It will be smaller than the other number if it is further to the left.
The numbers always go up (become "more positive") to the right and down (become "more negative") to the left on a number line. Numbers to the right are bigger than numbers to the left, and the opposite is true the other way around.
Thus, on a number line, plot the negative integers. The number that is further to the left will be less than the other.
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The center of an ellipse is located at (0, 0). One focus is located at (12, 0), and one directrix is at x =.
The answer can't be determined by the amount of data given in the question for ellipse.
What is ellipse?
In addition to being drawn outside the ellipse, the directrix of the ellipse is parallel to its latus rectum. There are two directions on the ellipse that are parallel to its principal axis. The ratio of distances between any point on an ellipse and its foci, as well as the directrix of the ellipse, is used to define an ellipse's eccentricity, and it is less than 1.
The standard equation for an ellipse is (x-h)²/a²+(y-k)²/b² = 1
a, b = semi-major and semi-minor axes respectively.
The center of the ellipse is at (0,0).
here, h=0, k=0.
One focus is at (12, 0)
Therefore
c = 12,
We can't find out the directrix with the given data.
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What’s the answer for this equation: x<-x+7(x-2)
Answer:
x > 2.8
Step-by-step explanation:
x < -x + 7(x - 2)
Expand using the Distributive Property
x < -x + 7x - 14
x < 6x - 14
Subtract x from both sides
0 < 6x - 14 - x
0 < 5x - 14
Add 14 for both sides
5x > 14
x > 14/5
x > 2.8
Evaluate x³ + 16 ÷ 4 for x = 2
Answer: 6
Step-by-step explanation:
2x2=4x2=8
8+16=24
24÷4=6
last answer is 3 btw
Answer:
the rd one
Step-by-step explanation:
its the -21/2
if u need help tell me
if roy is 4 years older than his brother and the product of their ages is 165, how old is roys younger brother
Roy's younger brother's age is 11 years.
According to the question,
We have the following information:
If Roy is 4 years older than his brother and the product of their ages is 165.
Now, let's take the age of Roy's younger brother to be x years.
Age of Roy = 4+x
So, we have the following expression:
x(4+x) = 165
[tex]x^{2} +4x-165=0[/tex]
Now, we will factorize this equation by splitting the middle term:
[tex]x^{2}[/tex]+15x-11x-165 = 0
Now, taking x as a common factor from the first two terms and -11 as a common factor from the last two terms:
x(x+15)-11(x+15) = 0
Taking (x+15) as a common factor:
(x+15) (x-11) = 0
x+15 = 0 and x-11 = 0
x = -15 and x = 11
Now, we know that age can not be negative.
Hence, Roy's younger brother is 11 years old.
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Write a linear function rule for the data in the table. x 0 1 2 3 4 y 3 1 –1 –3 –5 A. f(x) = 2x + 3 B. f(x) = –2x + 3 C. f(x) = 2x – 6 D. f(x) = –2x – 6
Answer:
f(x) = –2x + 3
Step-by-step explanation:
a stem club has 30 members. how many ways are there to choose 4 members of the club to serve on an executive committee?
A stem club has 30 members and to find out how many ways are there to choose 4 members of the club to serve on an executive committee is as follows:
Given the stem club has 30 members.
The number of ways to choose 4 members of the club to serve on an executive committee is to be considered as 30c4
we know that the formula is
[tex]n{cr}[/tex] = [tex]\frac{n!}{(n-r)!r!}[/tex]
there n = 30 and r = 4
that is., [tex]30_{c4}[/tex] = [tex]\frac{30!}{(30-4)!4!}[/tex]
= [tex]\frac{30!}{26!4!}[/tex]
= 29x15x7x9 = 27,405
Hence, the number of ways to choose 4 members of the club to serve on an executive committee is equal to 27,405.
Hence the number of ways to choose an executive member = 27,405
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For a two-tailed test, the p-value is the probability of obtaining a value for the test statistic as.
For a two-tailed test, the p-value is the probability of obtaining a value for the test statistic are as follows:
p-value = 0.09 is the probability of obtaining a value for the test statistic.
We are going step by step
Step 1) the p-value is the probability of obtaining a value for the test statistic at least as extreme as that provided by the sample
Step 2) Here the Confidence level is equal to 0.95
So the level of significance is equal to 0.05
p-value = 0.09
Since the p-value is higher than the level of significance that we do not reject the null hypothesis.
Hence the answer, the p-value = 0.09 is the probability of obtaining a value for the test statistic.
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how large a sample is needed to ensure that the probability that the sample mean differs from the population mean by more than 2.0 hours is less than 0.05?
The required sample size for the probability that the sample mean differs from the population mean by more than 2.0 hours is less than 0.05 is 68.
Given that the number of hours spent studying by students on large campus in the week before final exams follows a normal distribution with a standard deviation of 8.4 hours.
we want to find the size of the sample which is needed to ensure that the probability that the sample mean differs from the population mean by more than 2.0 hours is less than 0.05.
Here, the margin of error is E=2 and the level of significance is α=0.05
The critical value is Zα/2=Z₀.₀₂₅
or the critical value is 1.96
Now, we will find the sample size
n=((Zα/2)×σ/E)²
n=(1.96×8.4/2)²
n=67.76
n≈68
Hence, the size of sample which is needed to ensure that the probability that the sample mean differs from the population mean by more than 2.0 hours is less than 0.05 is 68.
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Which points are on the graph of k(x)=(1/4)^x ?
Select each correct answer.
Responses
(−1, 4)
begin ordered pair negative 1 comma 4 end ordered pair
(0, 14)
begin ordered pair 0 comma 1 fourth end ordered pair
(3, 164)
begin ordered pair 3 comma 1 over 64 end ordered pair
(1, 4)
Answer:
(3, 1/64)
(−1, 4)
Step-by-step explanation:
took the test
Answer:
(3, 1/64)
(−1, 4)
Step-by-step explanation: toom the test :)
A bag contains 5 red marbles, 7 blue marbles and 2 green marbles. If two marbles are
drawn out of the bag, what is the probability, to the nearest 1000th, that both
marbles drawn will be blue?
The probability that both marbles drawn will be blue is 0.218.
What is probability?
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
Since there are 7 blue marbles in the bag.
The first blue marble drawing likelihood is 7/15.
The second blue stone has a 7/15 chance of being drawn.
The likelihood that both marbles are chosen will be blue is equal to 7/15*7/15,
= 49/225,
=0.218
Hence the probability of that both marbles drawn will be blue is =0.218
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Make your angle measures correct to the nearest degree and side measures to 1 decimal place
The measure of angle Z is 34°, side length of YZ is 34.1, and the side length of XZ is 41.1. The correct option is the third option ∠Z = 34°, YZ = 34.1, XZ = 41.1
Calculating measures of angles and side measures of a triangleFrom the question, we are to determine the angles measures of and the side measures of the given triangle XYZ
From the given information,
∠Y = 90°
XY = 23
∠X = 56°
First, we will determine the measure of angle Z
m ∠X + m ∠Y + m ∠Z = 180° (Sum of angles in triangle)
56° + 90° + m ∠Z = 180°
m ∠Z = 180° - 56° - 90°
m ∠Z = 34°
Now, since the measure of one of the angles is 90°, ΔXYZ is a right triangle.
Thus,
From SOH CAH TOA, we can write that
tan X = |YZ| / |XY|
∴ tan 56° = |YZ| / 23
|YZ| = 23 × tan 56°
|YZ| = 34.0989
|YZ| ≈ 34.1
Also,
cos X = |XY| / |XZ|
cos 56° = 23 / |XZ|
|XZ| = 23 ÷ cos 56°
|XZ| = 41.1307
|XZ| ≈ 41.1
Hence, ∠Z = 34°, |YZ| = 34.1, and |XZ| = 41.1
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A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes. Each small box can hold 20 books and each large box can hold 35 books. There were twice as many small boxes sent as large boxes, which altogether can hold 225 books. Determine the number of small boxes sent and the number of large boxes sent
The number of small boxes sent is 6 and the number of large boxes sent is 3.
Given:
Each small box can hold 20 books and each large box can hold 35 books. There were twice as many small boxes sent as large boxes, which altogether can hold 225 books.
Let x be the number of small boxes and y be the number of large boxes.
20x + 35y = 225
x = 2y
20(2y) + 35y = 225
40y + 35y = 225
75y = 225
divide by 75 on both sides
75y/75 = 225/75
y = 225/75
y = 3 large boxes.
x = 2y
= 2*3
x= 6 small boxes.
Therefore the number of small boxes sent is 6 and the number of large boxes sent is 3.
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At a local prechool there i a ratio of 3 boy to every 4 girl. If there are 245 total prechooler how many are boy
If there are 245 total preschoolers, there will be 105 boys.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
Fraction of boys = 3/7Fraction of girls = 4/7Total number of students = 245The number of boys will be:= 3/7 × 245.= 105 boysTherefore, there are 105 boys in the school.
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help I WILL GIVE BRAINLIEST
use the picture to determine x and y
The unknown value of x and y from the attached picture of a square is 8 and 11 respectively.
What is the variable in the square?A square is a four sided polygon with 4 equal angles and length.
The angle at each corner of a square = 90°The fourth corner = 90° - 36°
= 54°
Recall,
Alternate angles are equal
So,
(4x + 4)° = 36°
substract 4 from both sides
4x = 36 - 4
4x = 32
divide both sides by 4
x = 32/4
x = 8
(4y + 10)° = 54°
substract 10 from both sides
4y = 54 - 10
4y = 44
divide both sides by 4
y = 44/4
y = 11
In conclusion, the value of the following given equations are:
(4x + 4)° = 36°
4(8) + 4 = 36
32 + 4 = 36
36° = 36°
(4y + 10)° = 54°
4(11) + 10 = 54
44 + 10 = 54
54 ^= 54°
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How much do you share on social media? Do you have accounts linked to your computer, phone, and tablet? The average teen spends around five hours per day online, and checks his or her social media account about 10 times each day.
When an image or post is shared publicly, some students are surprised at how quickly their information travels across the internet. The scary part is that nothing online is really private. All it takes is one friend sharing your photo or updates with the public to create a very public viral trend.
For this project, you will use what you have learned about exponential functions to study what happens if a social media post is shared publicly.
Social Sharing
Three Algebra 1 students are comparing how fast their social media posts have spread. Their results are shown in the following table:
Student Amber Ben Carter
Description Amber shared her photo with 3 people. They continued to share it, so the number of shares increases every day, as shown by the function. Ben shared his post with 2 friends. Each of those friends shares with 3 more every day, so the number of shares triples every day. Carter shared his post with 10 friends, who each share with only 2 people each day.
Social Media Post Shares f(x) = 3(4)x
Day Number of Shares
0 2
1 6
2 18 Carter shared his post with 10 friends, who each share with only 2 people each day.
Write an exponential function to represent the spread of Ben's social media post.
Write an exponential function to represent the spread of Carter's social media post.
Graph each function using at least three points for each curve. All graphs should be placed together on the same coordinate plane, so be sure to label each curve. You may graph your equation by hand on a piece of paper and scan your work, or you may use graphing technology.
Using the functions for each student, predict how many shares each student's post will be received on Day 3 and then on Day 10. Justify your answers.
If Amber decides to mail copies of her photo to the 45 residents of her grandmother's assisted living facility, the new function representing her photo shares is f(x) = 3(4)x + 45. How does this graph compare with the original graph of Amber's photo share?
Based on your results, which student's post travels the fastest? How is this shown in the equation form of the functions?
If you had to choose, would you prefer a post with fewer friends initially but more shares, like Amber, or more friends initially but fewer shares? Justify your answer with your calculations from previous questions.
1) Exponential function to show the spread of Ben' s social media post is
y = 2(3)ˣ.
2) Exponential function to represent the spread of Carter's social media post is y = 10(2)ˣ.
Define exponential function.The mathematical expression f(x)=exp or ex denotes the exponential function. The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras. When b > 0 and b 1, an exponential function has the form f(x) = bˣ. The base is b, and the exponent is x, just like in any exponential expression. The development of bacteria is an illustration of an exponential function. Some germs multiply by two per hour.
Given,
1) Exponential function to show the spread of Ben' s social media post:
y = 2(3)ˣ
2) Exponential function to represent the spread of Carter's social media post:
y = 10(2)ˣ
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El cateto más corto de un triangulo rectángulo es 9m más corto que la hipotenusa y 7m más corto que el cateto adyacente. Calcula el área de dicho triangulo, ayuda plis. Jijijiji
Resolviendo una ecuación cuadratica encontraremos los catetos del triangulo, y con eso veremos que el area es:
A = 60.92m²
¿Como encontrar el area del triangulo?
Para un triangulo rectangulo podemos definir:
x = cateto corto.y = cateto largoh = hipotenusa.Por el teorema de Pitagoras sabemos que:
x² + y² = h²
Y el area se escribe como:
A = x*y/2
Sabemos que:
x = h - 9m
x = y - 7m
Entonces:
h = x + 9m
y = x + 7m
Reemplazando eso en la ecuacion de Pitagoras:
x² + y² = h²
x² + (x + 7m)² = (x + 9m)²
x² + x² + 14m*x + 48m² = x² + 18m*x + 81m²
x² + x² - x² + 14m*x - 18m*x + 48m² - 81m² = 0
x² - 4m*x - 33m² = 0
las soluciones de la ecuación cuadratica son:
x = (4m ± √( (4m)² - 4*1*(-33m²))/(2)
x = (4m ± 12.16m)/2
Solo nos importa la solución positiva:
x = (4m + 12.16m)/2 = 8.08m
Entonces el otro cateto mide:
y = 8.08m + 7m = 15.08m
Y el area del triangulo será:
A = (8.08m)*(15.08m)/2 = 60.92m²
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hi guys the question and numbers are in the image. could someone explain this in detail pls? I need to be able to do this by myself to.
Last week, the price of apples at the grocery store was $1.75 per pound This week, the price has decreased by 20%. What are the prices of apples this week?
Answer:
The prices of apples this week is $1.40.
Step-by-step explanation:
First, convert the 20% into 0.20, then on a calculator, type this equation into it:
0.20 x 1.75 = 0.35
0.35 isn't the answer, but we use 0.35 to subtract it from 1.75:
1.75 - 0.35 = $1.40
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 15 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
excel's binom.dist function can be used to compute . a. cumulative binomial probabilities b. binomial probabilities c. bin width for histograms d. binomial probabilities and cumulative binomial probabilities
Excel's binom.dist function can be used to compute both binomial probabilities and cumulative binomial probabilities
The Excel BINOM.DIST function returns the individual term binomial distribution probability. You can use BINOM.DIST to calculate probabilities that an event will occur a certain number of times in a given number of trials. BINOM.DIST returns probability as a decimal number between 0 and 1.
We use BINOM.DIST in problems with a fixed number of tests or trials, when the outcomes of any trial are only success or failure, when trials are independent, and when the probability of success is constant throughout the experiment.
For example, BINOM.DIST can calculate the probability that two of the next three babies born are male.
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The figure shows three quadrilaterals on a coordinate grid:
A coordinate plane is shown. Quadrilateral D has sides measuring 3 units and 1 unit. Quadrilateral F has sides measuring 3 units and 1 unit. Quadrilateral E has sides measuring 2 units and 6 units.
Which of the following statements is true about the three quadrilaterals? (4 points)
Group of answer choices
D and E are similar but not congruent.
F and D are similar but not congruent.
E and F are similar and congruent.
D and E are similar and congruent.
The true statements about the three quadrilateral is
D and E are similar but not congruent.F and D are similar but not congruent.The measurements of quadrilateral D = 3 units and 1 units
The measurements of quadrilateral F = 3 units and 1 units
The measurements of quadrilateral E = 2 units and 6 units
The similar figure defined as the figures that have the same shape but not same size
The congruent is defined as the figures that have the same shape and size
Here D and F are congruent but they are not similar because they have same size
D and E are similar but not congruent because of same shape and different size.
Hence, true statements about the three quadrilateral is
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4 in has a force of 50 applied. What is the pressure?
The pressure applied on a cubic object with side 4inches with 50N force is 50N/m
What is Pressure?Pressure is defined as the physical force exerted on an object. The force applied is perpendicular to the surface of objects per unit area. The basic formula for pressure is F/A (Force per unit area). Unit of pressure is Pascals (Pa).
1 inch= 0.025m
4inches= 0.025×4= 0.1m
Pressure = Force/area
area= 0.1×0.1= 0.01m^2
therefore Pressure= 50/0.01
= 5000N/m^2
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how many two-digit prime numbers can be formed by choosing two different digits from the set $\{2, 7, 8, 9\}$ to be used as the tens digit and units digit?
Two digit prime numbers formed by choosing two different digits from the given {2,7,8,9} set of numbers are 97, 29, 79, 89.
As given in the question,
Given set of numbers are :
{ 2,7,8,9}
Two digit prime numbers formed by given set of numbers are as follow:
When 2 and 8 are at unit place, number formed is a even composite number which is not prime.
Number formed when 7 at unit place are:
27, 87, 97 from which only 97 is prime.
Number formed when 9 at unit place are:
29, 79, 89 all three are prime numbers.
Therefore, two digit prime numbers formed by choosing two different digits from the given {2,7,8,9} set of numbers are 97, 29, 79, 89.
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