what is the volume of the solid generated when the region in the first quadrant bounded by the graph of y=x3 y = x 3 , the y y -axis, and the horizontal line y=1 y = 1 is revolved about the y y -axis?

Answers

Answer 1

Given: The region in the first quadrant bounded by the graph of y=x3, y=0, and the horizontal line y=1 is revolved about the y-axis.

To find: The volume of the solid generated when the region in the first quadrant bounded by the graph of y=x3, y=0, and the horizontal line y=1 is revolved about the y-axis.Solution:The region in the first quadrant bounded by the graph of y = x³, y = 0,

and the horizontal line y = 1 is shown below: \(\int_{0}^{1} π (y)^2dx\) \(= π \int_{0}^{1} y^2 dx\) \(= π \int_{0}^{1} y^2 (dx/dy)dy\) \(= π \int_{0}^{1} y^2 (1/3y^3)dy\) \(= π/3 \int_{0}^{1} y^5 dy\) \(= π/3 [(y^6/6)]_{0}^{1}\) \(= π/18\)Hence, the volume of the solid generated when the region in the first quadrant bounded by the graph of y = x³, y = 0, and the horizontal line y = 1 is revolved about the y-axis is \(π/18\).

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Related Questions

Training Trista
is training for a marathon and is running 2 miles the first week she plans to add 2 miles each week to her training if the pattern continues after how many weeks will she run 26 miles

Answers

i think it’s 13 miles

2.3 Find measure of angle by finding x first

Solve for x.

I need help I have forgotten how to solve for x..

2.3 Find measure of angle by finding x firstSolve for x.I need help I have forgotten how to solve for

Answers

Answer:

x=5

Whole angle/9x=45

Step-by-step explanation:

sum of all three angles in a triangle is 180 degrees so we can add all of these angles together and set it equal to 180 like this


9x+65+70=180

Simplify

9x+135=180

Subtract both sides of 135

9x+135=180

   -135.  -135

9x=45

since 9x equals 45 that is how much the angle is

Divide both sides by 9 to find x


9x=45

/9.  /9

x=5

Hopes this helps please mark brainliest

*I WILL MARK BRAINLIEST* PLS HELP ASAP

*I WILL MARK BRAINLIEST* PLS HELP ASAP

Answers

What?

joshuasalazar697 avatar

A because u should have gotten a 3x after adding them together since u do what is inside the () before anything

fionaferlich1 avatar

3+x does not equal 3x

joshuasalazar697 avatar

y not

fionaferlich1 avatar

because 3x equals x times x times x not 3+x

joshuasalazar697 avatar

but why is it d

joshuasalazar697 avatar

they did it right u have to divide it from the right to the left

fionaferlich1 avatar

a rule of inequalities is when you divide by a negative the sign switches. so because u had to divide the entire thing by -6 it should be x is greater than -1

joshuasalazar697 avatar

no u have to divide it by positive 6 cause u are taking it the 6 from the right and moving it under the 6 from the left wich u would divide

fionaferlich1 avatar

u always divide by the coefficient of x and that's -6

joshuasalazar697 avatar

no cause since u moved all the letters to the right and all the lone numbers to the left u have to take that last one and divide it from the one with the x

fionaferlich1 avatar

the one with the x is the coefficient of x which is -6

joshuasalazar697 avatar

yeah i know that ut u don't divide the 6 from the -6x like u gonna divide -6x by 6

joshuasalazar697 avatar

also if i am wrong what happened to the 3 and why did it turn to an 18

fionaferlich1 avatar

so say that's what you're supposed to do (which it is ) but then u would get -x>1 and x must be positive

joshuasalazar697 avatar

i should have paid attention in algebra no wonder I don't get geometry but geometry is way easier

joshuasalazar697 avatar

i see what u are getting to now

joshuasalazar697 avatar

still don't see how 3 turned into 18

joshuasalazar697 avatar

i just say this hole thing is written wrong from the start and made it all wrong

there is ur explanation

Answer:

d

Step-by-step explanation:

since when u divide by a negative it switches signs

after fitting a linear regression model to a dataset, the model's slope and intercept are -3 and 0 respectively. now, if we change our independent variable by adding 4.5 units to x, what is the absolute value of the change in the predicted value of dependent variable y?

Answers

The absolute value of change in the predicted value of dependent variable Y is 18.

Any variable whose value is influenced by an independent variable is said to be dependent. The thing that is measured or assessed in an experiment or mathematical equation is the dependent variable. The phrase "the outcome variable" is another name for the dependent variable.

Slope = b = -4

Intercept = a = -2.8

So, the equation of the regression line is

y  =  a + bx

y = -2.8 - 4x              ...Equation 1

Now suppose the value of x is changed by adding 4.5

i.e. put x = x + 4.5

So,

y = -2.8 - 4(x + 4.5)

y = -2.8 -4x - 18         ...Equation 2

Comparing 1 and 2 ,

We get the predicted value of dependent variable Y as 18

Therefore The absolute value of change in the predicted value of dependent variable Y is 18

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Your anova is statistically significant. How will you determine which groups are different?.

Answers

If the ANOVA test is statistically significant, then we can determine which groups are different by means of the F statistic, which is defined by the ratio of the mean sum square to the average square error (none of the options are correct).

What is the ANOVA test?

The ANOVA test can be defined as a strategy to assess when differences between two or even more groups and or populations in the same are statistically significant.

Moreover, the F statistic refers to the results of the ANOVA, which is used to show statistically significant differences between groups in the sample.

Therefore, with this data, we can see that the ANOVA test is used to determine when differences between groups in the sample are significant enough to explain a given working hypothesis, and it is associated with the F statistics.

Complete question:

Your ANOVA is statistically significant. How will you determine which groups are different?

Use planned or unplanned comparisons.

Look at what the means in each group are.

Conduct Levene's test.

None of the above

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Explain whether you could have used fraction ships with any other denominator to find the difference. If so what is the denominator

Answers

It is obtained that the equivalent fraction with the largest numerator is \(\frac{15}{12},\) therefore the largest fraction is \(\frac{5}{4}.\)

Order of Rational Numbers :

To compare fractions, we must work with their equivalent expressions, which lead to expressing them through a single denominator.

That equivalent fraction that has the smallest denominator is the smaller of the two fractions studied.

To determine which is the largest of 4 fractions we must first find the least common multiple of the denominators and then calculate the equivalent fractions by applying the least common multiple.

To equivalent fraction that has the largest numerator is the largest.

Let's see what we have outlined above with an example

If we have the following fractions

\(\frac{1}{2},\frac{2}{3},\frac{5}{4} and \frac{7}{6}\)

Now let's calculate which of the 4 given fractions is the largest one.

So, we have:

The L.C.M of 2, 3, 4 and 6 is \(2^2.3=12\)

Then, L.C.M (2, 3, 4, 6) = 12.

Now, we apply the L.C.M to each of the fraction to obtain the equivalent ones.

Thus, we have:

For \(\frac{1}{2}\) the equivalent fraction is \(\frac{6}{12}.\)

For \(\frac{2}{3}\), the equivalent fraction is \(\frac{8}{12}.\)

For \(\frac{5}{4}\), the equivalent fraction is \(\frac{15}{12}\)

For \(\frac{7}{6},\) the equivalent fraction is \(\frac{14}{12}.\)

It is obtained that the equivalent fraction with the largest numerator is \(\frac{15}{12},\) therefore the largest fraction is \(\frac{5}{4}.\)

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The given question is incomplete, So we take the similar question :

If you have 4 fractions with different denominators, and you have to determine which is greater. What should you do to figure that out?

Please check the attached picture, please answer thoroughly!

Please check the attached picture, please answer thoroughly!

Answers

The selection depends on individual needs, preferences, and the intended use of the tiny house.

a) To find the amount of space inside each house, we need to calculate the volume for each design.

House on the left:

Volume = length x width x height = 2.5 m x 18 m x 2.8 m = 126 m³

Triangular house:

Volume of a triangular prism = (base area x height) / 2

Base area = (1/2) x base x height = (1/2) x 4 m x 10 m = 20 m²

Volume = (20 m² x 7 m) / 2 = 70 m³

b) When comparing the environmental impacts of each house, several factors need to be considered:

Positive impacts:

1. Material usage: Tiny houses use fewer materials, reducing resource consumption and waste generation.

2. Energy efficiency: Smaller living spaces require less energy for heating, cooling, and lighting, leading to lower energy consumption.

3. Land utilization: Tiny houses can be built on smaller plots of land, preserving green spaces and reducing urban sprawl.

Negative impacts:

1. Construction materials: Although tiny houses use less material overall, the environmental impact depends on the types of materials used. Sustainable and eco-friendly materials should be prioritized.

2. Water and waste management: Adequate provisions for water supply and waste disposal should be implemented to minimize environmental impacts.

3. Transportation: The transportation of tiny houses to their locations can contribute to carbon emissions if not done efficiently.

c) The choice of design for a tiny house depends on personal preferences and priorities. However, considering the provided information:

The house on the left offers a larger interior space of 126 m³, providing more room for living and storage. It may be suitable for individuals or couples who desire more space and functionality within their tiny house.

The triangular house has a smaller interior volume of 70 m³ but offers a unique design and aesthetic appeal. It may be preferred by individuals who prioritize a distinctive architectural style or who are looking for a minimalist and cozy living space.

Ultimately, the selection depends on individual needs, preferences, and the intended use of the tiny house. Factors such as lifestyle, desired amenities, and personal values regarding sustainability and resource conservation should be considered when making the final decision.

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the diagonals of a trapezoid are perpendicular and have lengths $3$ and $4$. find the length of the median of the trapezoid.

Answers

The correct answer is 5/2. The median trapezoid is the line segment that bisects the area of the trapezoid and has its end points on the 2 bases of the trapezoid.

The median length is √( (3/2)^2 + (4/2)^2 ) = √(9/4 + 16/4) = √(25/4) = 5/2. So, the length of the median of the trapezoid is 5/2.

Since the diagonals of a median trapezoid bisect each other, the median of the trapezoid is the line segment that connects the midpoints of the diagonals. To find the median length, we can use the distance formula, which is the square root of the sum of the squares of the differences in the x-coordinates and y-coordinates of the 2 points. In this case, the median length is the square root of the sum of the squares of 1/2 length of the diagonals.

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The length of the median of the trapezoid will be 5/2 units.

Given that the median trapezoid is the line segment that divides the trapezoid's area and has its ends on its two bases,

The median length will be:

√( (3/2)^2 + (4/2)^2 )

= √(9/4 + 16/4)

= √(25/4)

= 5/ units

So, the length of the median of the trapezoid is 5/2.

The median of a median trapezoid is the line segment that links the midpoints of the diagonals since the diagonals of a median trapezoid bisect one another. We may use the distance formula, which is the square root of the sum of the squares of the differences in the x-coordinates and y-coordinates of the two points, to get the length of the median. The median length in this instance is equal to the square root of the sum of the squares of the diagonals' half-lengths.

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7) Tom is deciding whether or not he should become a member of the gymſto use their basketball courts. The
membership cost is $135. Members pay $2 to rent out the basketball courts. Non-members can rent the court also, but
they have to pay $11 each time. How many times would Tom need to rent the court in order for it be cheaper to be a
member than a non member?

Answers

Answer:

15 times for it to be equal, 15+ to be cheaper

Step-by-step explanation:

135+2x=11x

135=9x

135/9=x

15=x

135+2(15)=165$

11(15)=165$

Answer:

16 times

Step-by-step explanation:

Create an inequality where x represents the number of times he rents out the court:

2x + 135 < 11x

Solve for x:

135 < 9x

15 < x

So, Tom would have to rent the court out 16 times for it to be cheaper

What are the domain and range of the function?

What are the domain and range of the function?

Answers

Answer:

i think it should be option 4bas it's cube root not square root

Find the value of x so that the ratios 8 : x and 12 : 18 are equivalent.

Answers

Answer:

12

Step-by-step explanation:

12:18=2:3 multiply by four to get 8 as the first term

8:12

8:x

so x is 12.

*this could be wrong so check my work

Answer:

x = 12

Explanation:

8 : x

12 : 18

to find the value of x, we need to convert 12 into 8. since they both have a common factor of 4, we can divide 12 by 3 to get 4, and then multiply it by 2 to get 8. in numerical terms, this is:

12 ÷ 3 = 4

4 × 2 = 8

now, we can do the same for 18.

18 ÷ 3 = 6

6 × 2 = 12

thus, 12 : 18 is equivalent to 8 : 12. x = 12.


The table shows the number of points scored by a basketball team in their first seven games.

The table shows the number of points scored by a basketball team in their first seven games.

Answers

Answer:

15

Step-by-step explanation:

the range is the largest number take away the smallest number

56-41=15

The Irrational Club wants to build a tree house. They have a 9-foot ladder that must be propped diagonally against the tree. If the base of the ladder is 5 feet from the bottom of the tree, how high will the tree house be off the ground? Group of answer choices

Answers

Answer:

Is there a picture to match?

Answer:

Step-by-step explanation: its 15 so yeah

The table below shows the predicted number of words Janae can type, y, in x minutes. Time (x, in minutes) Words Typed (y) 5 150 10 300 15 450 20 600 Which describes the pattern in the table? A. Janae types 25 words each minute. B. Janae types 30 words each minute. C. Janae types 145 words each minute. D. Janae types 150 words each minute.

Answers

Answer:

(B) 30 words each minute

Step-by-step explanation:

If you take any of the inputs and multiply it by 30 you will get the output of the number you chose

Janae can type 30 words each minute. which is the correct answer would be an option (B)

What are Arithmetic operations?

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.

/ Division operation: Divides left-hand operand by right-hand operand

For example 4/2 = 2

We have been given that the table indicates the expected number of words Janae can type, y, in x minutes.

Time (x, in minutes)     Words Typed (y)

 5                                       150

10                                       300

15                                       450

20                                      600

We have to determine the pattern which describes in the given table.

Words typed (y) divided by time (x, in minutes)

As per the table,

⇒ 150/5 = 30

⇒ 300/10 = 30

⇒ 450/15 = 30

⇒ 600/20 = 30

Therefore, he can type 30 words each minute.

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Round the number shown to the underlined place value 7.657

Answer choices
a.7.66
B.7.66
C. 7.67
D.7.68

Answers

the answer is A. 7.66 and B. which is also 7.66

4 A home-decorating company is determining the amount of fabric required for a customer's window treatments. A single window requires 13 yards and a double 7 window requires 16, yards of fabric. If there are two single windows and one double window, how much fabric is required?

Answers

The solution will be that the home-decorating company will require 42 yards of fabric for the customer's window treatments.

As per the information we have received from the question,

A single window requires 13 yards and a double window requires 16 yards of fabric. We are asked to find out the length of fabric that will be required by the home-decorating company, in case there were 2 single windows and 1 double window. The total amount of fabric that will be required by the home-decorating company is hence equal to

13×(no of single windows)+ 16×(no of double windows)

Here, no of single windows= 2

And, no of double window= 1

Hence, total fabric length=13×2 + 16×1=26 + 16=42 yards

Hence the solution is 42 yards of fabric.

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A supplier of portable hair dryers will make x hundred units of hair dryers available in the market when the unit price is p = 36 + 2.8x
dollars. Determine the producers' surplus if the market price is set at $8/unit. (Round your answer to two decimal places.)

Answers

The producers' surplus if the market price is set at $8/unit is $21000

Determining the producers' surplus

Given that

Price, p = 36 + 2.8x

The quantity  function is

q = 100x

So, the revenue at $8/unit is

R = 100x * 8

R = 800x

The total cost is calculated as

T(x) = (36 + 2.8x) * 100x

By calculation, we have the producers' surplus function to be

P = (36 + 2.8x) * 100x - 800x

Differentiate and set to 0

-560x - 2800 = 0

So, we have

x = 5

Recall that

P = (36 + 2.8x) * 100x - 800x

So, we have

P = (36 + 2.8 * 5) * 100 * 5 - 800 * 5

P = 21000

Hence, the producers' surplus is 21000

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Please help me, I'm giving away the rest of my points for this 2 part question..

for the second part the answer choices are

A: Right
B: Obtuse
C: Isosceles
D: Equilateral

Please help me, I'm giving away the rest of my points for this 2 part question..for the second part the
Please help me, I'm giving away the rest of my points for this 2 part question..for the second part the

Answers

Answer:

First part

angle ABC=94 degrees

angle BCD=25 degrees

angle ACB=43 degrees

Second part

C) isosceles and obtuse because angle ABC is greater than 90 degrees and angle ACB=angle CAB

Step-by-step explanation:

All triangles contain 180 degrees.

Triangles ADB and CDB are congruent because side-angle-side theorem.

Since angle ABD=133 degrees,  angle CBD=133 degrees because corresponding angles of congruent triangles are equal.

angle ABC=360-133-133=94 degrees

angle BCD=180-133-22=25 degrees

angle ACB=(180-94)/2=43

Angle ABC= 360 -(133+133) = 94 degrees
Angle BCD = 180 - (22+133) = 25 degrees
Angle ACD = (180-44)/2 = 68
Angle ACB = 68-25 = 43 degrees

For the second part, triangle ABC is isosceles

Answer fast please

ILL GIEV BRAINLIEST TO FIRST AND CORRECT ANSWER

Answer fast pleaseILL GIEV BRAINLIEST TO FIRST AND CORRECT ANSWER

Answers

Answer:

The area of the new rectangle is 9 times larger than the original rectangle

Step-by-step explanation:

For example if the length of a rectangle was 7 and the width was 6, to find area we multiply them. So 7×6=42

If we triple the length and width, we get 21×18=378.

378÷42=9.

This means the new rectangle's area is 9 times larger than that of the original.

find x for 3x + 10 = -5 and
find x for 3x - 12 = 9 please help

Answers

Answer:

3x+10=-5

3x=-15

x=-5

3x-12=9

3x=21

x=7

Answer:

1. \(x=-5\)

2. \(x=7\)

Step-by-step explanation:

First Equation

1. For the first equation, \(3x+10=-5\) we need to move all the constants to one side.

\(3x+10=-5\\3x=-15\)

2. Once that is done, we need to divide both sides by 3 to get \(x\) by itself.

\(3x=-15\\\frac{3x}{3}=\frac{-15}{3}\)

3. Now, we have our final answer.

\(x=-5\)

Second Equation

1. For the second equation, \(3x-12=9\) we need to move all the constants to one side.

\(3x-12=9\\3x=21\)

2. Once that is done, we need to divide both sides by 3 to get \(x\) by itself.

\(3x=21\\\frac{3x}{3} =\frac{21}{3}\)

3. Now, we have our final answer.

\(x=7\)

Hope this helped C:

A landscaper is designing a display of flowers for an area in a public park. The flower seeds will be planted at points that lie on a circle that has a diameter of 8 feet. the point where any seed is planted must be 2 feet away from the seeds on either side of it. what is the maximum number of flower seeds that can be planted using the design?

after planting the flower seeds the landscaper has 20 seeds left over. the landscaper wants to plant all of the remaining seeds in another circle so that the seeds are 2 feet apart. what is the diameter of the smallest circle that the landscaper can use to plant all of the remaining seeds?

Answers

The z-score for P(? ≤ z ≤ ?) = 0.60 is approximately 0.25.

The z-score for P(z ≥ ?) = 0.30 is approximately -0.52.

How to find the Z score

P(Z ≤ z) = 0.60

We can use a standard normal distribution table or a calculator to find that the z-score corresponding to a cumulative probability of 0.60 is approximately 0.25.

Therefore, the z-score for P(? ≤ z ≤ ?) = 0.60 is approximately 0.25.

For the second question:

We want to find the z-score such that the area under the standard normal distribution curve to the right of z is 0.30. In other words:

P(Z ≥ z) = 0.30

Using a standard normal distribution table or calculator, we can find that the z-score corresponding to a cumulative probability of 0.30 is approximately -0.52 (since we want the area to the right of z, we take the negative of the z-score).

Therefore, the z-score for P(z ≥ ?) = 0.30 is approximately -0.52.

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Which expression is equivalent to StartFraction 7 Superscript 5 Over 7 squared EndFraction? (7 times 5) (7 times 2) (7 times 7 times 7 times 7 times 7) (7 times 7) StartFraction 7 times 5 Over 7 times 2 EndFraction StartFraction 7 times 7 times 7 times 7 times 7 Over 7 times 7 EndFraction.

Answers

To solve the problem we will use the basic exponent properties.

What are Expressions?

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

What are the basic exponent properties?\({a^m} \cdot {a^n} = a^{(m+n)}\)\(\dfrac{a^m}{a^n} = a^{(m-n)}\)\(\sqrt[m]{a^n} = a^{\frac{n}{m}}\)

The solution to the given expression is \((7 \times 7 \times 7)\).

Given to us

\(\dfrac{7^5}{7^2}\)

Basic exponent properties,

To solve the problem we will use the basic exponent properties,

\(\dfrac{7^5}{7^2}\)

Using the property \(\dfrac{a^m}{a^n} = a^{(m-n)}\),

\(=\dfrac{7^5}{7^2}\\\\= 7^{(5-2)}\\=7^3\\=7 \times 7 \times 7\)

Hence, the solution to the given expression is \((7 \times 7 \times 7)\).

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Answer:

StartFraction 7 times 7 times 7 times 7 times 7 Over 7 times 7 EndFraction or d

Step-by-step explanation:

A sports store has 7 cans of tennis balls. The store sells 14 of those tennis balls and has 21 tennis balls left. How many tennis balls are in each can

Answers

Each can initially contains 5 tennis balls.

To find the number of tennis balls in each can, we can use the information given:

Initial number of cans of tennis balls = 7

Number of tennis balls sold = 14

Number of tennis balls left = 21

Let's assume that each can initially contains 'x' tennis balls.

Initially, the total number of tennis balls in the store is 7 cans * x balls/can = 7x.

After selling 14 tennis balls, the number of tennis balls left is 7x - 14.

We are given that the number of tennis balls left is 21, so we can set up the equation:

7x - 14 = 21

Simplifying the equation:

7x = 21 + 14

7x = 35

Dividing both sides of the equation by 7:

x = 35/7

x = 5

Therefore, each can initially contains 5 tennis balls.

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If −7∘C denotes a temperature of 7∘C below 0∘C, what does 5∘C mean
Can some pls sey someting

Answers

Answer:

123

Step-by-step explanation:

Answer:

temperature of 5° C above 0° C

Step-by-step explanation:

Which of the following best describes a triangle with one right angle and two congruent sides

Answers

Answer:

isosceles triangle

(-10)-(-6) ( subtracting integers)​

Answers

Negative when subtracted is counted as positive because negative multiplied with negative gives positive

-10-(-6)

-10+6

-4 answer

Answer:

-4

Step-by-step explanation:

(-10)-(-6)=

-10 + 6=

-4

hope this helps

have a good day

PLEASE NO LINKS AND NO NEGATIVITY

PLEASE NO LINKS AND NO NEGATIVITY

Answers

Step-by-step explanation:

Answer is student 1 and 3 ( the second option is correct )

Answer:

The answer is Student 1 and 3.

Step 1: Break down each multiple-choice.

Student 1: -(5r-3s+1)

Given the distributive law of multiplication, -, which is also known as -1, should be multiplied by every other term in the expression, which gives us -5r+3s-1

Student 2: -5r+3s+1 (given)

Student 3: -5r+3s-1

The values of Student 1 and 3 are the same, thus the answer is Student 1 and 3.

My song has put off her adornments. She has no pride of dress and decoration. Ornaments would mar our union; they would come between thee and me; their jingling would drown thy whispers. My poet’s vanity dies in shame before thy sight. O master poet, I have sat down at thy feet. Only let me make my life simple and straight, like a flute of reed for thee to fill with music. –"Song VII," Rabindranath Tagore Which line contains an example of personification? "O master poet, I have sat down at thy feet. " ". . . Like a flute of reed for thee to fill with music. " "My poet’s vanity dies in shame before thy sight. " "Only let me make my life simple and straight. . . ".

Answers

The passage does not contain any examples of personification. Personification is a figure of speech in which non-human things or ideas are given human attributes or qualities.

What is Personification?

Personification is a literary device in which non-human objects or concepts are given human-like qualities or characteristics, such as emotions or actions. For example, a common example of personification is when we describe the wind as "howling" or "whistling", which are human actions, even though the wind is not capable of producing those sounds on its own.

In the given passage, there are no instances of non-human objects or concepts being given human-like qualities or characteristics. Instead, the passage contains examples of metaphor and symbolism. For instance, the line "Like a flute of reed for thee to fill with music" is a metaphor comparing the speaker's life to a simple and straight flute that can be filled with music by the master poet. The line "My poet's vanity dies in shame before thy sight" is a symbolic expression of humility, as the speaker is expressing how he feels in the presence of the master poet.

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Probability: Sample Space, (In)dependent events

A coffee shop offers French roast and
Italian roast coffee.

Answers

Judgement will call the French toast

7 feet tall and casts a shadow of 12 feet. if the shadow of the backboard of the basketball hoop next to him is 24 feet tall, how tall is the backboard?

Answers

the backboard is 14 feet tall.by using similar Triangle properties (Height of person) / (Length of person's shadow) = (Height of backboard) / (Length of backboard's shadow)

Let's use similar triangles to find the height of the backboard.

Step 1: Identify the given measurements.
The person is 7 feet tall and casts a shadow of 12 feet. The shadow of the backboard is 24 feet.

Step 2: Set up a proportion using similar triangles.
(Height of person) / (Length of person's shadow) = (Height of backboard) / (Length of backboard's shadow)
7 ft / 12 ft = (Height of backboard) / 24 ft

Step 3: Solve for the height of the backboard.
To find the height of the backboard, cross-multiply and solve for the unknown value.
7 ft * 24 ft = 12 ft * (Height of backboard)

Step 4: Calculate the height of the backboard.
7 ft * 24 ft = 168 ft²
168 ft² / 12 ft = (Height of backboard)
14 ft = (Height of backboard)

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