Find Mx, My, and (x, y) for the lamina of uniform density rho bounded by the graphs of the equations. y = x2/3, y = 0, x = 1

Answers

Answer 1

The required value for the lamina of uniform density [tex]\bar x\\[/tex] and  [tex]\bar y[/tex] are written below,

[tex]\bar x = \dfrac{5}{8}\\[/tex]

[tex]\bar y = \dfrac{5}{14}[/tex]

Given that:

The density of lamina: ρThe graph for the lamina: [tex]y = x^{\frac{2}{3}}[/tex], y = 0, and x = 1

Calculus's core idea of integration entails determining a function's integral. It is a reverse process of differentiation that enables us to compute cumulative numbers, find the area under a curve, solve differential equations, and more.

The function can be written as,

[tex]m = \rho\int_0^1x^{\frac{2}{3}}dx\\= \rho\left[\dfrac{x^{\frac{5}{3}}}{\frac{5}{3}}}\right]\\=\dfrac{3}{5}\rho[/tex]

The value of Mx can be calculated as,

[tex]M_x = \rho\int_0^1\dfrac{x^{\frac{2}{3}}}{2}}\times x^{\frac{2}{3}}dx\\=\dfrac{\rho}{2}\left[\dfrac{x^{(\frac{2}{7})}}{\frac{7}{3}}\right]_0^1\\=\dfrac{3}{14}\rho[/tex]

Calculate the value of My,

[tex]M_y =\rho \int_0^1 x\times x^{\frac{2}{3}}dx\\=\rho \left[\frac{x^\frac{8}{3}}{\dfrac{8}{3}}\right]\\=\dfrac{3}{8}{\rho[/tex]

The value of [tex]\bar x\\[/tex] will be calculated as,

[tex]\bar x = \dfrac{M_x }{m}\\=\dfrac{ \dfrac{3}{8}\rho}{\dfrac{3}{5}\rho}\\=\dfrac{5}{8}[/tex]

The value of [tex]\bar y\\[/tex] is calculated as,

[tex]\bar y= \dfrac{M_y }{m}\\=\dfrac{ \dfrac{3}{14}\rho}{\dfrac{3}{5}\rho}\\=\dfrac{5}{14}[/tex]

Therefore, the required values are [tex]\bar x = \dfrac{5}{8}\\[/tex] and  [tex]\bar y = \dfrac{5}{14}[/tex].

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Related Questions

What is the quotient of 1 1/4 divided by 21 1/4

Answers

Answer: 1/17

Explanation:

1 1/4 = 5/4
21 1/4 = 85/4

5/4 divide by 85/4
= 5/4 x 4/85
= 1/17

Answer:

quotient of 11/4 to be divided by 21 /1/4

gives you 7/8/11

James is studying different kinds of weather. Rain has water drops that are larger than 0.02 inch in diameter. Small hailstones are less than 14 inch in diameter. Complete the statement that best represents the different kinds of weather James studied. Select one correct answer from each box to complete the sentence.

Answers

Answer:

wheres the stament

Step-by-step explanation:

Answer:

huh

Step-by-step explanation:

HELP! WILL MARK BRAINLIEST!

Answers

Answer:

The answer to this question is C.

Step-by-step explanation:

All that you have to do is multiply the exponents.

Match each equation with its solution equation n-13=-12

Answers

Answer:

n=1, :) :P UwU TwT -_-

Answer:

n = 1

Step-by-step explanation:

n-13=-12

n-13-(-12)=0

n-1=0

n=1

Given the equation y=12x, x representing number of hours worked, y representing amount of money earned, how much would John earn if he worked 6 hours?

Answers

9514 1404 393

Answer:

  72

Step-by-step explanation:

Substitute 6 for x in the equation and do the arithmetic.

  y = 12x

  y = 12·6 = 72

John earns 72 money units in 6 hours.

how long does it take an airplane if it files a distance of 2000 miles at a rate of 500mph

Answers

Answer:

4 hours

Step-by-step explanation:

We can find the time using the formula [ t = d/s ] where d = distance and s = speed.

t = 2000/500

t = 4 hours

Best of Luck!

Can someone help me out and fast?​

Answers

Answer:

yes, lets see...no that is not a function.

Step-by-step explanation:

no explanation...that's where your on your own, sorry. (its very hard to explain,

but i know that its impossible to have a function like THAT)

Answer:

no because there are 2 lines on the same x axis

Step-by-step explanation:

what divide by -1/2 equals -7/3

Answers

It would be 3/14 hope that helps :)

HELP ASAP PLEASE

Given x^2=81, select all possible values of x.

A. -9
B. -3
C. 0
D. 3
E. 9

Answers

Answer:

A and E

Step-by-step explanation:

x² = 81

~Take the square root of both sides

x = ±9

Best of Luck!

Answer:

The answer is a and e

Step-by-step explanation:

Dominique has $13.75 in her piggy bank. All of the money are quarters. How many quarters are in the piggy bank?

Answers

Answer: I think its 0.55

Step-by-step explanation: if you do 25 times 0.55 because quarter's are 25 cents it equals 13.75

The number of quarters in the piggy bag will be 55.

What is unit conversion?

Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure. Unit conversion is the process of changing a quantity's measurement between different units, frequently using multiplicative conversion factors.

Given that Dominique has $13.75 in her piggy bank. All of the money is quarters.

The number of the quarters will be calculated as:-

1 dollar ⇒ 4 quarters

13.75 dollars ⇒ 13.75 x 4 quarters

13.75 dollars ⇒ 55 Quarters

Therefore, the number of quarters in the piggy bag will be 55.

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The endpoints of EF¯¯¯¯¯ are located at E (−3, 2) and F (3, 8). Point D divides EF¯¯¯¯¯ such that ED : DF is equal to 1 : 3. For each box, select the values in the dropdown that make the statement true. The x-coordinate of point D is and the y-coordinate of point D is

Answers

Answer:

[tex]D(x,y) = (-1.5,3.5)[/tex]

Step-by-step explanation:

Given

[tex]E = (-3,2)[/tex]

[tex]F = (3,8)[/tex]

[tex]ED: DF = 1 : 3[/tex]

Required

Determine the coordinates of D

This is calculated as thus:

[tex]D(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]

Where:

[tex](x_1,y_1) = (-3,2)[/tex]

[tex](x_2,y_2) = (3,8)[/tex]

[tex]m:n = 1:3[/tex]

[tex]D(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]

[tex]D(x,y) = (\frac{1 * 3 + 3 *-3}{1+3},\frac{1 * 8 + 3 * 2}{1+3})[/tex]

[tex]D(x,y) = (\frac{-6}{4},\frac{14}{4})[/tex]

[tex]D(x,y) = (-1.5,3.5)[/tex]

I need to find the missing angle of this triangle or whatever it is

Answers

Answer:

×=126+28

=154 degrees

A bug starts at the origin of the coordinate plane. The bug moves One-fourth units right and One-fourth units down to point A. Which graph shows the location of point A?

Answers

Answer:

the answer would be d

Step-by-step explanation:

i took the test on edge2020

Answer:

D

Step-by-step explanation:

Edg 2020

A magazine includes a report on the energy costs per year for​32-inch liquid crystal display​ (LCD) televisions. The article states that 14 randomly selected​ 32-inch LCD televisions have a sample standard deviation of ​$3.42 . Assume the sample is taken from a normally distributed population. Construct 98 ​% confidence intervals for​ (a) the population variance sigma squared and​ (b) the population standard deviation sigma .
Interpret the results. ​(a) The confidence interval for the population variance is ​(___,___ ​). ​(Round to two decimal places as​ needed.)
Interpret the results. Select the correct choice below and fill in the answer​ box(es) to complete your choice. ​(Round to two decimal places as​ needed.)
A. With 98 ​% ​confidence, you can say that the population variance is less than ___.
B. With 2 ​% ​confidence, you can say that the population variance is between nothing and ___ .
C. With 98 ​% ​confidence, you can say that the population variance is between ___ and ___ .
D. With 2 ​% ​confidence, you can say that the population variance is greater than ___
​(b) The confidence interval for the population standard deviation is ​(n___,___​). ​(Round to two decimal places as​needed.)
Interpret the results. Select the correct choice below and fill in the answer​ box(es) to complete your choice. ​(Round to two decimal places as​ needed.)
A. With 98​% ​confidence, you can say that the population standard deviation is between ___ and ___ dollars per year.
B. With 98​% ​confidence, you can say that the population standard deviation is greater than ___ dollars per year.
C. With 2​% ​confidence, you can say that the population standard deviation is less than ___ dollars per year.
D. With 2​% ​confidence, you can say that the population standard deviation is between ___ and ___ dollars per year.

Answers

Answer:

a

The confidence interval for the population variance is ​[tex] 5.49 < \sigma^2 < 37.02 [/tex]  

The correct option is  C

b

The confidence interval for the population standard deviation is [tex] 2.34 < \sigma < 6.08 [/tex]

The correct option is  A

Step-by-step explanation:

From the question we are told that

    The sample size is  n =  14

    The standard deviation is  [tex]s = \$3.42[/tex]

Generally the degree of freedom is mathematically represented as

     [tex]df =  14 -1[/tex]

=>   [tex]df =  13 [/tex]    

Given that the confidence level is  98%  then that level of significance is  

     [tex]\alpha = (100 -98) \%[/tex]

=>  [tex]\alpha = 0.02[/tex]

Generally the 98% confidence interval for the variance  is mathematically represented as

     [tex]\frac{(n- 1) s^2}{x^2 _{[\frac{\alpha }{2} , df]}}  < \sigma^2 < \frac{(n- 1) s^2}{x^2 _{[1- \frac{\alpha }{2} , df]}}[/tex]

=> [tex]\frac{(14- 1) (3.42)^2}{x^2 _{[\frac{0.02 }{2} , 13]}}  < \sigma^2 < \frac{(14- 1) (3.42)^2}{x^2 _{[1- \frac{0.02 }{2} , 13]}}[/tex]

From the chi -distribution table  

     [tex]x^2 _{[1- \frac{0.02 }{2} , 13]} = 4.107[/tex]

and

    [tex]x^2 _{[\frac{0.02 }{2} , 13]} = 27.689[/tex]

So

=> [tex]\frac{(14- 1) (3.42)^2}{27.689}  < \sigma^2 < \frac{(14- 1) (3.42)^2}{4.107}[/tex]    

=> [tex] 5.49 < \sigma^2 < 37.02 [/tex]    

Generally the 98% confidence interval for the standard deviation   is mathematically represented as

   [tex]\sqrt{\frac{(n- 1) s^2}{x^2 _{[\frac{\alpha }{2} , df]}}}   < \sigma <\sqrt{ \frac{(n- 1) s^2}{x^2 _{[1- \frac{\alpha }{2} , df]}}}[/tex]

=> [tex]\sqrt{5.49}  < \sigma < \sqrt{37.02 }[/tex]

=> [tex] 2.34 < \sigma < 6.08 [/tex]

64 mi/h to ft/s HELP HELP HELP HELP NOW!!!! WILL PUT 5 STARS AND MARK BRAINLIEST!!!

Answers

Answer:

Multiply 64 x 5280

Step-by-step explanation:

You will get your answerhello

Answer:

64 mi/h = 93.9 ft/s I have the answer guide

(11 points!) PLEASEEEEEEEEE Find the value of x for numbers 6,7,8,and 9 and please attach work or a good explanation thank you sm in advance!❤️

Answers

(6) 2xº = 86º  ==>  x = 43

(7) 108º = 3xº  ==>  x = 36

(8) 72º = 4xº  ==>  x = 18

(9) 111º = (x + 21)º  ==>  x = 90

Answer:

1.

2x=86

x=43

2.

3x=108

x=36

3.

4x=72

x=18

4.

x+21=111

x=90

Pleaseeeeeee I rlly need help y’all help me out PLEASE HELP ASAP WILL GIVE BRAINLEIST
Mr. Velasquez wants to make a scale drawing of a set for an upcoming play. If the actual width of the stage is 18 feet and the scale he is using is LaTeX: \frac{1}{2}in
1
2
i
n
: 15 feet. What would the width of the stage be in the scaled drawing?



Answer as a decimal.

Answers

Answer:

0.6 in

Step-by-step explanation:

Scale of drawing = ½ inch to 15 ft (½ in : 15 ft)

That is, ratio of the width on paper to actual width.

Given an actual width of 18 ft, the width of the stage on paper can be calculated as shown below:

½ in : 15 ft = x in : 18 ft

[tex] \frac{\frac{1}{2}}{15} = \frac{x}{18} [/tex]

[tex] \frac{1}{2}*\frac{1}{15} = \frac{x}{18} [/tex]

[tex] \frac{1*1}{2*15} = \frac{x}{18} [/tex]

[tex] \frac{1}{30} = \frac{x}{18} [/tex]

Cross multiply

[tex] 30*x = 18*1 [/tex]

[tex] 30x = 18 [/tex]

Divide both sides by 30

[tex] \frac{30x}{30} = \frac{18}{30} [/tex]

[tex] x = \frac{18}{30} = \frac{6}{10} [/tex]

[tex] x = 0.6 [/tex]

Width of the stage in scale drawing = 0.6 in

Yousef typed a 36-word paragraph in 23 minute. What is his typing speed, in words per minute?

Answers

Answer:

1.5652173913 words per minute.

Step-by-step explanation:

When you divide 36 words/ 23 minutes, you get 1.5652173913.

Multiply 3/5 by 10/21 Express your answer in simplest form ​

Answers

Answer:

2/7

Step-by-step explanation:

Answer:

3/5 * 10/21= 2/7

How many 3-digit natural numbers are there?

Answers

Answer:

900

Step-by-step explanation:

natural numbers are all positive numbers that dont include 0

The Dean of the Business School at State University would like to test the hypothesis that no difference exists between the average final exam grades for the Introduction to Marketing course and the Introduction to Finance course. A random sample of eight students who took both courses was selected and their final exam grades for each course are shown below.

Student 1 2 3 4 5 6 7 8
Marketing 82 86 74 93 90 76 87 100
Finance 76 91 70 79 96 70 85 81

If Population 1 is defined as the Marketing exam scores and Population 2 is defined as the Finance exam scores. Which of the following test is appropriate for Dean's hypothesis?

a. One-way ANOVA
b. Paired samples t- test
c. One sample t- test
d. Independent samples t-test

Answers

Answer:

Paired samples t- test is appropriate for Dean's hypothesis

Step-by-step explanation:

Given Data :

Student           1     2     3      4      5      6      7      8

Marketing      82  86   74    93    90    76   87   100

Finance         76   91    70    79    96     70  85   81

We are supposed to find the test which is appropriate for Dean's hypothesis

We are given the grades of two different subjects for same student

We perform the paired t test because the final grades for the Marketing and Finance  is taken for the same student.

So, Option B is correct

Hence Paired samples t- test is appropriate for Dean's hypothesis

If 5/9 of a tank can be filled in 2minutes , how many minutes will it take to fill the whole tank?

Answers

Answer:

4 1/2 minutes

Step-by-step explanation:

.

As shown in the table, prizes are awarded to students who Benjamin, a student in the class, answers 80 math probalems correctly. His grandmother pays $0.25 per correct answer. His uncle gives him a donation. If benjamin receives $45 from his grandmother ans uncles, how much money does his uncles give him? Explain.

Answers

1.80$ probably worng





explain:




2
10x2 - 724
100x2 + 140xy + 4972 10x + 7y

Answers

Answer:

14xy/(10x+7y)^

Step-by-step explanation:

Six and forty-two ten-thousandths as a decimal

Answers

6.0042 is the answer
6.042 is the answer hope u get this

Find the midpoint of the line segment joining the points ​R(3​,​3) and ​S(​-2,6​).

Answers

Answer: 2,9

(3,3) & (-2,6) midpoints

Answer:

(0.5,4.5)

Step-by-step explanation:

Use the midpoint formula to find the answer: ((x1+x2/2),(y1+y2/2))

((3-2/2),(3+6/2))

((1/2),(9/2))

(0.5,4.5)

True or False: A triangle can be formed with sides 3inches, 3inches, 6inches. Explain your choice.

Answers

Answer: It's true because 3+3+6 = 12 and a triangle has 3 sides and 12/3 is 4 that's why a triangle can be fored with these measurments.

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

It would be classified as an isosceles triangle.

Hope this helps!

t> -5
can someone show step by step how to solve this equation?

Answers

Answer: The equation cannot be simplified any further.

Explanation: The variable(t) is greater than any number than negative five.

Plz mark brainliest:)

17-6r=25-3r answer it please

Answers

Answer: r = - 8/3

Step-by-step explanation: im pretty sure thats the write answer

is this a keep, change, change?
-9-8

Answers

Answer:

Yes, they cancel each other out.

Step-by-step explanation:

Personally never liked the keep, change, change method. Pemdas is what I use, however this is an easy one so nothing so major.

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For a program to be successful, readiness for training should be assessed on two dimensions: employee characteristics and work environment. The employee characteristics that are relevant to training are the ability to learn the subject matter, attitudes toward training, and motivation to learn. Even if these are present, however, training will not be effective unless there is a positive work environmentan environment that encourages learning and eliminates obstacles for trainee success. An important characteristic of employee readiness is having basic learning skills, especially cognitive ability that includes using written and spoken language, solving math problems, and using logic to solve problems. If employees lack certain basic skills, they may have to attend some remedial classes before participating in job-related training. Seeing potential benefits from training programs may increase employee motivation to participate. 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Elizabeth really doesn't think top management is going to allocate enough money to train everyone on the new software this year. 4. Although Jane really wanted to participate in the diversity training program, she knew it was impossible to get away from the office for three days in order to participate. 5. Ed was excited to hear about the new technical training program, but disappointed when he heard his boss say that he really didn't think the training was the time and effort a. Social Support b. Situational Constraints c. Employee Readiness aaaaaaaaaaaaaaaaaaaaa Find the distance between (8,-4,7) and (8,5,3)