Answer:
I = 91.125
Step-by-step explanation:
Given that:
[tex]I = \int \int_E \int zdV[/tex] where E is bounded by the cylinder [tex]y^2 + z^2 = 81[/tex] and the planes x = 0 , y = 9x and z = 0 in the first octant.
The initial activity to carry out is to determine the limits of the region
since curve z = 0 and [tex]y^2 + z^2 = 81[/tex]
∴ [tex]z^2 = 81 - y^2[/tex]
[tex]z = \sqrt{81 - y^2}[/tex]
Thus, z lies between 0 to [tex]\sqrt{81 - y^2}[/tex]
GIven curve x = 0 and y = 9x
[tex]x =\dfrac{y}{9}[/tex]
As such,x lies between 0 to [tex]\dfrac{y}{9}[/tex]
Given curve x = 0 , [tex]x =\dfrac{y}{9}[/tex] and z = 0, [tex]y^2 + z^2 = 81[/tex]
y = 0 and
[tex]y^2 = 81 \\ \\ y = \sqrt{81} \\ \\ y = 9[/tex]
∴ y lies between 0 and 9
Then [tex]I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \int^{\sqrt{81-y^2}}_{z=0} \ zdzdxdy[/tex]
[tex]I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \begin {bmatrix} \dfrac{z^2}{2} \end {bmatrix} ^ {\sqrt {{81-y^2}}}_{0} \ dxdy[/tex]
[tex]I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \begin {bmatrix} \dfrac{(\sqrt{81 -y^2})^2 }{2}-0 \end {bmatrix} \ dxdy[/tex]
[tex]I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \begin {bmatrix} \dfrac{{81 -y^2} }{2} \end {bmatrix} \ dxdy[/tex]
[tex]I = \int^9_{y=0} \begin {bmatrix} \dfrac{{81x -xy^2} }{2} \end {bmatrix} ^{\dfrac{y}{9}}_{0} \ dy[/tex]
[tex]I = \int^9_{y=0} \begin {bmatrix} \dfrac{{81(\dfrac{y}{9}) -(\dfrac{y}{9})y^2} }{2}-0 \end {bmatrix} \ dy[/tex]
[tex]I = \int^9_{y=0} \begin {bmatrix} \dfrac{{81 \ y -y^3} }{18} \end {bmatrix} \ dy[/tex]
[tex]I = \dfrac{1}{18} \int^9_{y=0} \begin {bmatrix} {81 \ y -y^3} \end {bmatrix} \ dy[/tex]
[tex]I = \dfrac{1}{18} \begin {bmatrix} {81 \ \dfrac{y^2}{2} - \dfrac{y^4}{4}} \end {bmatrix}^9_0[/tex]
[tex]I = \dfrac{1}{18} \begin {bmatrix} {40.5 \ (9^2) - \dfrac{9^4}{4}} \end {bmatrix}[/tex]
[tex]I = \dfrac{1}{18} \begin {bmatrix} 3280.5 - 1640.25 \end {bmatrix}[/tex]
[tex]I = \dfrac{1}{18} \begin {bmatrix} 1640.25 \end {bmatrix}[/tex]
I = 91.125
Find each product. Then determine which conclusion can be drawn based on the results.
√2•√2
√5•√7
√ 2•18
√2•√6
The product of two irrational numbers is always rational.
The product of two irrational numbers can be rational or irrational.
The product of two irrational numbers is always irrational.
The product of two irrational numbers cannot be determined.
Answer:
Second answer:
"The product of two irrational numbers can be rational or irrational"
Step-by-step explanation:
notice from the first product
[tex]\sqrt{2} \,* \,\sqrt{2} = \sqrt{4} = 2[/tex]
that the product of two irrational numbers can give us a rational one.
from the other three examples, the answer for the products always contains a square root that cannot be reduced, so they all result in an irrational number.
Then, depending on the type of irrationals used, the product can be either rational or irrational.
solve for y. y/6 = 3/9 simplify your answer as much as possible
Answer: y=2
Step-by-step explanation:
y/6 = 3/9 multiply both sides by 6/1 (since 6/1 times y/6 equals 1y or just y)
y = 18/9 now that y is isolated, just simplify 18/9
y=2 18 divided by 9 is 2
find the mode in the set 3,5,7,13,7,9,3
Answer:
3 and 7
Step-by-step explanation:
The mode of a set is the number that appears the most frequently. There can be multiple modes in a set. Looking at the given set, we see that the numbers that show up the most are 3 and 7 so that is our answer.
Answer:
3 and 7
Step-by-step explanation:
The mode means the number that appears the most.
hope this helps you :)
Mr.rodriguez invests half money in land a tenth in stocks and a twentieth in bonds he puts the remaining 35,000 in his savings account what is the total amount of money that Mr Rodriguez saves and invests
Answer:
Step-by-step explanation:
Sam can prepare 30 wall paintings in four weeks.How much time will he need to do 90 wall painting s
You and two friends pay $40 for tickets. The cost was divided three ways in the ratio 1 : 3 : 6. How much did each person pay
Answer:
first person payed$4, second person payed$12 and the third person payed $24
Step-by-step explanation:
find the sum of the ratio
find
1 divided by the total ratio time $40 to get first person
follow in that order to get the amount each person payed.
(-2.8)^6 (Round to three decimal places as needed)
Answer:
481.890
Step-by-step explanation:
481.890304 rounded to the nearest hundredth will be 481.890
) LaTanya is decorating her living room and draws
a floorplan to help look at placement.
10
9
co
A. LaTanya wants to hang a pictur at the center
of the back wall. How do you find the point at
the center between A and B?
Answer:
56
Step-by-step explanation:
calculate the length of the base of a parallelogram if the area is 135cm and it's height is 9cm
Answer:
15cm
Step-by-step explanation:
The formula to calculate the area of a parallelogram is base x height.
Since we know the height and area, we can write the equation:
135 = base x 9
Now we can just divide 9 from both sides to solve for base:
135/9=basex9/9
So we get:
Base = 135/9=15
The length of the base is 15cm.
Hope this helped!
Answer:
lol
Step-by-step explanation:
2. haha
3. haha.5.jsj
can i plz get help? on these ?
Step-by-step explanation:
she is showing how many wheels are on each bike and skateboard,on each bike there are 2 wheels,on each skateboard there are 4 wheels. sarahs is different because she shows how many wheels are on each of those bikes
a+2a-1=11
Be quick please :D
Answer:
[tex]a=4[/tex]
Step-by-step explanation:
So we have the equation:
[tex]a+2a-1=11[/tex]
First, combine like terms:"
[tex]3a-1=11[/tex]
Now, add 1 to both sides:
[tex]3a=12[/tex]
Divide both sides by 3:
[tex]a=4[/tex]
And we're done!
jayden has two jobs. his full time job pays $17 an hour. a part time job pays $9 an hour. last week jayden worked 32 hours at his full time job and 14 hours at his part time job
Answer:
670
Step-by-step explanation:
32 hours at 17 plus 14 hours at 9
32 *17 + 14 *9
544+126
670
Answer:
job 1 = 544 dollars he made job 2 = 126$
Step-by-step explanation:
You multiply the amount he made for 1 hour by the total hours same thing with job 2.
HELP PLZ NEED ASAP AND BRAINLIEST Simplify the complex fraction. In complete sentences, explain the process that you followed to simplify the fraction. Include the LCD and simplified form in your answer. Complete your work in the space provided or upload a file that can display math symbols if your work requires it.
A-9/a / 1-3/a=
Answer:
the answer is a+9/2
Step-by-step explanation:
a-9/a/1-3/a
=a-9/a/-2/a
=a+9/a/2/a.
( dividing two negatives is equal to positive)
=a+9/a*a/2
doing reciprocal
=a+9*1/2
reduce the expression"a"
=a+9/2
find the product
answer is a+9/2
I need help with #2 and 4 please help me T^T
Answer:
2. w = -90
4. b = 8
Step-by-step explanation:
Multiply both sides by the reciprocal of the number multiplying the variable.
2.
[tex] -\dfrac{2}{3}w = 60 [/tex]
[tex] -\dfrac{3}{2} \times (-\dfrac{2}{3}w) = -\dfrac{3}{2} \times 60 [/tex]
[tex] w = -\dfrac{180}{2} [/tex]
[tex] w = -90 [/tex]
4.
[tex] 9.6 = 1.2b [/tex]
[tex] \dfrac{1}{1.2} \times 9.6 = \dfrac{1}{1.2} \times 1.2b [/tex]
[tex] 8 = b [/tex]
[tex] b = 8 [/tex]
Hello what is 50+3 ? c h a t w i t h p e p s
Answer:
50+3=53
Step-by-step explanation:
mark as Brainliest
Answer:
53
Step-by-step explanation:
5+5+5+5+5+5+5+5+5+5+1+1+1
find two consecutive odd integers such as that 6 times the lesser integer is 7 more than 5 times the greater integer
Answer:
The first consecutive integer is 17 while the second is 19
Step-by-step explanation:
Let us say that the first odd integer is x
At this point, the second odd integer will be x+2.
This is because to obtain the next consecutive odd integer, 2 will have to be added to the original number.
From the question, we can set up an equation as shown below:
[tex]6x= 7+5(x+2)[/tex]
from this, we can simply evaluate and find out the value of x
[tex]6x=7 +5x +10\\x=17[/tex]
therefore, the first consecutive integer is 17 while the second is 19
\dfrac{4}{9},-\dfrac{4}{3},4, 9 4 ,− 3 4 ,4,
Answer:
[tex]-\frac{8}{9}[/tex]
Step-by-step explanation:
[tex]\dfrac{4}{9}-\dfrac{4}{3}\\\\\mathrm{Least\:Common\:Multiplier\:of\:}9,\:3:\quad 9\\\\\mathrm{Adjust\:Fractions\:based\:on\:the\:LCM}\\\\\frac{4}{3}=\frac{4\times\:3}{3\times\:3}=\frac{12}{9}\\\\=\frac{4}{9}-\frac{12}{9}\\\\\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\\\\\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\\\=\frac{4-12}{9}\\\\=\frac{-8}{9}\\\\=-\frac{8}{9}[/tex]
Answer:
what?
Step-by-step explanation:
Can you please help with question 2 and explain your work?
Answer:
Find AC+CB
Step-by-step explanation:
Answer:
Find [tex]AC + CB[/tex]; 10
Find AB; 10
Step-By-Step Explanation:
[tex]AC (3) + CB (7) = 10[/tex]
Find AB is the same thing, just phrased differently.
70% of 120 = 120x70/100
How do you figure this out
A store recorded the number of sweatshirts sold on several days throughout the year. The
scatterplot shows the relationship between the average daily temperature and the number of
sweatshirts sold.
Complete the following statement.
For every 10-degree increase in temperature, the store sells approximately
fewer
sweatshirts
A. 5
B. 10
C 30
D.50
Answer:
30
Step-by-step explanation:
For every 10-degree increase in temperature, the store sells around 50 fewer sweatshirts. The correct option is D.
What is regression analysis?Regression analysis is a group of statistical procedures used in statistical modeling to determine the relationships between a dependent variable and one or more independent variables.
A scatter plot is a particular kind of plot or mathematical diagram that displays values for typically two variables for a collection of data. It uses Cartesian coordinates. When the points are coded, a further variable can be seen.
Given that store recorded the number of sweatshirts sold on several days throughout the year. The scatterplot shows the relationship between the average daily temperature and the number of sweatshirts sold.
Here is the scatter plot, it is observed that by increasing the temperature the number of sweatshirts sold is decreasing. For every 10-degree depression of temperature, the number of the sells is decreased by 50.
Therefore, for every 10-degree increase in temperature, the store sells around 50 fewer sweatshirts. The correct option is D.
To know more about regression analysis follow
https://brainly.com/question/26755306
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Question #1:
Select all the statements that are true of a least-squares regression line.
The regression line maximizes the residuals between the observed values and the predicted values.
The slope of the regression line is resistant to outliers.
In the equation of the least-squares regression line, ġ is an observed value when x is known.
The sum of the residuals is always close to zero.
The coefficient of determination measures how much of the variation in the y-values is explained by the regression line.
In the equation of the least-squares regression line, is a predicted value when x is known.
Answer:
1. The sum of the residuals is always close to zero.
2.The coefficient of determination measures how much of the variation in the y-values is explained by the regression line.
3. In the equation of the least-squares regression line, y hat is a predicted value when x is known
Step-by-step explanation:
The least square regression line is a line that makes distance from data points to the regression line to be as minimal as possible. This line is a best fit for the data points. Let's say we have a collection of numbers and a scatter plot, this line is a line that exists and best fits the data.
Therefore, the least square regression line minimizes sum of squared error to be close to zero. R² measures the extent to which variations in the value of y is explained by the regression line. In the equation of this line, y hat is a predicted value when x is known.
The least square regression line minimizes the sum of squared error such that the sum of the residual is zero or very close to 0. Hence, the true statements from the options given are :
Sum of residuals is always close to 0The coefficient of determination measures how much of the variation in the y-values is explained by the regression line.[tex]y_{hat} [/tex] is the predicted value when x is known.The least square regression Line is used to create a Linear model in the form y = bx + c
The Coefficient of determination R² gives the proportion of the variation explained by the regression line.
The predicted value of y is obtained using the model of the Least Square Regression Line for a given value of x.
Outlier values often affects the performance and accuracy of the Least Square Regression Line.
Learn more :https://brainly.com/question/18405415
Use Polya's four-step problem-solving strategy and the problem-solving procedures presented in this lesson to solve the following exercise. The number of ducks and pigs in a field totals 38. The total number of legs among them is 100. Assuming each duck has exactly two legs and each pig has exactly four legs, determine how many ducks and how many pigs are in the field. ducks pigs
The function g is defined below . g(x) = (x - 5)/(x ^ 2 - 36) Find all values of x that are NOT in the domain of g. If there is more than one value, separate them with commas.
Answer:
-6, 6
Step-by-step explanation:
So we have the rational function:
[tex]g(x)=\frac{x-5}{x^2-36}[/tex]
The domain of a rational function is all real numbers except for when x is a zero of the denominator.
Thus, to determine the domain restrictions, set the denominator to 0 and solve for x:
[tex]x^2-36=0[/tex]
Add 36 to both sides:
[tex]x^2=36[/tex]
Take the square root of both sides:
[tex]x=\pm 6[/tex]
So, the values that are not in the domain of g is: -6, 6.
And we're done!
I need help with this ASAP
Answer:
x=5
Step-by-step explanation
Move all terms containing x to the left side of the equation.
4x-8=12
Move all terms not containing x to the right side of the equation.
4x=20
Divide each term by 4 and simplify.
x=5
(x-1)2/3+(x-1)1/3-6=0
Answer:
x=7
Step-by-step explanation:
Add 6 to both sides
Simplify
Expand the parentheses
Add 1 to both sides
A local library claims it has 2.73x103 books. If there are 42 people in the building, how many books per capita are there?
Answer:
63 books per capita in the library
Step-by-step explanation:
Given
[tex]Books = 2.73 * 10^3[/tex]
[tex]People = 43[/tex]
Required
Determine the book per capita
To do this, we simply divide the number of books by number of person;
[tex]Average = \frac{Books}{People}[/tex]
[tex]Average = \frac{2.73 * 10^3}{43}[/tex]
[tex]Average = \frac{2.73 * 1000}{43}[/tex]
[tex]Average = \frac{2730}{43}[/tex]
[tex]Average = 63.488372093[/tex]
[tex]Average = 63[/tex] (Approximated)
Hence;
There are 63 books per capita in the library
write a sentence as an equation
b is 380 more than the quantity y time 268
Answer:
b is → b =
380 more → + 380
y time 268 → 268y
combine
b = 268y + 380
what decimal is longer than 8.5 cm
Answer:
8.5555Step-by-step explanation:
This number is not only larger, but also longer in digits than 8.5.
___________________________________________________I AM ALWAYS HAPPY TO HELP :)
Identify the sequence below as arithmetic, geometric, or neither. Then find the next two terms a5 and a6
10, 30, 90, 270,
Answer:
Geometric sequence of common ratio = 3
a5 would be: 810,
and a6 = 2430
Step-by-step explanation:
The sequence is a geometric sequence because each term is produced by multiplying the previous one by the factor 3 (called the common ratio)
then terms a5 and a6 would be: 810, and 2430 respectively
Solve:
1. (12+a) / 47 = - 18
Answer:
a= -858
Step-by-step explanation:
46 times -18 equals -846
-846-12 equals -858
Answer:
a=-858
Step-by-step explanation:
12+a=846
a=-846-12
a=-858