evaluate the double integral. 7y2 da, d is the triangular region with vertices (0, 1), (1, 2), (4, 1) d
Answers
The value of double integral over the triangular region is \(\frac{77}{3}\) square units.
Given,
the vertices of triangular region are A(0, 1), B(1, 2), C(4, 1).
the double integral function is \(\int\limits\int\limits 7y^2 dA\)
The equation for line between A and C is:
y = 1
The equation for line between A and B is:
General equation is \(y = mx + b\)
The slope,
\(m_1 = \frac{ 2 - 1}{ 1 - 0 }\\\\ m_1 = 1\)
and the line passes over the point x = 0 y = 1; then
\(1 = 0 +b \\\\b = 1\)
equation becomes,
\(y = x + 1\\\\ x = y - 1\)
The equation for line between B and C is:
\(m_2 = \frac{ 1 - 2 }{ 4 - 1}\\\\m_2 = \frac{- 1}{3}\)
\(y = \frac{-1}{3}x + b\)
when (x, y) = (1, 2)
\(2 = \frac{- 1}{3}(1) + b\\\\2 + \frac{1}{3} = b\\\\b =\frac{7}{3}\)
Equation becomes,
\(y = - \frac{x}{3} + \frac{7}{3}\\\\x = 7 - 3y\)
The double integral becomes,
\(=\int\limits\int\limits 7y^2 dA\\\\\int\limits^2_1\int\limits^{7-3y}_{y-1} 7y^2 dxdy\\\\\int\limits^{2}_{y=1} 7 y^2dy\int\limits^{7-3y}_{x=y-1}dx\\\\\int\limits^{2}_{y=1} 7 y^2dy[x]|\limits^{7-3y}_{x=y-1}\\\\\int\limits^{2}_{y=1} 7 y^2dy[7-3y-(y-1)]\\\\=7[\frac{y^3}{3}][8-4y]|\limits^2_1\\\\=7[\frac{11}{3}]\\\\=\frac{77}{3}\)
Thus the value of double integral over the triangular region is \(\frac{77}{3}\) square units.
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Related Questions
On October 1, Manda Loya deposited $1,120 in a savings account that pays
5.5 percent interest compounded daily. On October 22, how much interest had
been earned on the principal in her account?
Answers
Answer:
that is it
Step-by-step explanation:
11200*(1.05)^21 is total amount of money she gets on October 22 , after 21 days2. 11200(1.05)^21-11200 total amount -original amount = how much interest earned
Using control charts, define five situations in which a process
is out of control and how it is recognizable on a control
chart.
Answers
Control charts are used to monitor and identify when a process is out of control. There are several situations that indicate an out-of-control process, and these can be recognized on a control chart. Here are five such situations:
A point falls outside the control limits: If a data point falls above the upper control limit or below the lower control limit, it indicates that the process is out of control. This suggests that there may be a significant change or variation in the process.
Nonrandom patterns: Nonrandom patterns in the data points on a control chart, such as a consistent upward or downward trend, cycles, or oscillations, suggest that the process is not stable. These patterns indicate the presence of special causes of variation.
Runs and streaks: A run or streak refers to a series of consecutive data points that are either above or below the central line on the control chart. Runs or streaks suggest a lack of randomness and indicate that the process is not in control.
Lack of points within control limits: If there are long stretches of data points that are consistently clustered near one control limit or the central line without points within the control limits, it suggests that the process is not stable and may be exhibiting a systematic bias or shift.
Excessive variation: If there is excessive variation in the data points on the control chart, indicated by a wide spread of points around the central line, it suggests that the process is not under control. This can be recognized when the data points exceed the expected range of variation. These situations provide clear indications that a process is out of control and requires investigation and corrective actions to address the underlying causes of the variations. Control charts help in quickly identifying these situations and facilitating timely interventions to maintain process stability and quality.
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prove(sec theta-tan theta)(sec theta+tan theta)=1
Answers
Answer:
\(( \sec \theta - \tan \theta)( \sec \theta + \tan \theta)\)
from difference of two squares:
\({ \boxed{ \tt{( {a}^{2} - {b}^{2}) = (a - b)(a + b) }}}\)
\( = { \sec }^{2} \theta - { \tan}^{2} \theta \\ = (1 + { \tan}^{2} \theta) - { \tan}^{2} \theta \\ = 1\)
hence proved
Help needed ASAP! Please.
Answers
Answer: y=2x
Step-by-step explanation:
which graph shows the solution to the system of linear equations?
y=-1/3x+1
y=-2x-3
Answers
y = -1/3x + 1
y = -2x - 3
We can compare the equations to the graphs and see which graph represents the intersection point of the two equations.
The first equation, y = -1/3x + 1, has a negative slope (-1/3) and a y-intercept of 1.
The second equation, y = -2x - 3, also has a negative slope (-2) and a y-intercept of -3.
Based on the slopes and y-intercepts, we can identify the correct graph by finding the point where the two lines intersect.
Unfortunately, since the graphs are not provided, I am unable to determine which specific graph shows the solution to the system of linear equations. I recommend referring to the graph representation of the equations and identifying the intersection point to determine the correct graph.
Cost to store: $55
Markup. 120%
selling price :
quickly please <3
Answers
Answer:
Determine your COGS (cost of goods sold). ...
Find out your gross profit by subtracting the cost from the revenue. ...
Divide profit by COGS.Step-by-step explanation:
Find the circumference of this circle using 3 for π.
Answers
The circumference of the circle is 30 cm.
What is circumference measured in?Any unit for measuring length can be used to calculate the circumference, including feet, miles, metres, millimetres, etc.
By substituting 3 for, we can use the following formula to determine the circle's circumference:
C = 2πr
where r is the radius and C is the circumference.
We can observe from the provided diagram that the circle's radius is 5 cm. Thus, by changing r = 5 cm and = 3 in the formula, we obtain:
C = 2(3)(5) = 30
The circle's circumference is 30 cm as a result.
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4(3q + 10) = 6( 2q - 9 )
Answers
Sorry if wrong
How do I solve this?
Answers
Answer:
I can't see it.
Step-by-step explanation:
-9/15 - (-5/15)
PLEASE HELP!!
Answers
Answer:
-4/15 would be your answer
Step-by-step explanation:
an easier way to recognize this would be to ignore the parenthesis and take the 2 negatives that would then be next to each other, and combine them into a positive, making them -9/15+5/15=-4/15 as your answer.
At a certain school, 7/8 of the students are boys. Today, 3/4 of the boys brought their lunch. What fraction of the students are boys who brought their lunch today?
Answers
Answer:
6/8
Step-by-step explanation:
7/8 of students are boys and we need a fraction that matches the denominator. 3/4 can also be represented as 6/8 if you multiply by 2. therefore, 6/8 boys brought lunch.
Select all expressions that are equivalent to 2 · 2 · 2 · 2 · 2 · 2
A. 23. 23
B. 22. 24
C. 25
D. 4(22)
E. (22)
Answers
Answer:
its 64
Step-by-step explanation:
2 x 2 = 4
4 x 2 = 8
8 x 2 = 16
16 x 2 = 32
32 x 2 = 64
algebra 1 mid term help!!
Answers
Answer:
Yes,
Step-by-step explanation:
Because no x- Values repeat.
Help me help me help me
Answers
Answer:
Step-by-step explanation:
Answer: A
Step-by-step explanation:
We need to convert each city to percentage. Los Angeles is 13/50 and we can double that to convert it to a percentage of 26%. Next is Seattle which is 3/10 and we can multiply that by 10 to get a percentage of 30%. Next is San Francisco, which is at 2/5 and we multiply that by 20 to get a percentage of 40%. Next is Boston which is 43%. The final city is New York City which is 48%. The order of these cities in least to greatest in percentage of public transport use is Los Angeles, Seattle, San Francisco, Boston, and New York City. Therefore the answer is A.
Help with geometry !!!!!!!!!!!
Answers
Answer
x = 18
You're welcome
Answer:
The answer would be x=18
An increase in the real interest rate will
A. most likely lower consumer's purchases of durable goods.
B. most likely lower the cost of borrowing.
C. cause consumers to spend more and save less.
D. most likely lower the reward to savings.
Answers
An increase in the real interest rate will most likely lower the reward to savings. The correct answer is D.
When the real interest rate increases, it means that the return on savings and investments is higher in real terms, adjusted for inflation. As a result, individuals are incentivized to save more as they can earn a higher return on their savings.
When the reward to savings is lower, it becomes less attractive for individuals to save. Higher interest rates can discourage borrowing and encourage saving, which reduces consumer spending on durable goods and other discretionary purchases.
Option A is incorrect because an increase in the real interest rate would likely lead to a decrease in consumer's purchases of durable goods, as higher interest rates increase the cost of borrowing, making it more expensive to finance large purchases.
Option B is incorrect because an increase in the real interest rate generally makes borrowing more expensive, as it increases the cost of borrowing for individuals and businesses.
Option C is incorrect because an increase in the real interest rate usually encourages individuals to save more and spend less, as the potential return on savings is higher.
The correct answer is D.
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Over the last twenty years, how have wages changed compared to the costs of housing. healthcare, and education?
a. Wages have increased at a slower rate than those costs
b. Wages have increased at the same rate as those costs
c. Wages have increased at a faster rate than those costs
d. Wages have decreased as those costs have increased
Answers
Option A. Wages have increased at a slower rate than those cost.
What is wages?Wages are actually a payment done to any worker or employee for doing a certain work.Consumer good prices are currently rising more quickly than both wages and the cost of other services.Real wages have increased by 32% past twenty years.Over this time, there has not been a significant divergence between average pay growth and productivity growth.A single real wage value, in some circumstances a real wage can be stated to have increased without a doubt.So wages have increased but at a slower rate than that of the cost.
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In ΔABC, m∠A = 119° and m∠B = 49°. Which statement about the sides of ΔABC must be true?
Answers
Answer:
It is not true
Step-by-Step:
^ABC, m<A = 119 degrees.
In triangle ABC, side BC is longer and side AB shortest side.
Given that, in ΔABC, m∠A = 119° and m∠B = 49°.
What is the triangle inequality theorem?The triangle inequality theorem describes the relationship between the three sides of a triangle. According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side.
Using angle sum property, we get
m∠A+m∠B+m∠C=180°
⇒ 119°+49°+m∠C=180°
⇒ m∠C=180°-168°
⇒ m∠C=12°
So, using triangle inequality theorem opposite to angle A, side BC is longer and opposite to angle C, side AB is shortest side.
Therefore, in triangle ABC, side BC is longer and side AB shortest side.
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bank of america's consumer spending survey collected data on annual credit card charges in seven different categories of expenditures: transportation, groceries, dining out, household expenses, home furnishings, apparel, and entertainment. using data from a sample of credit card accounts, assume that each account was used to identify the annual credit card charges for groceries (population 1) and the annual credit card charges for dining out (population 2). using the difference data, the sample mean difference was , and the sample standard deviation was . a. formulate the null and alternative hypotheses to test for no difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out. - select your answer - - select your answer - b. use level of significance. can you conclude that the population means differ? - select your answer - what is the -value? (to 6 decimals) c. which category, groceries or dining out, has a higher population mean annual credit card charge? - select your answer - what is the point estimate of the difference between the population means? round to the nearest whole number. what is the confidence interval estimate of the difference between the population means? round to the nearest whole number. ,
Answers
a. Null hypothesis: The population means credit card charges for groceries and dining out are equal.
Alternative hypothesis: The population means credit card charges for groceries and dining out are not equal.
b. Using a level of significance of 0.05, we can conclude that the population means differ since the calculated p-value is less than 0.05.
c. The point estimate of the difference between the population means is also not provided in the question. Therefore, we cannot calculate the confidence interval estimate of the difference between the population means.
a. To formulate the null and alternative hypotheses, you can use the following notation:
H0 (null hypothesis): μ1 - μ2 = 0 (There is no difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out)
Ha (alternative hypothesis): μ1 - μ2 ≠ 0 (There is a difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out)
b. To determine if the population means differ at a given level of significance (let's say α), you would need to perform a hypothesis test using the sample mean difference, sample standard deviation, and sample sizes for both populations. Unfortunately, you didn't provide these values, so I cannot perform the test or calculate the p-value.
c. To determine which category has a higher population mean annual credit card charge, you would need to compare the point estimate of the difference between the population means. Since you didn't provide the sample mean difference, I cannot determine which category has a higher population mean annual credit card charge.
We cannot determine which category, groceries or dining out, has a higher population mean annual credit card charge without additional information such as the sample mean credit card charges for each category. The point estimate of the difference between the population means is also not provided in the question.
Additionally, to calculate the confidence interval estimate of the difference between the population means, you would need the sample mean difference, sample standard deviation, and sample sizes. Without this information, I cannot provide the confidence interval estimate.
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On a coordinate plane, how are the locations of the points (4 , 2) and (-4 , 2) related?
Answers
Answer:
They both are y=2
Step-by-step explanation:
(x,y)
Answer:
(4 , 2) and (-4 , 2) are just on two opposite sides of the coordinate
plane (4 , 2) is on the top-right side of the coordinate planes, and (-4 , 2) is on the top left-hand side of the coordinate planes.
the distance midpoint between A (-6, 8) & B (6, -2)
Answers
Answer:
I think 2
Step-by-step explanation:
6-2is 4 8-6 2 both have common 6 and 2 multiple of 6is 2
x/4-6=10 PLEASE HELP I NEED HELP ASAP
Answers
\(\huge \bf༆ Answer ༄\)
Here's the solution ~
\( \sf \dfrac{x}{4} - 6 = 10\)\( \sf \dfrac{x}{4} = 10 + 6\)\( \sf \dfrac{x}{4} = 16\)\( \sf x = 16 \times 4\)\( \sf x = 64\)Value of x is 64
Ok done. Thank to me :>
A friend comes up to you and offers you a free ticket to the Cubs game one night, and you decide to attend the game. The game takes five hours and costs you $25 for transportation. If you had not attended the game, you would have worked at your part-time job for $12 an hour. What is the cost to you of attending the game
Answers
The cost to you of attending the game is $85.
Attending the Cubs game involves an opportunity cost, which is the value of the best alternative forgone when making a decision. In this case, your opportunity cost is the income you would have earned at your part-time job if you had not attended the game.
The game takes five hours, and you would have worked for $12 an hour at your part-time job.
Therefore, the lost income from not working is:
5 hours x $12 = $60.
Additionally, you spent $25 on transportation to attend the game.
To find the total cost of attending the game, you need to consider both the opportunity cost and the direct cost of transportation.
The total cost is:
$60 (lost income) + $25 (transportation) = $85.
In conclusion, the cost to you of attending the game is $85, which includes the $60 opportunity cost of not working at your part-time job and the $25 spent on transportation.
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Solve 3 + 4x > -5 for x
Answers
you have the following inequality:
3 + 4x > -5
in order to solve for x, proceed as follow:
3 + 4x > -5 subtract 3 both sides
4x > - 5 - 3
4x > -8 divide by 4 both sides
x > -8/4
x > -2
Hence, the solution to the given inequality is x > -2
you have a six-sided die t hat youroll once and observe the number of dotsfacing up,vards. \t\fhat is the sample space?\i\fhat is the probability of each sample outcome? \i\fhat is the probability of e, theevent that t he roll is even?
Answers
The sample space is {1, 2, 3, 4, 5, 6}.
The probability of each sample outcome is 1/6.
The probability of the event that the roll is even is 1/2.
james is in charge of the decorations. he hs a total budget of $50 to spend for all of the decorations. james spends $20 on one banner and would like to buy balloons that cost $2 each with the rest of the money. Write an equation to represent the situation.
How many balloons can james buy?
Answers
His budget (amount of money he can spend) is $50. If he spent $20 on the banner, that means he has $30 left. He wants to spend the rest on balloons $2 each. Simply- 30 divided by 2 which is 15
The rectangular prism is formed by six intersecting pkanes. Which word describes the relationship between AE and DH
A: perpendicular
B: intersecting
C: skew
D: parallel
Answers
Answer:
Parallel
Step-by-step explanation:
because theyre facing the same way to where they wouldnt ever intersect even if they went on forever.
If 150° and 3a are supplementary angles, find the value of a.
Answers
Answer:
a = 10
Step-by-step explanation:
Supplementary angles sum to 180° , so
150 + 3a = 180 ( subtract 150 from both sides )
3a = 30 ( divide both sides by 3 )
a = 10
help or i will fail my acellus
Answers
Answer:
I think it's 155 cm
Step-by-step explanation:
=(5×5×3)+(5×2×4)
= 75+40
= 155 cm2
answer the following, Round final answer to 4 decimal places. a.) Which of the following is the correct wording for the randon variable? r×= the percentage of all people in favor of a new building project rv= the number of people who are in favor of a new building project r N= the number of people polled r×= the number of people out of 10 who are in favor of a new building project b.) What is the probability that exactly 4 of them favor the new building project? c.) What is the probabilitv that less than 4 of them favor the new building project? d.) What is the probabilitv that more than 4 of them favor the new building project? e.) What is the probabilitv that exactly 6 of them favor the new building project? f.) What is the probability that at least 6 of them favor the new building project? 8.) What is the probabilitv that at most 6 of them favor the new building project?
Answers
In this problem, we are dealing with a random variable related to people's opinions on a new building project. We are given four options for the correct wording of the random variable and need to determine the correct one. Additionally, we are asked to calculate probabilities associated with the number of people who favor the new building project, ranging from exactly 4 to at most 6.
a) The correct wording for the random variable is "rv = the number of people who are in favor of a new building project." This wording accurately represents the random variable as the count of individuals who support the project.
b) To calculate the probability that exactly 4 people favor the new building project, we need to use the binomial probability formula. Assuming the probability of a person favoring the project is p, we can calculate P(X = 4) = (number of ways to choose 4 out of 10) * (p^4) * ((1-p)^(10-4)). The value of p is not given in the problem, so this calculation requires additional information.
c) To find the probability that less than 4 people favor the new building project, we can calculate P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3). Again, the value of p is needed to perform the calculations.
d) The probability that more than 4 people favor the new building project can be calculated as P(X > 4) = 1 - P(X ≤ 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)).
e) The probability that exactly 6 people favor the new building project can be calculated as P(X = 6) using the binomial probability formula.
f) To find the probability that at least 6 people favor the new building project, we can calculate P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10).
g) Finally, to determine the probability that at most 6 people favor the new building project, we can calculate P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6).
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