show that parametrizes the plane . then: (a) calculate , , and . (b) find the area of , where . (c) express in terms of and and evaluate . (a) ,

Answers

Answer 1

The final solution is:

(1) Tu=<7, 1, 13>, Tv=<0, -1, 1> and n(u,v)=<14, -7, -7>.

(2) the area of S=Φ(D): Area(S) = 514.39

(3) ∬sf(x,y,z)ds = 190√(294) = 3257.82

What is the double integral?

A multiple integral is a definite integral of a function of several real variables, for instance, f or f.

1. Φ(u,v) gives the parametrization with its x, y, and z components. So, x=7u+4, y=u-v, and z=13u+v.

We can use this to get the tangent vectors by taking the respective partial derivatives.

Tu=<7, 1, 13> by taking the u derivatives of the components, and Tv=<0, -1, 1> by taking the v derivatives of the components.

2. Taking the cross product of Tu and Tv will give the normal vector n(u,v), which is <14, -7, -7>.

3. To find Area(S), you have to multiply the area of D by the magnitude of the normal vector from the previous step. D is the region defined by 0<=u<=5 and 0<=v<=6, so the area of D is 5*6=30.

Multiply this by the magnitude of the normal vector to find that Area(S)=30√(294)

Area(S) = 514.39

4. To integrate, we first must put the initial function in terms of the parameters we found in the first step.

Replace y with u-v and z with 13u+v. Next, multiply this integrand by the magnitude of the normal vector (√294) and apply the given bounds for u (0<=u<=5) and v (0<=v<=6).

From here the problem can be integrated like any other double integral, the final answer being 190√(294).

Hence, The final solution is:

(1) Tu=<7, 1, 13>, Tv=<0, -1, 1> and n(u,v)=<14, -7, -7>.

(2) the area of S=Φ(D): Area(S) = 514.39

(3) ∬sf(x,y,z)ds = 190√(294) = 3257.82

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Complete Question:

Show that Φ(u,v)=(7u+4,u−v,13u+v) parametrizes the plane 2x−y−z=8. Then: (a) Calculate Tu , Tv, and n(u,v). (b) Find the area of S=Φ(D), where D=(u,v):0≤u≤5,0≤v≤6. (c) Express f(x,y,z)=yz in terms of u and v and evaluate ∬sf(x,y,z)ds(a) Tu= , Tv= , n(u,v)=_______________(b) Area(S)=_______(c) ∬sf(x,y,z)ds=___________


Related Questions

help pls asap due in 1 hour pls

help pls asap due in 1 hour pls

Answers

Subtract the amount of £1 coins from 50p coins:

256-172 = 84

84/3 coins = 28 people paid with 3 coins.

172 people paid using £1 coins

172 + 28 = 200 total people

percent who used 3 coins = 28/200 = 0.13 × 100 = 14%

Answer: 14%

Hope This Helps! Best Wishes.

Answer:

Subtract the amount of £1 coins from 50p coins:

256-172 = 84

84/3 coins = 28 people paid with 3 coins.

172 people paid using £1 coins

172 + 28 = 200 total people

percent who used 3 coins = 28/200 = 0.13 x 100 = 14% so the answer is 14%

Please help I don’t understand stand this

Please help I dont understand stand this

Answers

Answer:

The answer you have for the given statement, the converse would be saying the same thing as the given statement, but reversed. So instead of "if the toy block is a clover", you would put "if a toy block is red, then the toy block is a clover". Hope that clears it up

Write an expression in standard form for
the area of the rectangle.
4x - 1
+
2x + 5

Answers

Answer:

6x +4

Step-by-step explanation:

add or subtract like terms

I’m not sure I need help

Im not sure I need help

Answers

Answer:

D) \(1 < x\leq 4\)

Step-by-step explanation:

1 is not included, but 4 is included, so we can say \(1 < x\leq 4\)

D since the circle is not completely filled that’s why x is greater than 1 and less than equal to 4

x^3+(y+z)^3 factorise it broefly.​

Answers

Answer:

x^3 + y^3 + z^3

Step-by-step explanation:

x^3+(y+z)^3

Remove brackets

x^3 + y^3 + z^3

On her last reading quiz, Jianna got 87.5% of the questions correct. If she knows that she got 17.5 questions correct, how many questions were on the quiz?

Answers

There were 20 questions on the quiz.

Let's start by using algebra to solve the problem.

Let x be the total number of questions on the quiz.

If Jianna got 87.5% of the questions correct, then she got 0.875x questions

correct.

We also know that Jianna got 17.5 questions correct.

So we can set up the equation:

0.875x = 17.5

To solve for x, we can divide both sides by 0.875:

x = 20

Therefore, there were 20 questions on the quiz.

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HOW TO DO THIS QUESTION PLEASE ​

HOW TO DO THIS QUESTION PLEASE

Answers

Answer:

b = -10

c = 25

Step-by-step explanation:

Since the only solution to x is 5 that mean answer will look something like this:

(x-5) (x-5) = 0

x(x-5) -5(x-5)

x^2 -5x -5x + 25

x^2 -10x + 25

This is same as x^2 + bx + c = 0

where b is -10 and c is 25

Faizah is paid $11 per hour for her work at a factory. She works 9 hours a day and 24 days a month. She saves $594 a month. Express the amount she saves as a percentage of her income.​

Answers

Answer:

The amount she saves is 25% of her income

Step-by-step explanation:

She is paid $11 per hour

She works 9 hours per day

and for 24 days per month

So, she works 9(24) hours per month

= 216 hours per month

Now, she is paid $11 hourly, so for 216 hours,

she will have 11(216) = $2376

Total income = $2376 per month

Saving = $594 per month

As a percentage, we divide the savings by the total income,

savings/(total income) = 594/2376 = 1/4 = 0.25

Hence we get 25%

The sum of the digits of a two-digit number is seventeen. The number with the digits reversed is thirty more than 5 times the tens' digit of the original number. What is the original number?

Answers

Therefore, the original number is 10x + y = 10(10) + 7 = 107.

Given that the sum of the digits is seventeen, we have the equation:

x + y = 17 (equation 1)

The number with the digits reversed is thirty more than 5 times the tens' digit of the original number. The number with the digits reversed would be 10y + x.

According to the given information, we have the equation:

10y + x = 5x + 30 (equation 2)

To solve the system of equations, we can substitute equation 1 into equation 2:

10(17 - x) + x = 5x + 30

Expanding and simplifying:

170 - 10x + x = 5x + 30

170 - 30 = 5x + 10x - x

140 = 14x

x = 10

Substituting the value of x back into equation 1:

10 + y = 17

y = 7

Therefore, the original number is 10x + y = 10(10) + 7 = 107.

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What is the probability that at least 2 of a group of 4 persons were born on the same day of the week?

Answers

To solve this problem, we'll use the complement rule: we'll find the probability that no two people were born on the same day of the week, and then subtract that from 1 to get the probability that at least two people were born on the same day of the week.

First, let's find the total number of possible ways that the four people could have been born on different days of the week. For the first person, any day of the week is possible. For the second person, there are 6 days of the week left to choose from (since one day has already been taken). For the third person, there are 5 days of the week left to choose from, and for the fourth person, there are 4 days of the week left to choose from. Therefore, the total number of ways that the four people could have been born on different days of the week is:

7 × 6 × 5 × 4 = 840

Now, let's find the total number of possible ways that the four people could have been born on any day of the week (without any restrictions). For each of the four people, there are 7 possible days of the week that they could have been born on. Therefore, the total number of possible ways that the four people could have been born on any day of the week is:

7 × 7 × 7 × 7 = 2401

Therefore, the probability that no two people were born on the same day of the week is:

840/2401 ≈ 0.35

And the probability that at least two people were born on the same day of the week is:

1 - 0.35 = 0.65

So there is a 65% chance that at least two people in the group of four were born on the same day of the week.

what is 1/3 of 48 in numbers

Answers

Answer:

16

Step-by-step explanation:

Multiply it by 1/3 and it equals 16

Answer:

16

Step-by-step explanation:

48/3=16

Alex can run 26 miles in 6 hours, Bethany can run 26 miles in 5 hours and Carol can run 26 miles in 4 hours. If they start together and each run at their constant speeds, how many hours does it take for them to finish a total of 26 miles among the three of them

Answers

It takes approximately 86.67 hours for Alex, Bethany, and Carol to collectively finish a total of 26 miles. This is determined by calculating the harmonic mean of their individual running speeds.


To determine how many hours it takes for Alex, Bethany, and Carol to collectively run a total of 26 miles, we need to consider their individual running speeds. Alex runs at a rate of 26 miles in 6 hours, Bethany runs at a rate of 26 miles in 5 hours, and Carol runs at a rate of 26 miles in 4 hours.

To find the total time it takes for them to finish 26 miles together, we can calculate the harmonic mean of their individual running speeds. The harmonic mean is used because it accounts for the different rates at which they run.

The formula for the harmonic mean is given by:

Harmonic Mean = Total Distance / (1 / Speed1 + 1 / Speed2 + 1 / Speed3)

Substituting the values, we have:

Harmonic Mean = 26 / (1 / 6 + 1 / 5 + 1 / 4)

To simplify the equation, we find the common denominator:

Harmonic Mean = 26 / ((5 + 6 + 7) / 60)

Harmonic Mean = 26 / (18 / 60)

Harmonic Mean = 26 / (3 / 10)

Harmonic Mean = 26 * (10 / 3)

Harmonic Mean ≈ 86.67

Therefore, it takes approximately 86.67 hours for Alex, Bethany, and Carol to collectively finish a total of 26 miles.

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I need help and I will give five stars and a big thank you comrades

I need help and I will give five stars and a big thank you comrades

Answers

Answer:

A.

Step-by-step explanation:

A way to find the equation of the graph is to find the solutions.

On the graph, the solutions are where the function intersects the x-axis. That would be where x = -2, x = 1, and x = 3.

In the equations, you will need to find factors when the x is inputted, the factor equals 0. For example, one of the factors is (x + 2). This is because x + 2 = 0, so x = 0 - 2, so x = -2. So, the three factors are (x + 2), (x - 1), and (x - 3).

The correct equation is A.

Hope this helps!

The table shows ordered pairs of the function . What is the value of y when ?

A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 1, 1, 4, 8, 10. The second column is labeled y with entries 14, 10, 6, 0, question mark, negative 12.

–20
–8
8
48

Answers

Answer:

(B) -8

Step-by-step explanation:

Given the 2-column table below:

\(\left|\begin{array}{c|c}x&y\\--&--\\-3&14\\-1&10\\1&6\\4&0\\8&?\\10&-12\end{array}\right|\)

Taking the pair (-3,14) and (-1,10)

\(Slope, m=\dfrac{10-14}{-1-(-3)} =\dfrac{-4}{2} =-2\)

Taking the pair (1,6) and (4,0)

Slope, \(m=\dfrac{0-6}{4-1} =\dfrac{-6}{3} =-2\)

Since the slope is constant, the table represents a linear function whose slope is -2. Therefore:

Taking the pair (8,y) and (4,0)

Slope, \(m=\dfrac{0-y}{4-8} =-2\)

\(\dfrac{-y}{-4} =-2\\y=-2*4=-8\)

Therefore, the value of ? on the y-column is -8.

Answer:

-8

Step-by-step explanation:

Please help me figure out this algebra

Please help me figure out this algebra

Answers

Answer:

x = 0

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtract Property of Equality

Algebra I

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

x + 3 + 2x = x + 3

Step 2: Solve for x

Combine like terms:                   3x + 3 = x + 3Subtract x on both sides:           2x + 3 = 3Subtract 3 on both sides:           2x = 0Divide 2 on both sides:              x = 0

There are 10 teams in a basketball competition. Each team must play each of the other teams once. How many games will each team play? (A) 14 (B) 9 (C) 70 (D) 63​

Answers

Two teams can be selected out of 10 teams in C(10,2) = 10!/8! 2! = 45 ways

=> If each team plays exactly 3 matches with each other team, number of matches will be 45 x 3 = 135.

:-)

Answer:

(B) 9

Step-by-step explanation:

Number of teams = 10

Each team play each of the other 9 teams once.

Correct choice is B

What's the quotient and the remainder of 17÷7

Answers

Answer:

The quotient is equal to 2

The remainder is equal to 3

Explanation:

We want to find the quotient and the remaider of the given expression.

\(\begin{gathered} \frac{17}{7}=\frac{14+3}{7}=\frac{14}{7}+\frac{3}{7} \\ =2+\frac{3}{7} \end{gathered}\)

Therefore;

The quotient is equal to 2

The remainder is equal to 3

alfreda made a container shaped like a triangular prism, as shown in the diagram what is the volume of the volume of the container in cubics inches?

Answers

since there's no picture attached, worked with the one in the file that I attached in order to enable you to understand what you are expected to do in this sort of circumstance.
Answer:
120cm^2
Step-by-step explanation:
please kindly go through the attached file for more explanation.

can you help me with these 3 qustions?

can you help me with these 3 qustions?

Answers

Answer:

14. no (16 = 11 + 3*1, not equal since 16=14 is wrong)

15. yes (-19 = 1 - 4*5, equal)

16. yes ( -5 = 2-14/2, equal)

Choose the kind(s) of symmetry: point, line, plane, or none.
(A)
none
plane
point
line

Answers

it would be a Line  

The line would be vertical right through the middle

can i get brainliest?

Find the distance, slope, and midpoint of the segment with endpoints A(5,4) and B(-1, 12)​

Answers

Answer:

Step-by-step explanation:

Find the distance, slope, and midpoint of the segment with endpoints A(5,4) and B(-1, 12)

ASAP please help right now

ASAP please help right now
ASAP please help right now

Answers

Answer:

1

Step-by-step explanation:

Because the shape divided has to create another shape and for 1 it's an oval at the beginning and then after the lines of symmetry go through its seen as 8 triangles.

Simplify the expression by combining all the like terms 6+2x+5+4x

Answers

Answer:

6x+11

Step-by-step explanation:

6+2x+5+4x

4x+2x+6+5

(4x+2x)+(6+5)

6x+11

Answer:

6x +11

Step-by-step explanation:

group like terms (terms with the same variable and powers) together

(2x+4x) + (6+5)

6x +11

A poll taken by GSS asked whether people are satisfied with their financial situation. A total of 478 out of 2038 people said they were. The same question was asked two years later, and 537 out of 1967 people said they were. Get a 90% confidence interval for the increase in the proportion of people who were satisfied with their financial condition. The CI is

Answers

We can say with 90% confidence that the increase in proportion of people satisfied with their financial situation is between 1.05% and 6.71%.

To calculate the confidence interval for the increase in proportion of people satisfied with their financial situation, we need to first calculate the proportions for both years:

Proportion in year 1 = 478/2038 = 0.2342
Proportion in year 2 = 537/1967 = 0.2730

The increase in proportion is:
0.2730 - 0.2342 = 0.0388

To calculate the confidence interval, we can use the formula:
CI = (point estimate ± (critical value x standard error))

The point estimate is the increase in proportion we just calculated: 0.0388

The critical value can be found using a z-table for a 90% confidence level. The z-value for a 90% confidence level is 1.645.

The standard error can be calculated using the formula:
sqrt[(p1(1-p1)/n1) + (p2(1-p2)/n2)]

where p1 and n1 are the proportion and sample size for year 1, and p2 and n2 are the proportion and sample size for year 2.

Plugging in the values, we get:
SE = sqrt[(0.2342(1-0.2342)/2038) + (0.2730(1-0.2730)/1967)] = 0.0174

Now we can plug in all the values to get the confidence interval:
CI = (0.0388 ± (1.645 x 0.0174)) = (0.0105, 0.0671)

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Under what circumstances is a score that is located 5 points above the mean a central value, relatively close to the mean?

a. When the population standard deviation is much less than 5

b. When the population mean is much less than 5

c. When the population mean is much greater than 5

d. When the population standard deviation is much greater than 5

Answers

The circumstance that the score is located 5 points above the mean a central value, relatively close to the mean is when the population standard deviation is much greater than 5.

What is the standard deviation?

Standard Deviation is a measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists. The standard deviation indicates a “typical” deviation from the mean. It is a popular measure of variability because it returns to the original units of measure of the data set.

Here, we have

The circumstance is a score that is 5 points above the mean considered a central value.

We have to find under what circumstances is a score that is 5 points above the mean considered a central value--meaning it is relatively close to the mean.

We concluded from the above statement that when the population standard deviation is much greater than 5.

Hence, when the population standard deviation is much greater than 5 then, the score that is 5 points above the mean is considered a central value.

Therefore, the correct option is D.

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The scatterplot and table show the weekly profit in dollars earned from the sale of pastries at seven different prices. The data can be modeled by a quadratic function.
Which function best models the data?
A)y = 0.001x2 - 0.426x + 35.672
B)y = -60.4x2+ 348.1x - 334.2
C)y = 0.001x2+ 35.672
D)y = -60.4x2 - 334.2

The scatterplot and table show the weekly profit in dollars earned from the sale of pastries at seven

Answers

The table is an illustration of a quadratic regression model

The function that best models the data is y = -60.4x^2 +348.1x -334.2

How to determine the function that models the data?

To determine the function that models the data, we make use of a graphing calculator.

Using the graphing calculator, we have the following calculation summary

a = -60.4

b = 348.1

c = -334.2

A quadratic regression model is represented as:

y = ax^2 + bx + c

So, we have:

y = -60.4x^2 +348.1x -334.2

Hence, the function that best models the data is y = -60.4x^2 +348.1x -334.2

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What is the simplified form of
72x16
50x36
? Assume x+0.
6
5x10
6
5x2
10

What is the simplified form of72x1650x36? Assume x+0.65x1065x210

Answers

Answer:

The simplified form is  \(\frac{6}{5x^{10} }\) ⇒ A

Step-by-step explanation:

To simplify a root divide the power of the variable by 2 to cancel itFactorize the coefficient of the variable and take out the repeated factor twice out the root

Let us solve the question

∵ The expression is \(\sqrt{\frac{72x^{16}}{50x^{36}}}\)

→ At first, divide simplify the coefficient of the variable

∵ \(\frac{72}{50}=\frac{36}{25}\)

∵ 36 = 6 × 6 and 25 = 5 × 5

→ 6 and 5 repeated twice then the can go out the root one 6 and one 5

∴ \(\sqrt{\frac{36}{25}}=\frac{6}{5}\)

→ Let us use the exponent rule with division \(\frac{a^{m} }{a^{n}}=a^{m-n}\)

∵ \(\frac{x^{16}}{x^{36}}=x^{(16-36)}=x^{-20}\)

→ To cancel the root divide the power by 2

∵ -20 ÷ 2 = -10

∴ \(\sqrt{x^{-20}}=x^{-10}\)

∴  \(\sqrt{\frac{72x^{16}}{50x^{36}}}\) = \(\frac{6}{5}\) × \(x^{-10}\)

→ To change the power of x from (-) to (+) reciprocal x

∴ \(x^{-10}=\frac{1}{x^{10}}\)

∴  \(\sqrt{\frac{72x^{16}}{50x^{36}}}\) = \(\frac{6}{5x^{10} }\)

The simplified form is  \(\frac{6}{5x^{10} }\)

Point C is located between points B and D. Also BC = 5x + 7, CD = 3y + 4, BD = 38, and BD = 2x + 8y. Find the values of x and y

Answers

Using location of points and a system of equations, it is found that:

The value of x is 3.The value of y is 4.

----------------------------------

Point C is located between points B and D means that:

\(BD = BC + CD\)

----------------------------------

We are given that:

\(BC = 5x + 7\)\(CD = 3y + 4\)\(BD = 38\)\(BD = 2x + 8y\)

From this, two equations can be built.

\(2x + 8y = 38\)

Dividing both sides by 2:

\(x + 4y = 19\)

\(x = 19 - 4y\)

----------------------------------

Finding y:

\(BC + CD = BD\)

\(5x + 7 + 3y + 4 = 38\)

\(5x + 3y + 11 = 38\)

\(5x + 3y = 27\)

Since \(x = 19 - 4y\)

\(5(19 - 4y) + 3y = 27\)

\(95 - 20y + 3y = 27\)

\(17y = 68\)

\(y = \frac{68}{17}\)

\(y = 4\)

----------------------------------

Finding x:

\(x = 19 - 4y = 19 - 4(4) = 19 - 16 = 3\)

The value of x is 3.

The value of y is 4.

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7/13=x/5 rounded to the nearest tenth.

Answers

Step-by-step explanation:

x/5 = 7/13      multiply both sides of the equation by to get

x = 5 * 7/13  =  35/ 13     then use calculator = ~  2.7

Answer:

7/13 = x/5 can be solved by cross-multiplication of the terms.

13*x = 5 *7

13x = 35

x = 35/13 = 2.69 = 2.7

Question 1: A gardener uses a total of 81.5 gallons of gasoline in one month. Of the total amount of
gasoline, 2/5 was used in his lawn mowers. How many gallons of gasoline did the gardener use in his
lawn mowers in the one month?
A. 12.3 gal
B. 203.75 gal
C. 0.326 gal
D. 32.6 gal

Answers

Answer: D

Step-by-step explanation:

The amount of gasoline used in the lawn mowers is 2/5 of the total amount of gasoline used. Therefore:

Gasoline used in lawn mowers = (2/5) x 81.5 gallons

Gasoline used in lawn mowers = 32.6 gallons

Therefore, the answer is D. 32.6 gal.

Other Questions
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