Mathematics College

2s + 5 greater than or equal to 49

Answers

Answer 1

s is greater than or equal to 22

Answer 2

The value of s is greater or equal to 22.

What is inequality?

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

2s + 5 greater than or equal to 49.

This can be written as,

(2s + 5) ≥ 49

Solve for s.

2s + 5 ≥ 49

2s ≥ 49 - 5

2s ≥ 44

s ≥ 22

Thus,

s is greater than or equal to 22.

Learn more about inequalities here:

https://brainly.com/question/20383699

#SPJ2

Related Questions

0.8 is 10 times as great as which decimal

Answers

0.08 is the answer. :)

Suppose a and b give the population of two states where a>b . Compare the expressions and tell which of the given pair is greater or if the expression are equal.

b/a+b and 0.5

Answers

Suppose a = b, then [tex]\frac{b}{a+b}=\frac{b}{b+b}=0.5[/tex]

Since a > b, then a + b > b + b and thus [tex]\frac{b}{a+b}<\frac{b}{b+b}[/tex]

Therefore, [tex]\frac{b}{a+b}<0.5[/tex]

Blue shaded 20 squares on his hundreds grid. Becca shaded 30 squares on her hundreds grid. Write two decimals greater than Luke decimal in less than Bekkas decimal

Answers

Attached is the answer to your question.

A new restaurant is to contain two-seat tables and four-seat tables. Fire codes limit the restaurant's maximum occupancy to 72 customers. If the owners have hired enough servers to handle 22 tables of customers, how many of each kind of table should they purchase?

Answers

Let t and f be the number to two and four seat tables respectively.

t+f=22, solve for t

t=22-f, then we are told that capacity must be less than or equal to 72 people.

2t+4f≤72, using t found above in this equation we get:

2(22-f)+4f≤72 perform indicated multiplication on left side

44-2f+4f≤72 combine like terms on left side

44+2f≤72 subtract 44 from both sides

2f≤28 divide both sides by 2

f≤14 Since f=integer

f=14, and since t=22-f

t=8

So they should purchase 14 four seat tables and 8 two seat tables.

Final answer:

To adhere to the fire code and server capacity, the restaurant should ideally buy 18 four-seat tables and 4 two-seat tables. This results in a total of 22 tables and maximizes seating capacity at 72.

Explanation:

This problem can be solved using a system of linear equations. Let's denote the number of two-seat tables as T and the number of four-seat tables as F.

From the information given, we can establish two equations:

The total number of tables must not exceed 22, so T + F ≤ 22The total number of seats cannot exceed 72, so 2T + 4F ≤ 72

To figure out how many of each type of table they should purchase, we need to solve this system of equations.

The goal is to maximize the number of customers (seats) while not exceeding the limits on tables and seats. So, a possible solution to maximize seating would be to have 18 four-seat tables (F = 18) and 4 two-seat tables (T = 4). This gives a total of 22 tables and 72 seats.

Learn more about System of Linear Equations here:

https://brainly.com/question/33609849

#SPJ3

How do you write an equation that shows an estimate of each answer for 503+69

Answers

You have to round to the nearest whole number so it would be 500 and 70
so the equation would be 500+70

Final answer:

To estimate the sum of 503 and 69, one could round the numbers to the nearest tens or hundreds and then add the rounded numbers together. For example, rounding to the nearest tens would result in the equation 500 + 70 = 570.

Explanation:

The question asks for a method to write an equation that would allow them to estimate the sum of 503 and 69. This is more related to the concept of rounding numbers. We can estimate this sum by rounding these numbers to the nearest tens or hundreds, and then adding those rounded numbers together.

For example, if you round to the nearest tens, 503 can be rounded down to 500 and 69 can be rounded up to 70. Adding these rounded numbers together gives 500 + 70 = 570. Therefore, one possible equation could be: 500 + 70 = 570, which is a fairly close estimate of the original sum, 503 + 69.

Learn more about Rounding Numbers here:

https://brainly.com/question/28562556

#SPJ2

A local hamburger shop sold a combined total of 436 hamburger and cheeseburgers on Friday. There were 64 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Friday?

Answers

64 fewer cheeseburgers were sold than hamburgers. The total number of hamburgers sold on Friday was 250.

Use the concept of subtraction defined as:

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that,

Total number of hamburgers and cheeseburgers sold on Friday: 436.

The number of cheeseburgers sold was 64 fewer than the number of hamburgers.

The objective is to find the number of hamburgers sold on Friday.

To find out how many hamburgers were sold on Friday,

Set up a system of equations.

Let's denote the number of hamburgers as 'H' and the number of cheeseburgers as 'C'.

From the given information,

The total number of hamburgers and cheeseburgers sold is 436,

So write the equation,

H + C = 436.

Since there were 64 fewer cheeseburgers sold than hamburgers,

Which can be written as C = H - 64.

Now substitute the second equation into the first equation and solve for H:

H + (H - 64) = 436

Combine like terms,

2H - 64 = 436

Add 64 to both sides,

2H = 500.

Divide both sides by 2,

H = 250.

Hence,

250 hamburgers were sold on Friday.

To learn more about subtraction visit:

https://brainly.com/question/17301989

#SPJ5

Write the fractions in order from smallest to largest. 7/10, 3/20,22/25, 2/25

Answers

7/10 = 0.7
3/20 = 0.15
22/25 = 0.88
2/5 = 0.4

order from smallest to largest
3/20, 2/5, 7/10 and 22/25

I believe the order from smallest to largest would be:
2/25, 3/20, 7/10, 22/25

On average, the merchandise shop sells 80 CDs for every 1 vinyl record. Estimate how many vinyl records they are likely to sell if the merchandise shop sells 760 CDs.

Answers

The merchandise shop sells 80 CDs for every 1 vinyl record. We have to find how many vinyl records they are likely to sell if the merchandise shop sells 760 CDs:
         80 CDs -------------------- 1 vinyl record
        760 CDs --------------------- x vinyl records
     ---------------------------------------------------------
        80 : 760 = 1 : x
        80 x = 760
        x = 760 : 80
        x = 9.5 or 9 ( we need a whole number )
       Answer: They are likely to sell 9 vinyl records.

Answer:

10 vinyl records are expected to be sold.

Step-by-step explanation:

On average, the merchandise shop sells 80 CDs per 1 vinyl record. This is our conversion factor. To estimate the number of vinyl records likely to be sold when 760 CDs have been sold we will use proportions.

760 CD × (1 vinyl record/ 80 CD) = 9.5 ≈ 10 (we round it off because you cannot sell half a vinyl record).

10 vinyl records are expected to be sold.

Dr. Blumen invested $5,000 part of it was invested in bonds at a rate of 6% in the rest was invested in a money market at the rate of 7.5% if the annual interest of is 337.50 how much did she invest in bonds

Answers

so... let's say the amounts invested were "a" at 6% and "b" at 7.5%.

ok.. hmm what's 6% of a? well, (6/100) * a or 0.06a.
what's 7.5% of b? well, (7.5/100) * b or 0.075b.

now... we know, whatever "a" and "b" are, they total the investment of 5000 bucks, thus a + b = 5000

and the interest yielded was 337.50, thus 0.06a + 0.075b = 337.50

thus [tex]\bf \begin{cases} a+b=5000\implies \boxed{b}=5000-a\\ 0.06a+0.075b=337.50\\ ----------\\ 0.06a+0.075\left( \boxed{5000-a} \right)=337.50 \end{cases}[/tex]

solve for "a", to see how much was invested at 6%.

what about "b"? well, b = 5000 - a.

X = amount invested in bonds (5000-X) = amount invested in money mkt
X (.06) + (5000-X)(.075) = 337.50
.06X + 375 - .075 X = 337.50
375 - 337.50 = .075 X - .06X
37.50 = .015 X
X = $2500 invested in bonds

Find the surface area of a cylinder with a diameter of 2 and an altitude of 16

Answers

The surface area of the cylinder is given by:
S.A=2πr^2+πdl
hence, the s.a of our solid will be:
S.A.=2*π*1^2+π*2*16
=6.283+100.531
=106.814 sq. units

How do you write 2/100000 as a decimal?

Answers

.00002 Because it would be an exponent of notation (-5) so you would move the decimal point on 2, 5 places then fill the rest with zeros.

The fraction 2/100000 written in form of a decimal is 0.00002

Given the fraction 2/100000, we are to express this fraction as a decimal

The fraction can also be expressed as;

2/100000 = 2 * 1/00000

2/100000 = 2 * 0.00001

2/100000 = 0.00002

Hence the fraction 2/100000 written in form of a decimal is 0.00002

Learn more on fraction here:https://brainly.com/question/24191335

⦁ The point guard of a basketball team has to make a decision about whether or not to shoot a three-point attempt or pass the ball to another player who will shoot a two-point shot. The point guard makes three-point shots 30 percent of the time, while his teammate makes the two-point shot 48 percent of the time. Xi 3 0 P(xi) 0.30 0.70 Xi 2 0 P(xi) 0.48 0.52 ⦁ What is the expected value for each choice? ⦁ Should he pass the ball or take the shot himself? Explain

Answers

Answer:

The given data is

Pr(xi)=0.3*0.70

The expected value =0.90

Where as we calculated the probability=0.96

As 0.96>0.9

So he should pass the ball as probability is greater.

The lengths of the sides of a triangle are 4,5,6 can the triangle still be a right triangle

Answers

No. We can use the pythagorean theorem to prove this.The equation being a2 + b2 = c2. We then use two of the least of the three numbers, which are 4 and 5, to substitute for “a” and “b”. We get a value for “c” which is 6.4, rounded off to the nearest tenth. This value is greater than 6. Note that this is a very logical way of solving the problem since a greater number for “a” and “b” would lead a greater value for “c”

Hello there! Thank you for asking your question here at Brainly! I will be assisting you with answering this problem, and will teach you how to handle it on your own in the future.

First, we need to understand how the sides of a right triangle work.
There is a rule that geometry users practice to test if there is a proper right triangle. This rule is called the "3,4,5" rule.
This rule is known as the Pythagorean Theorum. The Pythagorean Theorum basically states that one leg of the triangle squared plus the other leg of the triangle squared is equal to the hypotenuse squared.

In written form:
a^2 + b^2 = c^2

To prove that the 3,4,5 rule works, let me apply this to the side lengths.
3 will represent a, 4 will represent b, and 5 will represent c.

3^2 + 4^2 = 5^2
Simplify all three squares.
9 + 16 = 25
25 = 25
This proves the 3,4,5 rule works.

Now, let's try to apply this rule with the side lengths 4, 5, and 6.
4 will represent A, 5 will represent B, and 6 will represent C.

4^2 + 5^2 = 6^2
Simplify the squares.
16 + 25 = 36
41 = 36

This does not apply to the Pythagorean Theorum, thus it is NOT a right triangle.

I hope this helps!

A building has an entry the shape of a parabolic arch 84 ft high and 42 ft wide at the base, as shown below. A parabola opening down with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 84 feet and its width from left to right is 42 feet. Find an equation for the parabola if the vertex is put at the origin of the coordinate system. (1 point)

Answers

The equation of the parabola with the given dimensions and vertex at the origin is y = -4x^2.

Finding the Equation of a Parabola

To find the equation of a parabola with a vertex at the origin and given dimensions, we can use the standard form of a parabolic equation, which is y = ax^2. In this case, since the parabola opens downward and the vertex is at the origin (0,0), the equation will have the form y = -ax^2. The value of 'a' can be determined using the dimensions provided for the parabola, which are a width of 42 feet (meaning that the points (21,0) and (-21,0) are on the parabola) and a height of 84 feet (the y-coordinate at the vertex).

Since the point (21, 0) lies on the parabola, substituting it into the equation y=-ax^2 gives us 0 = -a(21)^2, which leads us to find that a = -84/(21)^2. Substituting the value of 'a' back into the equation gives us the final equation of the parabola: y = -84/(21)^2
x^2.

The equation of the parabola is: [tex]\[ y = -\frac{2}{21}x^2 + 42 \][/tex] .

To find the equation of the parabola with its vertex at the origin, we can use the standard form of a parabolic equation, which is [tex]$ y = ax^2 $.[/tex]

Given that the parabola opens downwards, we know that a must be negative. To determine the value of ( a ), we need to find a point on the parabola.

We're given the dimensions of the arch: 84 feet high and 42 feet wide at the base. Since the arch is symmetrical, the highest point is at the midpoint of the base, which is ( x = 0 ). At this point,( y = 84 ).

So, substituting the coordinates of this point into the equation, we get:

[tex]\[ 84 = a \times 0^2 \][/tex]

This simplifies to ( 84 = 0 ), which doesn't give us any useful information. Instead, we need to consider another point on the parabola.

Since the arch is symmetric, we can choose a point where ( x = 21 ) (half of the width of the base), and ( y = 0 ).

Substituting these coordinates into the equation, we get:

[tex]\[ 0 = a \times (21)^2 \][/tex]

0 = 441a

Dividing both sides by 441, we find ( a = 0 ). However, this seems incorrect, as it would mean the arch is just a straight line, which it isn't. This suggests that our choice of coordinates may not be correct.

Let's reconsider. The midpoint of the base is x = 0, but the highest point might not be there. Instead, let's choose a point where ( x = 0 ) and ( y = 42 ), as this is the highest point of the arch.

Substituting these coordinates into the equation, we get:

[tex]\[ 42 = a \times 0^2 \][/tex]

42 = 0

This also doesn't give us useful information. It seems we might have approached this problem incorrectly. Let's try a different strategy.

Since we know the arch is a parabolic shape, and the parabola opens downwards, we can write its equation in the form:

[tex]\[ y = ax^2 + c \][/tex]

To find the values of a and c , we need two points on the parabola. We already have one: the highest point of the arch, which is at x = 0 and (y = 42 ).

Now, we need to find another point. Since the arch is symmetric, we can use any point along the base. Let's choose the point where x = 21 , which is half of the width of the base. At this point, y = 0 .

Substituting these points into the equation, we get:

[tex]\[ 42 = a \times 0^2 + c \][/tex]

[tex]\[ 0 = a \times 21^2 + c \][/tex]

The first equation simplifies to ( c = 42 ).

Substituting this value of ( c ) into the second equation, we get:

[tex]\[ 0 = a \times 21^2 + 42 \][/tex]

Solving for a :

[tex]\[ a \times 441 = -42 \][/tex]

[tex]\[ a = \frac{-42}{441} \][/tex]

[tex]\[ a = -\frac{2}{21} \][/tex]

So, the equation of the parabola is:

[tex]\[ y = -\frac{2}{21}x^2 + 42 \][/tex]

What is the relationship between the 6s in the number 7,664?

Answers

Answer:

10s

100s

Step-by-step explanation:

One of the 6s are in the 10th digit position

the other one is in the 100th digit position

twice a number and 5 more is 100

Answers

Hello there! Thank you for asking your question here at Brainly! I will be assisting you with answering this question today, and will be teaching you how to handle it on your own in the future.

First, let's take a look at our problem.
"Twice a number and 5 more is 100."
Based on this context, we are looking for a specific number to plug in.

To solve for this, I will rewrite the problem. As I do so, I will be writing (in parenthesis) the translation of an equation.

Twice a number (2x) and 5 more (+5) is 100 (=100).

Let's rewrite everything that's in parenthesis.
2x + 5 = 100

This is our equation.
To solve for this, we will need to do some basic algebra. Of course, I will teach you how to handle this on your own in future scenarios.

2x + 5 = 100
To solve for x, we need to isolate 2x, and then divide both sides by 2.

2x + 5 = 100
Subtract 5 from both sides to isolate 2x.
5 - 5 = 0
100 - 5 = 95

We now have the following equation:
2x = 95
Divide both sides by 2 to solve for x.

2x / 2 = x
95 / 2 = 47.5

x = 47.5

47.5 is your number.

I hope this helps!

A roof rises 9 feet for every 12 feet of run. What is the slope of the roof?

Answers

The slope is 9/12 or 0.75

Since slope, m, is defined as the rise/run; then m = 9/12

simplify m = 3/4

A random sample of 12 graduates of a certain secretarial school typed an average of 79.3 words per minute with a standard deviation of 7.8 words per minute. assuming a normal distribution for the number of words typed per minute, find a 95% confidence interval for the average number of words typed by all graduates of this school.

Answers

We will use the following formula to work out the confidence interval

Upper limit = μ + z* (σ/√n)
Lower limit = μ - z* (σ/√n)

We have
μ = 79.3
σ = 7.8
n = 12
z* is the z-score for 95% confidence level = 1.96

Substitute these into the formula, we have

Upper limit = 79.3 + 1.96 (7.8/√12) = 83.7
Lower limit = 79.3 - 1.96 )7.8/√12) = 74.9

Final answer:

To find the 95% confidence interval for the average number of words typed, use the formula: sample mean ± (critical value) * (standard deviation / square root of sample size).

Explanation:

To find the 95% confidence interval for the average number of words typed by all graduates of the secretarial school, we can use the formula:

Confidence Interval = sample mean ± (critical value) * (standard deviation / square root of sample size)

Plugging in the given values, we have:

Confidence Interval = 79.3 ± (1.96) * (7.8 / √12)

Simplifying, the 95% confidence interval is approximately 75.6 to 83.0 words per minute.

Learn more about 95% confidence interval here:

https://brainly.com/question/30265803

#SPJ11

Solve p=10a+3b for a.

Answers

see attached picture for solution

Given a mean of 8 and a standard deviation of 0.7, what is the z-score of the value 9 rounded to the nearest tenth?

Answers

[tex]\mu[\tex]=8
[tex]\sigma[\tex]=0.7
x=9

Z=(x-[tex]\mu[\tex])/[tex]\sigma[\tex]
=(9-8)/0.7
=1.43
=1.4 [to the nearest tenth]

Answer: The z-score of the value 9 rounded to the nearest tenth = 1.4

Step-by-step explanation:

Given: Mean [tex]\mu=8[/tex]

Standard deviation [tex]\sigma=0.7[/tex]

The given random value x= 9

Now, the formula to calculate the z score is given by:-

[tex]z=\dfrac{x-\mu}{\sigma}\\\\\Rightarrow\ z=\dfrac{9-8}{0.7}\\\\\Rightarrow\ z=1.42857142857\approx1.4[/tex]

Hence, the z-score of the value 9 rounded to the nearest tenth = 1.4

In one day,Annie traveled 5 times the sum of the number of hours Brian traveled and 2. Together they traveled 20 hours.Find the number of hours each person traveled.

Answers

The answer is Brian traveled 3 hours
And Annie traveled 17 hours

Annie traveled 5 times + 2 more hours than Brian, which is 3x5+2=17 add them together and you get the 20 hours

Find all numbers for which the rational expression is undefined z^2+6/z^2-7z-8

Answers

now.. if a fraction has a denominator that's 0, the fraction is undefined... so hmm for this to happen to this fraction, then it'd look like [tex]\bf \cfrac{z^2+6}{0}\impliedby unde fined[/tex]

now, for that to happen, well, the denominator must be equal to 0, and that happens when z²-7z-8 = 0... when is that? well, let's check.

[tex]\bf \cfrac{z^2+6}{z^2-7z-8}\\\\ -------------------------------\\\\ z^2-7z-8=0\implies (z-8)(z+1)=0\implies z= \begin{cases} 8\\ -1 \end{cases}\\\\ -------------------------------\\\\ \boxed{z=8}\qquad \cfrac{z^2+6}{(8)^2-7(8)-8}\implies \cfrac{z^2+6}{64-56-8}\implies \cfrac{z^2+6}{0} \\\\\\ \boxed{z=-1}\qquad \cfrac{z^2+6}{(-1)^2-7(-1)-8}\implies \cfrac{z^2+6}{1+7-8}\implies \cfrac{z^2+6}{0}[/tex]

Simple interest formula: P=Irt
Solve for t

Answers

the formula should be I=Prt but whatever

if you had I=Prt then divide both sides by Pr to get I/(Pr)=t

if you want to use P=Irt, divide both sides by Ir to get P/(Ir)=t

The value of t in the simple interest formula P = Irt is t = P / (Ir).

To solve the simple interest formula P = Irt for t, we need to isolate the variable t on one side of the equation.

The formula can be rearranged as follows:

P = Irt

First, divide both sides of the equation by I:

P/I = rt

Next, divide both sides of the equation by r:

(P/I) / r = t

Simplifying further:

t = P / (Ir)

Therefore, the value of t in the simple interest formula P = Irt is t = P / (Ir).

To know more about Simple interest click here :

https://brainly.com/question/30964674

#SPJ6

Suppose we are flipping a fair coin (i.e., probability of heads = 0.5 and probability of tails = 0.5). further, suppose we consider the result of heads to be a success. what is the standard deviation of the binomial distribution if we flip the coin 5 times?

Answers

here is your answer.

You've decided you want a plant for your room. At the gardening store, there are 4 different kinds of plants (tulip, fern, cactus, and ficus) and 4 different kinds of pots to hold the plants (clay pot, plastic pot, metal pot, and wood pot).
If you randomly pick the plant and the pot, what is the probability that you'll end up with a tulip in a plastic pot?

Answers

First find how many possibilities there are total. We can find this simply by multiplying the total number of plants, by the total number of pots.

4 x 4 = 16

There are 16 possibilities in all.
The probability that you'll end up with a tulip in a plastic pot is 1/16, because there's only one way to get a tulip in a plastic pot out of all 16.

The answer is 1/16. :)

The coefficient of the second term in the expansion of the binomial (4x + 3y)3

Answers

The coefficients of a binomial expansion are determined by the Pascal's triangle.

Take a look at the picture.

draw the Pascal's triangle up to the third row. (the row with only 1 is the zero'th row)

Also, notice that as we expand [tex](A+B) ^{3} [/tex],
in each term the power of A decreases by 1, starting from 3, and the powers of B increase by 1, up to 3.

According to these, the second term of [tex](A+B) ^{3} [/tex] is
[tex]3A^{2}B [/tex],

where A=4x, and B=3y,

substituting A an B:

[tex]3A^{2}B=3(4x)^{2}(3y)=3*16 x^{2} *3y=144 x^{2} y[/tex]

Answer: 144

The nutritional chart on the side of a box of a cereal states that there are 93 calories in a three fourths 3/4 cup serving. How many calories are in 5 cups of the cereal?

Answers

The answer for this question will be 620 calories.
In this case, 3/4 cup= 93 calories and you need 5 cups. First you need to count calorie per cups, it would be 1 cup/(3/4 cup) * 93 calorie = 124 calorie/cup.
Then 5 cup of cereal would be 5*124 calorie= 620 calories.

a patio is in the shape of a regular octagon. the sides have length 5m. Calculate the area of the patio

Answers

here is the solution.

Round the answer as needed.

Paige pays $532 per month for 5 years for a car. she made a down payment of $3,700.00. if the loan costs 7.1% per year compounded monthly, what was the cash price of the car?

Answers

Use the formula of the present value of annuity ordinary which is
Pv=pmt [(1-(1+r/k)^(-kn))÷(r/k)]
Pv present value?
PMT monthly payment 532
R interest rate 0.071
K compounded monthly 12
N time 5years
Pv=532×((1−(1+0.071÷12)^(−12
×5))÷(0.071÷12))
=26,803.15

So the cash price of the car including down payment is
26,803.15+3,700
=30,503.15...answer

Evaluate the surface integral. (give your answer correct to at least three decimal places.) s is the boundary of the region enclosed by the cylinder x2 + z2 = 1 and the planes y = 0 and x + y = 2

Answers

Split up the surface [tex]S[/tex] into three main components [tex]S_1,S_2,S_3[/tex], where

[tex]S_1[/tex] is the region in the plane [tex]y=0[/tex] bounded by [tex]x^2+z^2=1[/tex];

[tex]S_2[/tex] is the piece of the cylinder bounded between the two planes [tex]y=0[/tex] and [tex]x+y=2[/tex];

and [tex]S_3[/tex] is the part of the plane [tex]x+y=2[/tex] bounded by the cylinder [tex]x^2+z^2=1[/tex].

These surfaces can be parameterized respectively by

[tex]S_1:~\mathbf s_1(u,v)=\langle u\cos v,0,u\sin v\rangle[/tex]
where [tex]0\le u\le1[/tex] and [tex]0\le v\le2\pi[/tex],

[tex]S_2:~\mathbf s_2(u,v)=\langle\cos v,u,\sin v\rangle[/tex]
where [tex]0\le u\le2-\cos v[/tex] and [tex]0\le v\le2\pi[/tex],

[tex]S_3:~\mathbf s_3(u,v)=\langle u\cos v,2-u\cos v,u\sin v\rangle[/tex]
where [tex]0\le u\le1[/tex] and [tex]0\le v\le2\pi[/tex].

The surface integral of a function [tex]f(x,y,z)[/tex] along a surface [tex]R[/tex] parameterized by [tex]\mathbf r(u,v)[/tex] is given to be

[tex]\displaystyle\iint_Sf(x,y,z)\,\mathrm dS=\iint_Sf(\mathbf r(u,v))\left\|\frac{\partial\mathbf r(u,v)}{\partial u}\times\frac{\partial\mathbf r(u,v)}{\partial v}\right\|\,\mathrm du\,\mathrm dv[/tex]

Assuming we're just finding the area of the total surface [tex]S[/tex], we take [tex]f(x,y,z)=1[/tex], and split up the total surface integral into integrals along each component surface. We have

[tex]\displaystyle\iint_{S_1}\mathrm dS=\int_{u=0}^{u=1}\int_{v=0}^{v=2\pi}u\,\mathrm dv\,\mathrm du[/tex]
[tex]\displaystyle\iint_{S_1}\mathrm dS=\pi[/tex]

[tex]\displaystyle\iint_{S_2}\mathrm dS=\int_{v=0}^{v=2\pi}\int_{u=0}^{u=2-u\cos v}\mathrm du\,\mathrm dv[/tex]
[tex]\displaystyle\iint_{S_2}\mathrm dS=4\pi[/tex]

[tex]\displaystyle\iint_{S_3}\mathrm dS=\int_{u=0}^{u=1}\int_{v=0}^{v=2\pi}\sqrt2u\,\mathrm dv\,\mathrm du[/tex]
[tex]\displaystyle\iint_{S_3}\mathrm dS=\sqrt2\pi[/tex]

Therefore

[tex]\displaystyle\iint_S\mathrm dS=\left\{\iint_{S_1}+\iint_{S_2}+\iint_{S_3}\right\}\mathrm dS=(5+\sqrt2)\pi\approx20.151[/tex]

Other Questions

you can help prevent fatigue by .. A. getting as much rest as possible the night before driving B. taking frequent rest stops C. all of the above In which style are the musicians most likely to have training in classical music: art rock glam rock heavy metal? Which of the following systems possesses the highest entropy?A. a sugar crystal in a hot cup of coffeeB. a sugar cube in a hot cup of coffeeC. powdered sugar in a hot cup of coffeeD. no sugar in a hot cup of coffee This is the last name of the two plebeian brothers- tiberius and gaius- who attempted to pass land reform laws that would have given more power to more romans. they were assassinated for their efforts. Which of the numbers listed below are solutions to the equation? Check all that apply. x2 = 81 A.18 B.40.5 C.-9 D.162 E.9 F.6561 What are the three factors judges considering when setting bail? How does a scientific explanation differ from a nonscientific explanation? I announce I will sign an executive order to deny federal contracts to businesses that hire illegal immigrants. We are still a nation of immigrants ; we should be proud of it. But we also a nation of laws. Why does Truman believe the Taft-Hartley Act would threaten democratic freedoms? 3x+2y+4z=12X+y+2z=6 (X=0,y=4,z=1)Determine if the given 2 lines intersect at the given point. Explain your reasoning. -2x-4y+z=84x+2y=-5(x=-2,y=0,z=3) same as up above A study on responses to the death of a spouse found that a majoiryty of widows and wisowers ___ Use the zeros of the following quadratic to find the x-value of the vertex.y = x^2 + 2x -8A. 2B. 1C. -1D. -8PLEASE HELP ASAP Aspirin was first synthesized in: The karst topography is formed by the actions of Compared with the first new deal, the second new deal focused on __________ instead of relief programs. In an atom, electrons ____. a. are located in the nucleus c. travel outside the nucleus b. are paired with neutrons d. are always in the same place in an atom The death of a star occurs when its _____ stops A school did a survey among 100 students to find their sports preferences. The students were asked about their preferences for football or baseball. Out of the total 77 people who liked football, 48 also liked baseball. There were 65 people who liked baseball. Part A: Summarize the data by writing the values that the letters A to I in the table below represent. (5 points)A school did a survey among 100 students to find their sports preferences. The students were asked about their preferences for football or baseball. Out of the total 77 people who liked football, 48 also liked baseball. There were 65 people who liked baseball. Part A: Summarize the data by writing the values that the letters A to I in the table below represent. (5 points) Like footballDo not like footballTotal Like baseballADG Do not like baseballBEH TotalCFI Part B: What percentage of the survey respondents did not like either football or baseball? (3 points) Part C: Do the survey results reveal a greater dislike for football or baseball? Justify your answer. (2 points) A person wishes to mix coffee worth nine dollars per pound with coffee worth three dollars per pound to get 240 pounds of a mixture worth five dollars per pound how many pounds of the nine dollars and the three dollar coffee will be needed Something new with the united states, is the concept that birth (and residence or naturalization) in a country imparts basic rights Steam Workshop Downloader