A region R is shown. Decide whether to use polar coordinates or rectangular coordinates and write
Answers
Writing the integral in polar coordinates is less taxing:
[tex]\displaystyle\iint_Rf(x,y)\,\mathrm dA=\iiint_Rrf(r\cos\theta,r\sin\theta)\,\mathrm dr\,\mathrm d\theta[/tex]
The region R is captured by the set of points (in polar, of course)
[tex]R=\left\{(r,\theta)\mid1\le r\le3\land\dfrac{5\pi}4\le\theta\le2\pi\right\}[/tex]
so that the integral is
[tex]\displaystyle\int_{5\pi/4}^{2\pi}\int_1^3rf(r\cos\theta,r\sin\theta)\,\mathrm dr\,\mathrm d\theta[/tex]
In rectangular coordinates, we have to split up the region so that
[tex]R=R_1\cup R_2\cup R_3[/tex]
where
[tex]R_1=\left\{(x,y)\mid-\dfrac3{\sqrt2}\le x\le-\dfrac1{\sqrt2}\land-\sqrt{9-x^2}\le y\le x\right\}[/tex]
[tex]R_2=\left\{(x,y)\mid-\dfrac1{\sqrt2}\le x\le1\land-\sqrt{9-x^2}\le y\le -\sqrt{1-x^2}\right\}[/tex]
[tex]R_3=\left\{(x,y)\mid1\le x\le3\land-\sqrt{9-x^2}\le y\le0\right\}[/tex]
and the integral is split into 3 over these regions,
[tex]\displaystyle\iint_Rf(x,y)\,\mathrm dA=\sum_{n=1}^3\iint_{R_n}f(x,y)\,\mathrm dx\,\mathrm dy[/tex]
Related Questions
Determine if the set is a Pythagorean triple
Answers
Answer:
Pythagorean Triples are sets of whole numbers for which the Pythagorean Theorem holds true. The most well-known triple is 3, 4, 5. This means that 3 and 4 are the lengths of the legs and 5 is the hypotenuse.
Patty goes to the mall at 9:30 am and meets a friend at a movie at 11:15 am. Patty wants to shop and have 55 min for lunch before meeting her friend
How much time can patty spend shopping?
Answers
Answer:
50 minutes
Step-by-step explanation:
Time when patty goes to mall = 9:30 am
Time when he has to meet a friend = 11.15 Am
Spare time patty has is interval between Time when he has to meet a friend
and Time when patty goes to mall
which can be written as
Spare time patty has = 9:30 am to 10:30 am which is 1 hours 45 mins.
One hour has 60 minutes.
Thus total time in minutes patty has = 1*60 minutes + 45 minutes = 105 minutes.
Time which will be used by Patty to have lunch = 55 minutes.
Time left out if 55 minutes are used in lunch = total spare time - time for lunch = (105 - 55 ) minutes = 50minutes.
Patty wants to shop in the spare time after allocating 55 minutes to lunch.
Thus the rest of time which is 50 minutes, he can use to shop.
What’s the correct answer for this? Select the ones that apply
Answers
Answer:
B, C and E
Step-by-step explanation:
1) Proving that opposite sides have equal slopes as they are parallel also
2) Proving that opposite sides are parallel and equal
4(1 - x) + 2 x= -3( x + 1)
Answers
Answer:
x = -7
Step-by-step explanation:
Solve for x:
4 (1 - x) + 2 x = -3 (x + 1)
4 (1 - x) = 4 - 4 x:
2 x + 4 - 4 x = -3 (x + 1)
2 x - 4 x = -2 x:
-2 x + 4 = -3 (x + 1)
Expand out terms of the right hand side:
4 - 2 x = -3 x - 3
Add 3 x to both sides:
3 x - 2 x + 4 = (3 x - 3 x) - 3
3 x - 3 x = 0:
3 x - 2 x + 4 = -3
3 x - 2 x = x:
x + 4 = -3
Subtract 4 from both sides:
x + (4 - 4) = -4 - 3
4 - 4 = 0:
x = -4 - 3
-4 - 3 = -7:
Answer: x = -7
Answer:
X=-7
Step-by-step explanation:
Children under 10 years and older people over 65 years receive a discount on movie tickets. Let x represent the age
of a person who receives a discount.
Which inequality represents the age of a child who receives a discount?
Which inequality represents the age of an older person who receives a discount?
Which compound inequality represents the age of a person who receives a discount?
Done
h Intan
Answers
Answer:
Hi
Step-by-step explanation:
In
When the volume of a gas is
changed from mL to 852 mL,
the temperature will change from
315°C to 452°C.
Answers
Answer: The initial volume is 593.76mL
Step-by-step explanation:
As you do not say anithing about the pressure, i guess that the pressure remains constant.
If the gas is an ideal gas, we have:
P*V = n*R*T
where P is pressure, n is number of moles and R is a constant.
Now, initially we have:
P*Vi = n*R*315°C
finally we have:
P*825mL = n*R*452°C
Now we can take the quiotient of those two equations and get:
(P*Vi)/(P*852mL) = (n*R*315°C)/( n*R*452°C)
Now we have:
Vi/852mL = 315/452
Vi = (315/452)*852mL = 593.76mL
So when we expand the gas at constant pressure, we increase the temperature.
Answer:
691 mL
Step-by-step explanation:
Sa piajes egne baseball games this season. Her point totais for each game were 8. 14.4 7.6.14, 4 and 7. What was
the mean number of points she scoret per game?
Answers
Answer:
The mean number of scores per game is 8
Step-by-step explanation:
Since we know we can find the mean by adding all the numbers and dividing them by many numbers there were. Once you add 8, 14, 4, 7, 6, 4, and 7, you will get 64. Since there were 8 numbers, you divide 64 by 8 to get 8.
Write using only positive exponents. 16x^4z^4/36x-2yz^0
Answers
Answer:
Step-by-step explanation:
16x^4y^-3z^4 / 36x^-2yz^0
16x^4y^-3z^4 = 16x^4z^4/y^3
36x^-2yz^0 = 36x^-2y(1) =36x^-2y = 36y/x^2
16x^4y^-3z^4 / 36x^-2yz^0
= (16x^4z^4/y^3) / (36y/x^2)
= 16x^4z^4/y^3 * x^2/36y
= (4/9)x^6z^4/y^4
or another way
fist multiply it out
f(x) = 4x^(3/5) - x^(8/5)
now differentiate knowing d/dx(x^n) = n x^(n-1)
to get
4*(3/5) x^(-2/5) - 8/5 x^(3/5)
simplify to get
12/5/x^(2/5) - 8/5 x^(3/5)
If this is what your looking for please give me brainiest, i have done this problem in the past so i know how to solve it :)
Students at a certain school were surveyed, and it was estimated that 20% of college students abstain from drinking alcohol. To estimate this proportion in your school, how large a random sample would you need to estimate it to within 0.08 with probability 0.95, if before conducting the study (a) you are unwilling to predict the proportion value at your school and (b) you use the results from the surveyed school as a guideline.
Answers
Answer:
a) A sample size of at least 251 students is needed.
b) A sample of at least 97 students is needed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
(a) you are unwilling to predict the proportion value at your school
We need a sample size of at least n.
n is found when M = 0.08.
We wont predict a proportion value for the school, so we use [tex]\pi = 0.5[/tex]
So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.08 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.08\sqrt{n} = 1.96\sqrt{0.5*0.5}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.5*0.5}}{0.08}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.96\sqrt{0.5*0.5}}{0.08})^{2}[/tex]
[tex]n = 150.1[/tex]
Rounding up
A sample size of at least 251 is needed.
(b) you use the results from the surveyed school as a guideline.
Now we have that [tex]\pi = 0.2[/tex]
So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.08 = 1.96\sqrt{\frac{0.2*0.8}{n}}[/tex]
[tex]0.08\sqrt{n} = 1.96\sqrt{0.2*0.8}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.2*0.8}}{0.08}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.96\sqrt{0.2*0.8}}{0.08})^{2}[/tex]
[tex]n = 96.04[/tex]
Rounding up
A sample of at least 97 students is needed.
There were 4 golden retrievers at the dog park last Saturday, along with 4 other dogs.
Considering this data, how many of the next 18 dogs to arrive at the park next Saturday
should you expect to be golden retrievers?
Answers
Answer:
9 Golden Retrievers.
Step-by-step explanation:
If there were 8 dogs last Saturday, and half were golden retrievers, next Saturday should have half golden retrievers. 18 divided by 2 equals 9.
[tex]18 \div 2 = 9[/tex]
Hope this helped :)
Answer:
ryt
Step-by-step explanation:
What fraction of the circle would 3 pieces represent?
Answers
Answer:
3/4 would represent the shaded in parts of the circle
Step-by-step explanation:
I cannot give you an accurate answer seeing as you did not give much detail
What are the solutions of the quadratic equation (x + 3)2 = 49?
O x=-2 and x = -16
O x = 2 and x = -10
O x= 4 and x = -10
O x = 40 and x = -58
Answers
Answer:
4 and -10
Step-by-step explanation:
Take the square root:
x +3 = ±√49 = ±7
Subtract 3:
x = -3 ± 7
For the minus sign, we have ...
x = -3 -7 = -10
For the plus sign, we have ...
x = -3 +7 = 4
The solutions are x = 4 and x = -10.
The solutions of the quadratic equation x = 4 and x = –10
Step-by-step explanation:
Solve: x=4+(4x-4)1/2 x = 2
x = 10
x = 2 or x = 10
no real solution
Answers
Answer:
No real solution- Not any of the options anyway
Step-by-step explanation:
So I replaced the x's with the two possible equations and then tried to solve...
2=4+(4x2-4)1/2
2=4+(8-4)1/2
2=4+(4)1/2
2=8(1/2)
2=4 Which is not true
10=4+(4x10-4)1/2
10=4+(40-4)1/2
10=4+36(1/2)
10=40(1/2)
10=20 Which is also not true
Therefore, there is no real solution
Answer:
B: x = 10 on Edge 2020
Step-by-step explanation:
Whats happens when the value of the expression c + 2 as c increase
Answers
Answer:
c+2 increases linearly with c. That means that if c increases by 1, c+2 will increase by 1; if by 2, c+2 will increase by 2.
Step-by-step explanation:
A farmer has a large field that is x feet in length. He wants to fence in a rectangular section in the middle of the field, leaving a length of 100 feet of open field beyond each end of the fenced rectangle. He also wants the width of the fenced-in space to be 100 feet less than its length, as shown in the diagram.
Find the equation in standard form for the area of the fenced-in section in terms of the length of the field.
(area = length • width)
Answers
Answer:
y = x2 − 500x + 60,000
Step-by-step explanation:
The length of the fenced-in section is (x − 200) feet, and the width is (x − 300) feet.
area of the fenced-in section = length • width
y = (x − 200)(x − 300)
= x2 − 300x − 200x + 60,000
= x2 − 500x + 60,000
Answer:
y= x^2 − 500x + 60,000
Step-by-step explanation:
Other loser made a mistake
The length of the fenced-in section is (x − 200) feet, and the width is (x − 300) feet.
area of the fenced-in section = length • width
y = (x − 200)(x − 300)
= x^2 − 300x − 200x + 60,000
= x^2 − 500x + 60,000
According to the most recent census, the average total yearly expenses of households in Wake County is $45,900. It is also known that the distribution of household expense in Wake County is strongly skewed to the right with a standard deviation of $8,370. A researcher is going to randomly select a sample of 7 households from Wake County.
1. Which of the following is true?
Select all that apply:
a. The sampling distribution of the sample mean will have a smaller standard deviation than the population.
b. The sampling distribution of the sample mean will have a different standard deviation than the population.
c. The shape of the sampling distribution of the sample mean will be skewed right.
d. The sampling distribution of the sample mean will have a larger standard deviation than the population.
e. We cannot tell what the shape of the sampling distribution of the sample mean will look like.
f. The shape of the sampling distribution of the sample mean will be approximately symmetric.
Answers
Answer:
a. The sampling distribution of the sample mean will have a smaller standard deviation than the population.
b. The sampling distribution of the sample mean will have a different standard deviation than the population.
c. The shape of the sampling distribution of the sample mean will be skewed right.
Step-by-step explanation:
WILL GIVE BRAINLIEST ANSWER TO WHOEVER ANSWERS FIRST AND CORRECT PLEASE EXPLAIN WHY YOU ARE CORRECT
Answers
Answer:
x=2
Step-by-step explanation:
The midsegment AB=(DG+EF)/2
so (5x-4+8x+2)/2=12
*2 *2
13x-2=24
+2 +2
13x=26
:13 :13
x=2
Factor 4x^3 + 40x^2 + 100x
Answers
Answer:
4 x (x + 5)^2
Step-by-step explanation:
Factor the following:
4 x^3 + 40 x^2 + 100 x
Factor 4 x out of 4 x^3 + 40 x^2 + 100 x:
4 x (x^2 + 10 x + 25)
The factors of 25 that sum to 10 are 5 and 5. So, x^2 + 10 x + 25 = (x + 5) (x + 5):
4 x (x + 5) (x + 5)
(x + 5) (x + 5) = (x + 5)^2:
Answer: 4 x (x + 5)^2
Gavin, Colin and Dan share some sweets in the ratio 7:3:2. Gavin gets 75 more sweets than Dan. How many sweets does Colin get?
Answers
Answer:
45 sweets.
Step-by-step explanation:
Gavin gets 7(7+3+2) = 7/12 of the sweets.
Dan gets 2 /12 so Gavin gets 7/2 times as much as Dan
Let Dan get x sweets then
x + 75 = 7x /2
7x/2 - x = 75
5x/2 = 75
x = 75 * 2/5 = 30 sweets.
So Dan gets 30 sweets , Gavin gets 105 sweets and Colin gets 3/2 * 30
= 45 sweets.
Set up the inequality of $3.000 and $15
Answers
Answer:
$3.00 < $15.00
Step-by-step explanation:
It is unusual to see a dollar amount with three digits to the right of the decimal point. (This sometimes happens when prices are expected to be multiplied by large quantities.) On the other hand, it sometimes happens that a period gets substituted for a comma. So, some relevant inequalities might be ...
$3.00 < $15
$3,000 > $15
Find the unit rate.
Kenny reads
3/8 page in 2/3 minutes.
Answers
Answer:
15/ 16
Step-by-step explanation: 3/2 x 5/8= 15/16
you flip 2/3 to 3/2 and multiply it
Ivy corporation gave 79 people a bonus. If Ivy had given 5 more people bonuses, Ivy would have rewarded 3/5 of the workforce. How large is Ivy's workforce. HELP.
Answers
Answer:
140 people in Ivy's workforce
Step-by-step explanation:
First, add together the 79 workers and the 5 extra people.
79 + 5 = 84
Now take 84 divided by 3/5 to find the number of people who are in the workforce.
84/ 3/5 = 140 people in Ivy's workforce
Answer:
140
Step-by-step explanation:
First, add together the 79 workers and the 5 extra people.
79 + 5 = 84
Now take 84 divided by 3/5 to find the number of people who are in the workforce.
84/ 3/5 = 140 people in Ivy's workforce
What is the end behavior of the graph of the polynomial function f(x)=3x^6+30x^5+75x^4
Answers
Answer:
Step-by-step explanation:
write 820.341 in scientific notation
Answers
solve 5tanx= 5sqrt3 for 0
Answers
Answer:
60 degrees
Step-by-step explanation:
5 tan x = 5 root 3
tan x = root 3
sin x / cos x = root 3
(root(3) / 2) / (1/2) = root 3
sin x = root(3)/2
cos x = 1/2
x = 60 degrees
What is the next term in the pattern 1000, 500, 250, 125, 62.5, ……
Answers
Answer:
31.25
Step-by-step explanation:
Firstly, we need to identify the pattern.
Pattern: every next number is obtained by dividing the previous number by 2.
1st number = 1000
2nd number = 1000/2 = 500
3rd number = 500/2 = 250
4th number = 250/2 = 125
5th number = 125/2 = 62.5
6th number = 62.5/ 2 = 31.25.
_______________________________________________
It can be also solved using concept of geometric progression
In GP
any nth number is given by = [tex]ar^(n-1)[/tex]
where a is first number
r is the common ratio for the gp
r common ratio is calculated by = nth/(n-1)th
here r = 500/1000 = 1/2
a = 1000
next term which we need to find is 6th terms
Thus, 6th terms = [tex]1000*(1/2)^(6-1)[/tex]
[tex]=1000/2^5[/tex]
=1000/32 = 31.25
Which situation can be represented by the equation Y equals 74X
Answers
Answer:
X: amount of a spare part of price $74 per unit.
Y: cost of purchasing X spare parts.
Step-by-step explanation:
We can imagine that X represents the amount of an object, for example a car spare part, which price is $74 per unit.
Then, Y would represent the cost of purchasing X units of that spare part.
698,000 converted to scientific notation
Answers
｡☆✼★ ━━━━━━━━━━━━━━ ☾
Scientific notation is written as:
a x 10^n
where 'a' is a value between 1 and 10
In this case, it would be:
6.98 x 10^5
Have A Nice Day ❤
Stay Brainly! ヅ
- Ally ✧
｡☆✼★ ━━━━━━━━━━━━━━ ☾
Correct Answer:
6.98 x 10^5
100 POINTS PLEASE ANSWER IM BEGGING YOU!!!!!!
Answers
Answer:
[tex]4 \sqrt{5}[/tex]
Step-by-step explanation:
[tex]\sqrt{80}[/tex]
80 can be written as a product of 16 and 5.
[tex]\sqrt{16 \times 5}[/tex]
Distribute the square root to both terms.
[tex]\sqrt{16} \times \sqrt{5}[/tex]
16 is a perfect square 4×4.
[tex]4 \times \sqrt{5}[/tex]
Answer:
4 * sqrt(5)
Step-by-step explanation:
sqrt(80)
sqrt(16*5)
We know that sqrt (ab) = sqrt(a) sqrt(b)
sqrt(16) sqrt(5)
4 * sqrt(5)
A polar bear migrate north during winter to hunt for its food on sea ice. The daily average temperature decreases 3°C for every 100 km traveled. At the start of the bear's journey, the temperature is 2"C. What is the temperature after 200 km of its journey ?
Answers
Answer:
The average temperature after 200 kilometers of journey is -4 °C.
Step-by-step explanation:
The situation shows that change in average temperature is directly proportional to travelled distance:
[tex]T = 2^{\circ}C - \frac{3^{\circ}C}{100\,km} \cdot (200\,km)[/tex]
[tex]T = -4^{\circ}C[/tex]
The average temperature after 200 kilometers of journey is -4 °C.
Answer:
The temperature after 200 km of its journey is -4°C
Step-by-step explanation:
To find the new temperature, first, you need to find how much the temperature decreases, and then subtract this temperature decrease to the initial temperature.
The temperature decreases 3°C for every 100 km travelled, then, after 200 km the temperature decreases 2*3 = 6 °C.
At the start of the bear's journey, the temperature was 2 °C, after 200 km the temperature is 2 - 6 = -4°C