Estimate the volume of the solid that lies below the surface z = ex+y and above the rectangle
Answers
1. The volume under the surface [tex]f(x,y)=e^{x+y}[/tex] is given by the double integral,
[tex]\displaystyle\int_0^1\int_0^1e^{x+y}\,\mathrm dx\,\mathrm dy[/tex]
We split up the integration region into a 2x3 grid of rectangles whose upper right corners are determined by the right endpoints of the partition along either axis. That is, we split up the [tex]x[/tex] interval [0, 1] into 2 subintervals,
[0, 1/2], [1/2, 1]
with right endpoints given by the arithmetic sequence,
[tex]r_i=0+\dfrac{i(1-0)}2=\dfrac i2[/tex]
for [tex]i\in\{1,2\}[/tex], and the [tex]y[/tex] interval [0, 1] into 3 subintervals,
[0, 1/3], [1/3, 2/3], [2/3, 1]
with right endpoints
[tex]r_j=0+\dfrac{j(1-0)}3=\dfrac j3[/tex]
for [tex]j\in\{1,2,3\}[/tex].
Then the upper right corners of the 6 rectangles are the points
(1/2, 1/3), (1/2, 2/3), (1/2, 1), (1, 1/3), (1, 2/3), (1, 1)
generated by the sequence [tex](r_i,r_j)[/tex].
The integral is thus approximated by the sum
[tex]\displaystyle\sum_{j=1}^3\sum_{i=1}^2f(r_i,r_j)\dfrac{1-0}m\dfrac{1-0}n=\dfrac16\sum_{j=1}^3\sum_{i=1}^2f(r_i,r_j)=\frac{e^{5/6}+e^{7/6}+e^{4/3}+e^{5/3}}6[/tex]
or approximately 2.4334. (Compare to the actual value of the integral, which is close to 2.952.)
For the midpoint rule estimate, we replace the sampling points [tex](r_i,r_j)[/tex] with [tex](m_i,m_j)[/tex], i.e. the midpoints of each subinterval, so the set of sampling points is
(1/4, 1/6), (3/4, 1/6), (1/4, 1/2), (3/4, 1/2), (1/4, 5/6), (3/4, 5/6)
and the integral is approximately
[tex]\displaystyle\sum_{j=1}^3\sum_{i=1}^2f(m_i,m_j)\dfrac{1-0}m\dfrac{1-0}n=\frac{e^{5/12}+e^{3/4}+e^{11/12}+e^{13/12}+e^{5/4}+e^{19/12}}6[/tex]
or about 2.908.
2. We approach the second integral the same way. Split up the [tex]x[/tex] interval into 8 subintervals with left and right endpoints given respectively by
[tex]\ell_i=-2+\dfrac{(i-1)(2-(-2))}8=\dfrac{i-5}2[/tex]
[tex]r_i=-2+\dfrac{i(2-(-2))}8=\dfrac{i-4}2[/tex]
for [tex]i\in\{1,2,\ldots,8\}[/tex], and the [tex]y[/tex] interval into 2 subintervals with
[tex]\ell_j=0+\dfrac{(j-1)(2-0)}2=j-1[/tex]
[tex]r_j=0+\dfrac{j(2-0)}2=j[/tex]
for [tex]j\in\{1,2\}[/tex].
The upper left corners of the rectangles in this grid are given by the sequence [tex](\ell_i,r_j)[/tex]. So the integral is approximately
[tex]\displaystyle\sum_{j=1}^2\sum_{i=1}^8f(\ell_i,r_j)\frac{2-(-2)}m\frac{2-0}n=51[/tex]
(Compare to the actual value, 32.)
Related Questions
What are the mean and the median of 73, 77, 85, 84, 35, and 115.
Answers
Answer:
PLEASE GIVE BRAINLIEST AND THANKS
Mean=78.16666666666667 or 78.17 rounded
Median= 80.5
Step-by-step explanation:
Mean=add all up and divided by amount of numbers
median= order numbers from smallest to biggest and find the middle
The discriminant of the equation x2 + x - 30 = 0 is?
The solution(s) of the equation x +x-30 = 0 is/are?
Answers
Answer:
discriminant: 11solutions: -6, +5Step-by-step explanation:
Comparing your equation to the standard form, we can find the values necessary to compute the discriminant:
x^2 +x -30 = 0
ax^2 +bx +c = 0
So, we have ... a = 1, b = 1, c = -30
The discriminant is defined as ...
d = √(b² -4ac) = √(1² -4(1)(-30)) = √121
d = 11
The solutions are ...
x = (-b ± d)/(2a) = (-1 ±11)/2
x = {-6, +5}
QUESTION 1 of 10: You have planned activities of 30 minutes, 15 minutes, 1.5 hours, and .75 hours. How many total hours of activity do you
have planned?
DME
AR
ins
a) 1
Info
b) 2
C) 25
d) 3
Answers
Answer:
d) 3
Step-by-step explanation:
1.5= 1 hour and 30 mins
+ 30 mins = 2 hours
.75 hours = 45 mins
+ 15 mins = 1 hour
2 hours + 1 hour = 3 hours
The solution is, d) 3 hours of activity do you have planned.
What is addition?Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.
here, we have,
given that, You have planned activities of 30 minutes, 15 minutes, 1.5 hours, and .75 hours.
now, we have,
1.5= 1 hour and 30 mins
with that add,
+ 30 mins = 2 hours
again, we know,
.75 hours = 45 mins
adding with that,
+ 15 mins = 1 hour
finally, adding we get,
2 hours + 1 hour = 3 hours
Hence, The solution is, d) 3 hours of activity do you have planned.
To earn more on addition click:
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ASAP! GIVING BRAINLIEST! Please read the question THEN answer correctly! No guessing. Show your work or give an explaination.
Answers
Answer:
C) [tex]G(x) = (x-1)^2-1[/tex]
Step-by-step explanation:
Which two numbers multiply to -52 and add to 24?
Answers
Answer: -2 and 26
Step-by-step explanation:
-2 * 26 = -52
-2 + 26 = 24
Answer:
-2 and 26
Step-by-step explanation:
Check all that apply
Answers
Answer: 3 y -6
x=3 and x=-6
What is the value of X in the equation below 1/3×12 X -24 equals 16
Answers
Answer: The answer should be X=10
Step-by-step explanation: Trust me I actually know what I'm talking about.
emily is making a histogram for the data 12 24 56 7 34 75 34 86 34 78 and 96, which is the most appropriate first interval?
A. 0-5
B. 0-10
C. 0-50
D. 0-100
Answers
Answer:
Option B. is correct
Step-by-step explanation:
Given:
Data: 12 24 56 7 34 75 34 86 34 78 and 96
To find: the most appropriate first interval
Solution:
A histogram is a pictorial representation to display frequency data using rectangular bars.
In histogram, each bar is for a range of data.
For the given data, options A. is not appropriate as the least value given in the data is 7.
Option C. is not appropriate as then the data falls under just two intervals only.
Option D. is not appropriate as then the data falls under just one interval only.
Option B. is the most appropriate first interval
What kind of organizations are supported by economic interest groups? a. civil rights organizations b. professional organizations c. womens’ rights organizations d. business and trade organizations Please select the best answer from the choices provided A B C D
Answers
Answer: I think it’s A sorrykf I’m wrong
Step-by-step explanation:
Gita is a single taxpayer earning $50,000 in wages this year.
In addition, she received $750 in nonqualified dividends and $2,500 in capital gains from a stock she held for 10 months.
Use the following tables to complete the statement.
Single Taxpayers: Income Brackets
Tax Rate Income Bracket
10% 0 to 9,525
12% 9,526 to 38,700
22% 38,701 to 82,500
24% 82,501 to 157,500
32% 157,501 to 200,000
35% 200,001 to 500,000
37% > 500,000
Single Taxpayers: Qualified Dividends and Long-Term Capital Gains
Tax Rate Income Bracket
0% 0 to 38,600
15% 38,601 to 425,800
20% > 425,800
Gita must pay $ (blank) in taxes on her investment income.
Answers
Answer:
Gita must pay $ 487.50 in taxes on her investment income
Step-by-step explanation:
Without mincing words Gita falls into income tax brackets of $38,601 and $425,800 from qualified dividends and long-term capital gains perspective since he had wages of $50,000 and other income totaling $3,250($2500+$750)
As a result,the taxes on her investment income of $3,250 is 15% of the investment income.
investment income taxes=$3,250*15%=$ 487.50
Answer:
$715
Step-by-step explanation:
When a number is increased by 28%, the result is 47. What is the original number to the nearest tenth?
Answers
Answer:
The original number was 36.7.
Step-by-step explanation:
Multipliers:
The multiplier for a increase of a% is 1 + a/100.
The multiplier for a decrease of b% is 1 - b/100.
In this question:
The original value is x.
Increased by 28%, so we have that 1 + (28/100) = 1.28x. Equals 47. We have to find x.
1.28x = 47
x = 47/1.28
x = 36.7
The original number was 36.7.
xyz, for x = 2y = 3, and z = 10
Answers
Answer:
2y=3 = y = 3/2 = 1.500
z = 10 = z = 10
Steps below
Step-by-step explanation:
Solving a Single Variable Equation
Add 3 to both sides of the equation :
2y = 3
Divide both sides of the equation by 2:
y = 3/2 = 1.500
Hope this helps.
wat os 1 ploos 6
plssssszzzz hewlp i have a test tommwwrow
Answers
Answer: 7
Step-by-step explanation: 1 + 6 = 7
Tasty Things Bakery recently sold 20 desserts, including 8 brownies. Considering this data, how many of the next 5 desserts sold should you expect to be brownies?
Answers
Answer:
About 2 of their next 5 deserts sold would be brownies.
Let's represent this by fractions. If 8 out of the 20 desserts they sold were brownies, that would make the fraction 8/20 represent how many brownies were sold.
Now if you reduce this fraction, you get 2/5, which tells about how many brownies will be sold in the next 5 brownies judging by the other data.
14 in.
2 in.
2 in.
3 in.
3 in.
The volume of the figure
is
cubic in.
Answers
Answer: 68 inch
Step-by-step explanation:
Find the value of P that makes the equation true
P P P P P P
36
Find the value of P that makes the equation true
Answers
6p=36
Divide six by both sides to get the value of p
36/6 is 6
p is equal to six
A diver starts at the wreck of the Varanger and then ascends 8 feet every 5 minutes. What is the diver’s depth after one hour?
I NEED THE CORRECT ANSWER, THIS IS A MATH PROJECT!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
Step-by-step explanation:
60 minutes divided by 5 times 8
96 feet
are repeating decimals rational or irrational? explain your reasoning in detail and use examples to prove your response
Answers
Answer:
Rational
Step-by-step explanation:
Because the decimal is repeating like 3.33333333 repeating it would be rational because it can be predicted that the number after it would be 3. If the answer was .5647395043794 with more number after it then it wouldn't be able to be determined and would be irrational.
John can clean pools at a constant rate of 3/5 pools/hours. How many pools can John clean in 10 hours?
Answers
Answer:
30/5= 6
Explicción:
Lo utliplicas yl odivides ..m
Answer:
'peqdrit 8urehudhvh dn dhdhs c ch
Step-by-step explanation:
wehvcfkb,x bgc hd bhnld uhurheb egjyr g ehu just tryna get me some points
Which of the following is the result of expanding 5 £ n=1 (2n-2)?
Answers
Answer:B on edge (15.5)
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
Please help me and I’ll Try to help you
Answers
Answer:
12/35
Step-by-step explanation:
Find x in DEF
A. 6
B. 6 (square root 2)
C. 6 (square root 3)
D. 12
Answers
Answer:
B. 6√2
Step-by-step explanation:
We can use the Pythagorean Theorem to solve this out. The Pythagorean Theorem states that for any right triangle with the shortest sides (called legs) as a and b and the longest side (called the hypotenuse) as c:
a² + b² = c²
Here, a = b = 6, so:
6² + 6² = c²
36 + 36 = c²
72 = c²
c = √72 = 6√2
Now, we see the answer is B.
However, there's a trick to solving these kinds of problems. Notice that DEF is both an isosceles triangle and a right triangle. We call these 45-45-90 triangles because those are the angles of the triangle.
One characteristic of these types of triangles is that their leg to leg to hypotenuse ratio is 1 : 1 : √2, always. We could apply that here. We see that the legs are 6, so we could find the hypotenuse simply by multiplying 6 by √2, and we would get 6√2, which is exactly the value we obtained above.
Thus, the answer is B.
Researchers surveyed 1,000 randomly selected adults in the U.S. A statistically significant, strong positive correlation was found between income level and the number of containers of recycling they typically collect in a week.
1. Please select the best interpretation of this result.
Group of answer choices:
O This result indicates that earning more money influences people to recycle more than people who earn less money.
O We can not conclude whether earning more money causes more recycling among U.S. adults because this type of design does not allow us to infer causation.
O This sample is too small to draw any conclusions about the relationship between income level and amount of recycling for adults in the U.S.
Answers
Answer:
Null hypothesis: [tex]\rho =0[/tex]
Alternative hypothesis: [tex]\rho \neq 0[/tex]
The statistic to check the hypothesis is given by:
[tex]t=\frac{r \sqrt{n-2}}{\sqrt{1-r^2}}[/tex]
And is distributed with n-2 degreed of freedom. df=n-2[/tex]
For this case we got a significant result that means that the real correlation coefficient is different from 0 . And for this case the best interpretation would be:
This result indicates that earning more money influences people to recycle more than people who earn less money
Step-by-step explanation:
The correlation coeffcient is given by this formula:
[tex]r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}[/tex]
For this case we know that this value of r is positive and represent a string correlation between income level and the number of containers of recycling
In order to test the hypothesis if the correlation coefficient it's significant we have the following hypothesis:
Null hypothesis: [tex]\rho =0[/tex]
Alternative hypothesis: [tex]\rho \neq 0[/tex]
The statistic to check the hypothesis is given by:
[tex]t=\frac{r \sqrt{n-2}}{\sqrt{1-r^2}}[/tex]
And is distributed with n-2 degreed of freedom. df=n-2[/tex]
For this case we got a significant result that means that the real correlation coefficient is different from 0 . And for this case the best interpretation would be:
This result indicates that earning more money influences people to recycle more than people who earn less money
What’s the correct answer for this?
Answers
The equation of the circle:
[tex](x-x_0)^2+(y-y_0)^2=R^2[/tex]
[tex]x_0=-6;y_0=-3; R=12,so\\(x-(-6))^2+(y-(-3))^2=12^2\\(x+6)^2+(y+3)^2=144[/tex]
Answer: [tex](x+6)^2+(y+3)^2=144[/tex]
Need help with this question
I’ll report you if wrong
Answers
Step-by-step explanation:
Step 1: Graph the inequalities
x - 5y ≤ 2
x + y > 0
Look at the attachment:
Answer:
Look below for the graph
Explanation:
We need to graph
x + y > 0
x - 5y ≤ 2
Hope this helps
give brainliest if you please
Which system of equations can be used to find the roots of the equation 4 x Superscript 5 Baseline minus 12 x Superscript 4 Baseline + 6 x = 5 x cubed minus 2 x?
Answers
Answer:
D) StartLayout Enlarged left-brace 1st row y = 4 x Superscript 5 Baseline minus 12 x Superscript 4 Baseline + 6x 2nd row y = 5 x cubed minus 2 x EndLayout
Step-by-step explanation:
Edg test
Answer:
d
Step-by-step explanation:
plain and simple
ASAP! GIVING BRAINLIEST! Please read the question THEN answer correctly! No guessing. Show your work or give an explaination.
Answers
Answer:
B. Yes, because it passes the vertical line test.
Step-by-step explanation:
Let's review why the other answers are incorrect.
First, A would not be correct since a curved line doesn't necessarily indicate that it is a function, however, it is a non-linear function since it's not a straight line but rather a curved line as said. Now, you might be wondering why exactly A would not be correct even if it is a non-linear function, the reason is because most of time, you are asked to find and determine if a graph is a function or not using the vertical line test.
Second, C would not be correct since it is saying that a function has to be a straight line, but as we've covered that above, in which a function does not have to be linear and can be non-linear which means it's a curved line. Thus, C is not correct as non-linear functions exist.
Third, D would not be correct because this graph actually does pass the vertical line test. In order for the graph to fail the vertical line test, it has to touch the graph in the same x points. This graph passes the vertical line test, since the x coordinates haven't repeated yet, however in some cases, the direction of the line may suddenly change and touch upon the same x points. But, in theory, this line would be starting from the origin and heading to infinity with it's curvature.
Lastly, the reason why B is correct is due to it passing the vertical line test. Again, we already covered this in the 3rd reason but I must make it clear that, this is a function since it passes the vertical line test.
Answer:
B
Step-by-step explanation:
We can eliminate options A and C because in order to be a function, a graph doesn't have to be curved or a straight line. For examlpe, a straight line isn't curved, and a parabola isn't a straight line, but they are still functions. This leaves us with options B and D, which both pertain to the vertical line test. If we conduct this test, we will find that no vertical line intersects the graph and 2 points. Therefore, it passes the vertical line test, and is a function. Hope this helps!
TRUE or FALSE:
(a) Two lines parallel to a third line are parallel.
(b) Two lines perpendicular to a third line are parallel.
(c) Two planes parallel to a third plane are parallel.
(d) Two planes perpendicular to a third plane are parallel.
(e) Two lines parallel to a plane are parallel.
(f) Two lines perpendicular to a plane are parallel.
(g) Two planes parallel to a line are parallel.
(h) Two planes perpendicular to a line are parallel.
(i) Two planes either intersect or are parallel.
(j) Two lines either intersect or are parallel.
(k) A plane and a line either intersect or are parallel.
Answers
Answer:
Please see below
Step-by-step explanation:
The answers of True or False are given considering that the given statements correspond to lines and planes in a three-dimensional space.
(a) Two lines parallel to a third line are parallel. True
(b) Two lines perpendicular to a third line are parallel. False
(c) Two planes parallel to a third plane are parallel. True
(d) Two planes perpendicular to a third plane are parallel. False
(e) Two lines parallel to a plane are parallel. False
(f) Two lines perpendicular to a plane are parallel. True
(g) Two planes parallel to a line are parallel. False
(h) Two planes perpendicular to a line are parallel.
(i) Two planes either intersect or are parallel. True
(j) Two lines either intersect or are parallel. False
(k) A plane and a line either intersect or are parallel. True
(a) Two lines parallel to a third line are parallel. True
(b) Two lines perpendicular to a third line are parallel. False
(c) Two planes parallel to a third plane are parallel. True
(d) Two planes perpendicular to a third plane are parallel. False
(e) Two lines parallel to a plane are parallel. False
(f) Two lines perpendicular to a plane are parallel. True
(g) Two planes parallel to a line are parallel. False
(h) Two planes perpendicular to a line are parallel.
(i) Two planes either intersect or are parallel. True
(j) Two lines either intersect or are parallel. False
(k) A plane and a line either intersect or are parallel. True
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Please help................
Answers
[tex]184.5 \: ft {?}^{2} [/tex]
You have a total of 52 respondents to a survey
9 out of the 52 answered Adapting
8 out of the 52 answered Other
3 out of the 52 answered Yes
5 out of the 52 answered No
21 out of the 52 answered Absolutely
3 out of the 52 answered Maybe
What are the results in % form?
Answers
Answer:
17% , 15% , 6% , 10% , 40% , 6%
Step-by-step explanation:
You're going to have to divide the number of people who voted for those positions by the total number of people.
Adapting = 9 / 52 = 17%
Other = 8 / 52 = 15%
Yes = 3 / 52 = 6%
No = 5 / 52 = 10%
Absolutely = 21 / 52 = 40%
Maybe = 3 / 52 = 6%