Let R = [0,6] [0, 6]. Subdivide each side of R into m =n = 3 subintervals and use the Midpoint Rule to estimate the value f JI.(v 22) dA.
Answers
2f(3,1)
To use the midpoint rule to estimate the value of the double integral of a function f(x,y) over the region R=[0,6]x[0,6], we need to divide the region R into a grid of subintervals, with m subintervals in the x-direction and n subintervals in the y-direction. In this case, m=n=3, so we divide each side of the region R into 3 subintervals of equal length.
The midpoint rule states that the approximation of the integral is given by the sum of the areas of the rectangles formed by the subintervals, where the height of each rectangle is given by the value of the function at the midpoint of the subinterval.
To implement the midpoint rule, we first need to determine the width and height of each subinterval. The width of the subintervals in the x-direction is given by (6-0)÷3 = 2, and the width of the subintervals in the y-direction is also given by 2. The height of each rectangle is given by the value of the function f at the midpoint of the subinterval.
We can then evaluate the double integral by summing the areas of the rectangles formed by the subintervals. For example, the first rectangle would have a height equal to the value of the function at (0+2)÷2=1 and a width of 2, so its area would be 2f(1,1). The second rectangle would have a height equal to the value of the function at (2+4)÷2=3 and a width of 2, so its area would be 2f(3,1)
learn more about the midpoint rule on https://brainly.com/question/3508299
#SPJ4
Related Questions
Through (-20,4) and
perpendicular to y=x+5
Answers
========================================================
Explanation:
The given equation is the same as y = 1x+5 which is in y = mx+b form.
m = slope = 1b = y intercept = 5Anything perpendicular to this will have a slope of -1, which is the negative reciprocal of the original slope.
We'll use this perpendicular slope along with (x,y) = (-20,4) to find the equation of the perpendicular line.
y = mx+b
y = -1x+b ... plug in the perpendicular slope
4 = -1*(-20)+b ... plug in the x,y coordinates
4 = 20+b
4-20 = b
-16 = b
b = -16
Therefore, we go from y = mx+b to y = -x-16
If administrative assistants at Bookworm Publications make phone follow-ups after textbook reviews, more colleges and universities will adopt a new statistics book. The x + 600 publisher noticed that new book sales varied in the second year according to S(x) = A0 - , where S is total sales and x is the number of phone calls made to colleges which have adopted the book. Ao denotes the sales from the previous year. x2 Assuming A0 = 2600, what sales can Bookworm Publications expect if they make 50 follow-up phone calls? Round your answer to two decimal places if necessary. Answer Keypad Keyboard Shortcuts $I
Answers
Bookworm publications can expect 2599.74 sales. The solution has been obtained by using arithmetic operations.
What are arithmetic operations?
It is believed that the four fundamental operations, often known as "arithmetic operations," may explain all real numbers. The four mathematical operations that produce the quotient, product, sum, and difference are division, multiplication, addition, and subtraction.
We are given that the sales in second year vary according to
S(x) = A₀ - (x + 600) / x²
Now, we are given that A₀ = 2600 and x = 50.
On substituting these values in the equation, we get
⇒S(50) = [2600 - (50 + 600)] / 50²
⇒S(50) = 2600 - (650 / 2500)
⇒S(50) = 2600 - 0.26
⇒S(50) = 2599.74
Hence, Bookworm publications can expect 2599.74 sales.
Learn more about arithmetic operations from the given link
https://brainly.com/question/30283549
#SPJ1
Please answer the question in the photo :)
Answers
Answer:
it is correct I think it's right
Step-by-step explanation:
Please help me with this thank you
Answers
Answer:
I believe the answer to question (a) is 3085 ft and for (b) i think it's 238 ft
Answer:
hi how are you
Step-by-step explanation:
The wind-chill index W is the perceived temperature when the actual temperature is T and the wind speed is v, so we can write W = f(T, v).
Estimate the values of fT(−15, 50) and fv(−15, 50).
V 20 30 40 50 60 70
T
−10 −18 −20 −21 −22 −23 −23
−15 −25 −26 −27 −29 −30 −30
−20 −30 −33 −34 −35 −36 −37
−25 −37 −39 −41 −42 −43 −44
Answers
Answer:
value of Ft(-15,50) = 1.3
Value of Fv(-15,50) = -0.15
Step-by-step explanation:
W = perceived temperature
T = actual temperature
W = f( T,V)
Estimate the values of ft ( -15,50) and fv(-15,50)
calculate the Linear approximation of f at(-15,50)
\(f_{t}\) (-15,50) = \(\lim_{h \to \o}\) \(\frac{f(-15+h,40)-f(-15,40)}{h}\)
from the table take h = 5, -5
\(f_{t}(-15,40) = \frac{f(-10,40)-f(-15,40)}{5}\) = \(\frac{-21+27}{5} = 1.2\)
\(f_{t} = \frac{f(-20,40)-f(-15,40)}{-5}\) = 1.4
therefore the average value of \(f_{t} (-15,40) = 1.3\)
This means that when the Temperature is -15⁰c and the 40 km/h the value of Ft (-15,40) = 1.3
calculate the linear approximation of
\(f_{v} (-15,40) = \lim_{h \to \o} \frac{f(-15,40+h)-f(-15,40)}{h}\)
from the table take h = 10, -10
\(f_{v}(-15,40) = \frac{f(-15,50)-f(-15,40)}{10}\) = \(\frac{-29+27}{10} = -0.2\)
\(f_{v} (-15,40) = \frac{f(-15,30)-f(-15,40)}{-10}\) = \(\frac{-26+27}{-10}\) = -0.1
therefore the average value of \(f_{v} (-15,40) = -0.15\)
This means that when the temperature = -15⁰c and the wind speed is 40 km/h the temperature will decrease by 0.15⁰c
w = f(T,v)
= -27 + 1.3(T+15) - 0.15(v-40)
= -27 + 1.3T + 19.5 - 0.15v + 6
= 1.3T - 0.15v -1.5
calculate the linear approximation
\(\lim_{v \to \infty}\)\(\frac{dw}{dv} = \lim_{v \to \infty} \frac{d(1.3T-0.15v-1.5)}{dv}\) = -0.15
the lengths of the rectangle have been measured to the nearest tenth of a metre work out the following, writing down all the figures on your calculator display: a) The upper bound for the perimeter of the rectangle. b)The lower bound for the area of the rectangle. rectangle lengths = 15.8m width = 5.2m
Answers
Answer: Perimeter = 42.2 m
Area = 81.1125 m²
Step-by-step explanation:
Lower Upper
Length is given as 15.8 --> 15.75 ≤ L < 15.85
width is given as 5.2 --> 5.15 ≤ w < 5.25
Perimeter = 2L + 2w (Upper bound)
= 2(15.85) + 2(5.25)
= 31.7 + 10.5
= 42.2
Area = Length x width (Lower bound)
= 15.75 x 5.15
= 81.1125
Real numbers a and b satisfy
a + ab = 250
a - ab = -240
Enter all possible values of a, separated by commas.
Answers
The only possible value of "a" that satisfies the given equations is a = 5.
The possible values of "a" that satisfy the given equations, let's solve the system of equations:
a + ab = 250 ---(1)
a - ab = -240 ---(2)
We can solve this system by using the method of substitution. Rearranging equation (2), we get:
a = ab - 240 ---(3)
Substituting equation (3) into equation (1), we have:
(ab - 240) + ab = 250
2ab - 240 = 250
2ab = 250 + 240
2ab = 490
ab = 490/2
ab = 245
Now we have the value of "ab."
We can substitute this back into equation (3) to solve for "a":
a = (245) - 240
a = 5
For similar questions on possible value
https://brainly.com/question/21237643
#SPJ11
the are of the circle below is 28.26 ft. squared. What is the diameter
Answers
Answer: 8.06 Inches
The area of the circle is 28.26 ft². 3. The diameter of the circle is 8.06 inches.
Five computer program modules are ranked as M1, M2, M3, M4, and M5 according to the ascending order of effort required to debug them, among which M1 requires the least amount of effort and M5 requires the most amount of effort. A software engineer must randomly select three program modules from the five modules. He (or she) does not know the amount of effort each module costs when selecting.
A) What is the sample space?
B) Let A be the event that one selected module requires the least amount of effort. List the outcomes in A, and calculate the probability of A.
C) Let B be the event that the one selected module requires the most effort. List the outcomes in B, and calculate the probability of B.
D) List the outcomes in the compound event AnB, and calculate the probability of it.
E) List the outcomes in the compound event AUB, and calculate the probability of it.
F) List the outcomes in the compound event AnB, and calculate the probability of it.
G) List the outcomes in the compound event AUB, and calculate the probability of it.
H) Are events A and B mutually exclusive? Explain why?
Answers
Answer:
Follows are the solution to this question:
Step-by-step explanation:
Technician selects three out of 5 systems
In C(5,3)=10ways, this can be achieved
In part a:
Space sample chooses 3 of a 5 systems
\((M_1, \ M_2,\ M_3),\)\((M_1,M_2,M_4) \ (M_1,M_2,M_5) \ (M_1,M_3,M_4) \ (M_1,M_3,M_5),\)\((M_1,M_4,M_5) \ (M_2,M_3,M_4)\ (M_2,M_3,M_5) \ (M_2,M_4,M_5),(M_3,M_4,M_5)}\)
In point b:
A =MODULE WHICH INCLUDE M1 minimal amount of effort
Outcomes probable =
\((M_1,M_2,M_3),\ (M_1,M_2,M_4) \ (M_1,M_2,M_5)\ (M_1,M_3,M_4)\\\\(M_1,M_3,M_5),\ (M_1,M_4,M)5)\ =\ 6\)
\(\to p(A)=\frac{6}{10}\\\\\)
\(=0.6\)
In point c:
B = highest effort that is \(M_5\)
Potential result=
\((M_1,M_2,M_5) \ (M_1,M_3,M_5) \ (M_2,M_3,M_5)\(M_2,M_4,M_5) \\ (M_2,M_4,M_5), \ (M_3,M_4,M_5) \ =\ 6 \\\\\)
\(\to B= \frac{6}{10} \\\\\)
\(=0.6\)
\(\to P(B)=10\)
In point d:
\(\to \ A \ intersection \ B=(M_1,M_2,M_5), \ (M_1,M_3,M_5) \ ,(M_1,M_4,M_5)\)
\(\to A (A \ intersection \ B) = \frac{3}{10} \\\\\ \ \ \ \ \\)
\(=0.3\)
In point e:
\(\to (A \cup B) = (M_1,M_2,M_3),\ (M_1,M_2,M_4)\ (M_1,M_2,M_5)(M_1,M_3,M_4)\ (M_1,M_3,M_5), \\ (M_1,M_4,M_5)\ (M_2,M_3,M_5) \ (M_2,M_4,M_5),(M_3,M_4,M_5) \ = \ 9\)\(\to P(A \cap B)=\frac{9}{10}\)
\(= 0.9\)
In point f:
\(\to (A\cap B) = \frac{3}{10}\)
\(= 0.3\)
In point g:
\(\to (A \cup B) = \frac{7}{10}\)
\(=0.7\)
In point h:
\(\to p(A \cap B) = 0.3 \neq 0\)
Resulting set please help !!!!
Answers
The union of X and Y is {a,e,i,o,u}, the intersection of X and Z is {i,o} and the intersection of all the three is {o}.
What is ordered pair?The ordered pair is the pair of two numbers which represented in a manner that it provides a particular order.
In an order pair, the first term indicates the x-coordinate, while the second term indicate the y coordinates. The ordered pair are written in close bracket in the following way.
\((x,y)\)
The given set is U(a,e,i,o,u), in which,
\(X=(a,i,o)\\Y=(o,e,u)\\Z=(i,o,u)\)
\(X\cup Y\)For the union, write all the terms of X and Y set.
\(X\cup Y=(a,e,i,o,u)\)
\(X\cap Z\)For the intersection, write all the common terms of X and Z set.
\(X\cap Z=(i,o)\)
\(X\cap Y\cap Z\)For the intersection, write all the common terms of X , Y and Z set.
\(X\cap Y\cap Z=(o)\)
Hence, the union of X and Y is {a,e,i,o,u}, the intersection of X and Z is {i,o} and the intersection of all the three is {o}.
Learn more about the ordered pair here;
https://brainly.com/question/5754926
#SPJ1
Right angle FCD intersects Line A B and Ray C E at point C. AngleFCE is congruent to AngleECD. AngleECD is complementary to AngleDCB. A horizontal line has points A, C, B. Right angle F C D intersects the line at point C. A line extends from point C vertically to point E. Angle A C F is 45 degrees and angle F C D is 90 degrees. Which statement is true about AngleDCB and AngleACF? They are congruent and complementary. They are congruent and supplementary. They are complementary but not necessarily congruent. They are supplementary but not necessarily congruent.
Answers
Answer:
A: They are congruent and complementary.
Step-by-step explanation:
Just took the test hope this helps :D
Answer:
A
Step-by-step explanation:
it was correct on edge2020 so
(shrug)
A survey of 800 randomly selected adults in a certain country found that 82% believed that
protecting the rights of those with unpopular views is a very important component of a strong
democracy.
a. Verify the Central Limit Theorem conditions.
b. Find a 95% confidence interval for the proportion of adults in the country who believe that
protecting the rights of those with unpopular views is a very important component of a strong
democracy.
c. Would a 90% confidence interval based on this sample be wider or narrower than the 95%
interval? Give a reason for your answer.
Answers
a) the Central Limit Theorem conditions are met. b) The 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views is approximately 0.7934 to 0.8466.
c) . A 90% confidence interval would be wider than the 95% interval
How to Verify the Central Limit Theorem conditions.To verify the Central Limit Theorem (CLT) conditions, we need to check the following:
1. Random Sampling: The survey states that 800 adults were randomly selected, which satisfies this condition.
2. Independence: We assume that the responses of one adult do not influence the responses of others. This condition is met if the sample is collected using a proper random sampling method.
3. Sample Size: To apply the CLT, the sample size should be sufficiently large. While there is no exact threshold, a common rule of thumb is that the sample size should be at least 30. In this case, the sample size is 800, which is more than sufficient.
Therefore, the Central Limit Theorem conditions are met.
b. To find a 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views, we can use the formula for calculating a confidence interval for a proportion:
CI = p ± z * √(p(1-p)/n)
where:
- p is the sample proportion (82% or 0.82 in decimal form).
- z is the z-score corresponding to the desired confidence level. For a 95% confidence level, the z-score is approximately 1.96.
- n is the sample size (800).
Calculating the confidence interval:
CI = 0.82 ± 1.96 * √(0.82(1-0.82)/800)
CI = 0.82 ± 1.96 * √(0.82*0.18/800)
CI = 0.82 ± 1.96 * √(0.1476/800)
CI = 0.82 ± 1.96 * √0.0001845
CI ≈ 0.82 ± 1.96 * 0.01358
CI ≈ 0.82 ± 0.0266
The 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views is approximately 0.7934 to 0.8466.
c. A 90% confidence interval would be wider than the 95% interval. The reason is that as we increase the confidence level, we need to account for a larger margin of error to be more certain about the interval capturing the true population proportion. As a result, the interval needs to be wider to provide a higher level of confidence.
Learn more about confidence interval at https://brainly.com/question/73194
#SPJ1
Simplify each expression. Justify each step
4 x 9 x 50 =
Plz fast
Answers
So, at first, this looks a little bit tricky but, we can actually break it down and then multiply with easy numbers.
First off, we can multiply 4 by 9 which is 45 however, we still have that major 50 so, to make it easier, we can just change the 50 to a 5 and then add the 0 at the end when we get our answer.
45 * 5
= 225
Lastly, we just need at put and add a zero (0) to our answer so, in conclusion, the answer to this question is: 2250.
if a football team played 160 matches and won 65 percent of them,how many matches did it win
Answers
Answer:
65 x 160 / 100 = 104
Step-by-step explanation:
NO LINKS!!
Water covers 708%, or about 3.61 x 10⁸ km², of the Earth's surface. Approximate the total surface area of the Earth. (Round your answer to the nearest million.)
____________ km²
Answers
510,000,000 million km²
Let us represent the total surface area of the earth as = x
We are told in the question that:
Water covers 70.8%, or about 3.61 × 10⁸ km², of the Earth's surface.
70.8% = 0.708
Hence,
0.708 × x = 3.61 × 10⁸
x = 3.61 × 10⁸/0.708
x = 361000000/0.708
x = 509,887,005.65km²
Therefore, the total surface are the earth approximately to the nearest million = 510,000,000 million km²
This is the number "510 million"
=======================================================
Work Shown:
The times 10⁸ means "times 100 million"
3.61 x 10⁸ = 3.61 * 100 million = 361 million
S = surface area of the earth
70.8% of S = water coverage area
70.8% of S = 361 million square km
0.708S = 361 million square km
S = (361/0.708) million square km
S = 509.887 million square km
S = 510 million square km
S = 510,000,000 square km
A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the time read exactly 3:40 p.M. At this time, he started pumping gas into the tank. At exactly 3:44, the tank was full and he noticed that he had pumped 8.8 gallons. What is the average rate of flow of the gasoline into the gas tank?
Answers
The average rate of flow of gasoline into the gas tank is 2.2 gallons per minute.
What is the average?The average is the mean value of the data set values.
The mean is computed by dividing the total value by the number of items.
For the average rate of flow, divide the total gallons of gasoline filled by the driver, 8.8 gallons, by the number of minutes used in filling the tank.
In this case, the average rate of flow shows the speed that the driver used to fill the car with gasoline.
Starting time = 3:40 P.M.
Ending time = 3:44 P.M.
The difference in filling time = 4 minutes (3:44 - 3:40)
Total number of gallons of gasoline filled = 8.8 gallons
Average rate of flow of the gasoline = 2.2 gallons per minute (8.8/4)
Thus, at an average rate of 2.2 gallons per minute, the driver was able to fill his gas tank in 4 minutes.
Learn more about the average rate at https://brainly.com/question/24313700
#SPJ1
A stationery store wants to estimate the mean retail value of greeting cards that it has in its inventory. A random sample of 15 greeting cards indicates an average value of $3.00 and a s of $0.40. The critical value for a 99% confidence interval is
Answers
Answer:
The critical value for a 99% confidence interval is T = 2.9768
Step-by-step explanation:
We have the standard deviation of the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 15 - 1 = 14
Critical value
Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of \(1 - \frac{1 - 0.99}{2} = 0.995\). So we have T = 2.9768
The critical value for a 99% confidence interval is T = 2.9768
t all the correct answers.
= given two side lengths of 3 centimeters and 5 centimeters. Which measurement can you use for the length of the third side
Valid Triangle?
Answers
Answer:
Answer:
If x3 = 125, what is the value of x?
3
5
12
42
Step-by-step explanation:
Option B.
In this question the given expression is x³ = 125 and we have to find the value of x.
x³ = 125
x³ = 5³
x = ∛5³
x =
x =
x = 5
Step-by-step explanation:
Hope it help
Answer:
by adding
Step-by-step explanation:
Xavier is buying fencing to surround his garden if his garden has a perimeter of 30 yards and fencing cost six dollars a yard how much money will he need for the fencing
Answers
Answer:
$180
Step-by-step explanation:
If the perimeter is 30 yards and each yard costs $6 you times 30 and 6 and you get $180
Each big square below represents one whole.
What percent is represented by the shaded area?
%
Answers
Answer:
91%
Step-by-step explanation:
Answer:
91%
Step-by-step explanation:
Count the white blocks: 9
and subtract them from the blue blocks: 100 - 9 = 91%
please help
please hurry
Answers
Write the equation of the line that goes through the points: (2, -3) and (-4, -12).
Answers
(2,-3) and (-4,-12)
is
y=3/2x-6
Write the first 3 terms of the sequence 2+3
Answers
Answer:
5,10,15?
Step-by-step explanation:
???
Write this ratio as a fraction in simplest form without any units. 5 weeks to 21 days
Answers
Answer:
5/3
Step-by-step explanation:
1 week = 7 days
5 weeks = 5 × 7 days = 35 days
5 weeks to 21 days =
= 35 days to 21 days
= 35/21
= 5/3
Find the distance between A and B
Answers
Answer:
\(C. \ \sqrt{58}.\)
Step-by-step explanation:
1) coordinates of the given points are: A[-3;2] and B[4;-1];
2) the required distance can be calculated using the next formula:
\(d=\sqrt{(X_A-X_B)^2+(Y_A-Y_B)^2} ;\)
3) according to the folmula above the required distance is:
\(d=\sqrt{(-3-4)^2+(2--1)^2} =\sqrt{49+9} =\sqrt{58} .\)
It takes 60 cubic feet of sand to fill a sandbox. The length and
width of the sandbox are 5 feet and 6 feet. What is the height
of the sandbox
Answers
Answer: 2 feet tall
Step-by-step explanation: 5*6=30/60=2
Angles A and C are supplementary. Find the measure of angle C.
Angle EAB is 74 degrees. Angle FCD is undetermined.
How do I solve this problem?
Answers
In the given situation where ∠A and ∠C are supplementary, the angle ∠C is 106°.
What are supplementary angles?Angles that add up to 180 degrees are referred to as supplementary angles.
For instance, angle 130° and angle 50° are complementary angles since the sum of these two angles is 180°.
Two angles are complementary if their sum equals 90 degrees, and supplementary if their sum equals 180 degrees.
Because the three angles of a triangle sum up to 180° and the right angle has already taken up 90°, the two non-right angles in a right-angled triangle are complementary.
We say two angles "Complement" one other when their sums equal 90 degrees.
So, we already are aware of that:
∠A and ∠C are supplementary
∠A is 74°
Then, ∠C would be:
∠A + ∠C = 180
74 + ∠C = 180
∠C = 180 - 74
∠C = 106
Therefore, in the given situation where ∠A and ∠C are supplementary, the angle ∠C is 106°.
Know more about supplementary angles here:
https://brainly.com/question/12919120
#SPJ1
Correct question:
Angles A and C are supplementary. Find the measure of angle C.
(Refer to the image below)
Suppose the function h(x) = 2x - 9 is translated up 5 units to become a new
function, 1x). What's the equation of the new function?
A) 1x) = 2x - 4
B) 1x) = 2x - 14
C) 1x) = 7x-9
D) ix) = 7x-4
Answers
Please help!!! I will make brainliest
Answers
Answer:
I believe that all should be checked except for f(x) = x^6 which u already didn't check
Step-by-step explanation:
The equation is y = ab^x and all the equations, except that one, follow this formula
part A i already answer i only need part BPART B : IF JOSIE IS NOT CORRECT, FIX HER WORK TO DETERMINE THE VERTEX. IF SHE IS CORRECT, WHAT IS THE VERTEX?
Answers
ANSWER
Josie did not make a mistake
EXPLANATION
The vertex form of a quadratic equation is given in the form:
\(y=(x-h)^2\text{ + k}\)where (h, k) is the vertex
Jose rewrote the given equation to arrive at:
\(y\text{ = (x - }2)^2\text{ - 8 }\)And her vertex was (2, -8)
Comparing this with the general form written above, we see that every step taken and the final answer are correct.
Therefore, Josie did not make a mistake.