Suppose f is a continuous function defined on a rectangle R=[a,b]X[c,d]. What is the geometric interpretation of the double integral over R of f(X,y) if f(X,y)>0
Answers
If f(x,y) > 0 and is a continuous function defined over a rectangle R=[a,b]x[c,d], then the double integral over R of f(x,y) can be interpreted as the volume of a solid that lies in the first octant and under the graph of the function f(x,y) over the region R.
The geometric interpretation of the double integral over R of f(x,y) if f(x,y) > 0, where f is a continuous function defined on a rectangle R = [a,b] × [c,d] is given as follows:
The double integral of f(x,y) over R, if f(x,y) > 0, gives the volume under the graph of the function f(x,y) over the region R in the first octant.
Consider a point P (x, y, z) on the graph of f(x, y) that is over the region R, and let us say that z = f(x,y). If f(x,y) > 0, then P is in the first octant (i.e. all its coordinates are positive).
As a result, the volume of the solid that lies under the graph of f(x,y) over the region R in the first octant can be found by integrating the function f(x,y) over the rectangle R in the xy-plane, which yields the double integral.
The following formula represents the double integral over R of f(x,y) if f(x,y) > 0:
∬Rf(x,y)dydx
The geometric interpretation of the double integral over R of f(x,y) if f(x,y) > 0 is given by the volume of the solid that lies under the graph of the function f(x,y) over the region R in the first octant.
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Related Questions
sample size and the confidence level width have a (n) __________ relationship.
Answers
Sample size and the confidence level width have an inverse relationship. As the sample size increases, the confidence level width decreases.
When determining a confidence interval for a population parameter, such as the mean or proportion, a larger sample size provides more information about the population. This increased information leads to a narrower confidence interval.
The confidence level width is influenced by two factors: the sample standard deviation (or the variability of the data) and the critical value associated with the desired confidence level. As the sample size increases, the sample standard deviation becomes a more accurate estimate of the population standard deviation. This reduces the variability and leads to a narrower confidence interval.
A larger sample size leads to a decrease in the confidence level width, providing a more precise estimate of the population parameter with a higher level of confidence.
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Please guys help please me. Someone help me Dav use the function p(d)=20d - 22 calculator is dog walking business where P(D) is the net profit in dollars and D the number of dog he he walk interpret the meaning of the equation below using the context of the problem a) (3) =40. B) p(6)=100
Answers
Answer:
(a) The net profit for walking 3 dogs is $40
(b) The net profit for walking 6 dogs is $100
Step-by-step explanation:
There are mistakes in your question; however, the correct given parameter is
\(p(d) = 20d - 20\)
Required
Interpret p(3) = 40 & p(6) = 100
Interpreting p(3) = 40
Comparing this to \(p(d) = 20d - 20\)
d = 3 & p(d) = 40
This implies that:
The net profit for walking 3 dogs is $40
Interpreting p(6) = 100
Comparing this to \(p(d) = 20d - 20\)
d = 6 & p(d) = 100
This implies that:
The net profit for walking 6 dogs is $100
In a class of students, the following data table summarizes how many students have a
brother or a sister. What is the probability that a student chosen randomly from the
class has a brother and a sister?
Answers
Answer:the probability is 1/10
Which expression could represent the height of a soccer ball as it is in the air after being kicked?(1 point) A. −16t2+4t3 B.9t2+25t C.−16t2+25t+1 D.−16t+9
Answers
Answer:
Option C
Step-by-step explanation:
When an object is in the air, the only force acting on the object will be the gravitational force, so the only acceleration acting on the ball is the gravitational acceleration:
a(t) = -32ft/s^2
Now, for the velocity we integrate over time, and get:
v(t) = ( -32ft/s^2)*t + V0
where V0 is the initial vertical velocity, that it depends on how the ball was kicked.
For the position we integrate again over time:
p(t) = (1/2)*( -32ft/s^2)*t^2 + V0*t + p0
Where p0 is the initial position.
p(t) = (-16ft/s^2)*t^2 + v0*t + p0
Then the only option that fits this model is:
C: -16*t^2 + 25*t + 1.
HELP ME PLS IM DUMB
Answers
Answer:
Step-by-step explanation:
Slopes: - \(\frac{7}{3}\) and -x
y- intercepts: 3 and -6
can someone help me with this
Answers
x = 0 ⇒ (0⁵ + 32) = (0 + 2)⁵ ⇒ 32 = 32
x = -2 ⇒ [(-2)⁵ + 32] = (-2+2)⁵ ⇒ 0 = 0
So: (x⁵ + 32) = (x - 2)⁵ if x = -2 or x = 0
Ok done. Thank to me :>
Kyle's expenses are $1,850 each month. 1) How much money must Kyle earn each month to break even? A) $1,000 B) $1,675 C) $1,850 D) $2,000
Answers
-9 + 3x < x + 3 how do I solve this?
Answers
Answer:
x<6Step-by-step explanation:
-9+3x<x+3
3x-x<3+9
2x<12
x<12/2
x<6
If the interior angle of triangle are 3x,4x,and5x find the ize of angle of the traingle. Alo fing the difference between larget and malleat angle
Answers
Answer:
45, 60, 75
Difference between the largest and smallest angles
75 - 40 = 35
Step-by-step explanation:
First solve for x. The sum of the interior angles of a triangle is 180
3x + 4x + 5x =180 Combine like terms
12x + 180 Divide both sides by 12
\(\frac{12x}{12}\) = \(\frac{180}{12}\)
x = 15
3x = 3(15) = 45
4x = 4(14) = 60
5x = 5(15) = 75
Step-by-step explanation:
please, burn this into your brain for life :
the sum of all angles in a triangle is always (yes, no exceptions) 180°.
so,
3x + 4x + 5x = 180
12x = 180
x = 180/12 = 15
3x = 3×15 = 45°
4x = 4×15 = 60°
5x = 5×15 = 75°
the difference between largest and smallest angle is therefore
75 - 45 = 30°
Sara's office recycled a total of 12 pounds of paper over 4 weeks. How many weeks will it take Sara's office to recycle a total of 48 pounds of paper? Solve using unit rates
Answers
Answer:
They averaged 3lbs. a week for 4 weeks to get 12lb. They would need an additional 36lbs. to get to 48lbs. Averaging the same 3lbs. per week, this would take an additional 12 weeks for a total of 16 weeks.
I NEED TO PASS PLEASE ANSWER
Solve for p. 2p-29/4=4
A.p=-13/2 B.p=45/2 C.p=66 D.33/2
Answers
Answer:
B
Step-by-step explanation:
Plato
Find an angle between 0° and 360° that is coterminal with –150°.
Answers
Answer:
210 degrees
Step-by-step explanation:
-150 + 360 = 210
The angle between 0° and 360° is 210°
What is angle?In plane geometry a figure is formed by "two ray or lines and that shares same point is called an angle".
What is co terminal angle?Co terminal are angles in "standard position (angles with initial side along the positive x-axis) they have common terminal side".
According to the question,
The co terminal angle is 150°. The plane is formed by angle between 0° and 360°. In order to find angle is 150° + 360° = 210°.
Hence, the angle between 0° and 360° is 210°.
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Kenji just went down the slide at the playground. He walks 5 feet to get from the end of the slide back to the ladder. Then he climbs 8 feet to the top of the slide again. How long is the slide? If necessary, round to the nearest tenth.
Answers
Answer: Let's call the length of the slide "x". From the problem, we know that Kenji walks 5 feet after he slides down and climbs 8 feet to get to the top of the slide again. This means that the total vertical distance he traveled (height of the slide) is equal to 5 + 8 = 13 feet.
Using the Pythagorean theorem, we can find the length of the slide:
x^2 = 13^2 + h^2
where h is the height of the slide.
We know that h = 13 feet, so we can substitute that into the equation:
x^2 = 13^2 + 13^2
x^2 = 338
x ≈ 18.4 feet
Therefore, the length of the slide is approximately 18.4 feet. Rounded to the nearest tenth, this is 18.4 feet.
Step-by-step explanation:
Complete the inequality statement.
1/4 1/5 < >  =
Answers
Answer:
Step-by-step explanation:
Ggh
What is the salesperson's commission on a
$1300 sale if the commission rate is 10%?
Answers
Answer:
$130
Step-by-step explanation:
Answer:
$130
Step-by-step explanation:
1300×10%
$130
A line is drawn so it passes through the points (- 4, -12) and (0, - 6). What is the slope of the line? - 3 / 2 3 / 2 - 9 / 2 9 / 2
Answers
I think that is an option, can’t really tell.
You have a mortagege of $275,000
after down payment with an interest
rate of 3% for 30 years.
What does P, r,n, and t are equal to?
Answers
Answer:
Our calculator limits your interest deduction to the interest payment that would be paid on a $1,000,000 mortgage. Interest rate: Annual interest rate for this
Step-by-step explanation:
Find BD
2
В —
E
C С
D
2x-3
2x4
3 x 1
Answers
Answer:
BD= 12
Step-by-step explanation:
Please see the attached picture for the full solution.
equations
(x-3)(x+6)=0
Answers
Apply Zero Product Property
X-3 = 0 or x+6 = 0
x-3 = 0
Rearrange variables to the left side of the equation
X = 3
×+6=0
Rearrange variables to the left side of the equation
× =-6
Answer
× = 3 or x = -6
2. pvalue
3.critical value
4.test value
5.make a desision
Noise Levels in Hospitals In a hospital study, it was found that the standard deviation of the sound levels from 30 areas designated as "casualty doors" was 6.4 dBA and the standard deviation of 28 areas designated as operating theaters was 4.1 dBA. At a 0.10, can you substantiate the claim that there is a difference in the standard deviations? Use a, for the standard deviation of the sound levels from areas designated as "casualty doors." Part 1 of 5 (a) State the hypotheses and identify the claim. H_0: sigma_1^ = sigma_2^ _____
H_1: sigma_1^ ≠ sigma_2^ _____
This hypothesis test is a___test.
Answers
The hypotheses for the test are H₀: σ₁² = σ₂² and H₁: σ₁² ≠ σ₂². This is a two-tailed test to assess if there is a difference in the standard deviations of sound levels between the areas designated as "casualty doors" and operating theaters. The claim being investigated is whether or not there is a difference in the standard deviations.
The hypotheses for the test are:
H₀: σ₁² = σ₂² (There is no difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)
H₁: σ₁² ≠ σ₂² (There is a difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)
This hypothesis test is a two-tailed test because the alternative hypothesis is not specifying a direction of difference.
To substantiate the claim that there is a difference in the standard deviations, we will conduct a two-sample F-test at a significance level of 0.10, comparing the variances of the two groups.
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What is the difference of the fractions? Use the number line to help find the answer. 4/7-10/7
Answers
Answer:
4/7 - 10/7 = -6/7
Step-by-step explanation:
Answer:
4/7-10/7 =-6/7
Step-by-step explanation:
(A) 12n + 14m + 4 B) 2 (7n +3m + 7) c 3 (m + 4n+20) D) 14m + 12m + 4 CHECK ANSWER X 101 Use the expression 10m + 3 (n + 8) + 4 (m - 5) + 9n to find its simplified form Which expression is written correctly in standard form? Be sure to clear the parenthesis first and then combine like terms.
Answers
Answer:
"A) 12n + 14m + 4" would be the standard form.
Step-by-step explanation:
the expression written correctly in standard form would be "A) 12n + 14m + 4"
10m + 3(n + 8) + 4(m - 5) + 9n you need to first clear the parenthesis by applying distributive property:
10m + 3(n + 8) + 4(m - 5) + 9n = 10m + 3n + 24 + 4m - 20 + 9n
After that you combine like terms
= 10m + 4m + 3n + 9n + 24 - 20 = 14m + 12n + 4
"A) 12n + 14m + 4" would be the standard form.
Angela has 3 gallons of milk.how many quarts of milk dose she have
Answers
Answer:
12
Step-by-step explanation:
4 quest make 1 gallon so 4*3=12
Is the dilation an enlargement or a reduction? What is the scale factor of the dilation?
O reduction; 1/2
O enlargement; 2
Oreduction; 2
O enlargement;
1/2
Answers
Answer:
enlargement ; 2
Step-by-step explanation:
dilation is change in the size of the figure.
in the given scenario, figure's size is increasing so dilation is called enlargement and scale factor must be greater than 1.
scale factor = dimension of new shape / dimension of original shape
let's calculate the difference in terms of boxes of both figures to calculate the scale factor,
scale factor = 6/3
thus, in the given dilation we have enlargement of 2
The area of a rectangular window is 8526 cm?
If the length of the window is 98 cm, what is its width?
Answers
Answer:
87cm
Step-by-step explanation:
Length x width = area
98 x width = 8526
width=8526/98
width=87
The manager where you work with has made a contest to encourage you to learn more about a new company you are working with for business. Every time you get a correct answer to the managers question, you get to draw a $1, $5, or $10 bill from a bag. There are 10 bills in the bag, 5 are $1 bills, 4 are $5 bills, and 1 is a $10 bill.
If you are the first to draw, what is your expected value in rewards?
Possible answers:
A: $4.00
B: $3.50
C: $3.00
D: $4.50
Answers
Answer:
$3.50
Step-by-step explanation:
add the dollar amount of the bills together, 5x1 + 4x5 + 10x1= 35
then divide that by the total number of bills to get your answer of $3.50
Answer:
$3.50
Step-by-step explanation:
Difference between x=2 and x>2 in terms of their solutions
Answers
Answer:
When x = 2, there's a solid answer, if x > 2, it's an inequality
Step-by-step explanation:
How many liters of a 50% acid solution must be mixed with a 30% acid solution to get 180 L of a 40% acid solution?
Answers
Answer:
ninety liters
Step-by-step explanation:
Ninety liters of the 50% acid solution have to be mixed with 90 liters of the 30% solution to yield 180 liters of 40% solution.
Need help been trying for 20 min
Answers
Answer:
lol i think its false and ik the pain
Step-by-step explanation:
Inverse Functions (please help)
Answers
Answer:
The procedure for this case is add three, then divide by 5.
Step-by-step explanation:
if y=5x-3
to find the inverse, we exchange x and y then solve for the new y.
x=5y-3 add 3
x+3 = 5y divide by 5
(x+3)/5 = y
or
inverse, y=(x+3)/5
The procedure for this case is add three, then divide by 5.