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Natasha2012 [34]
3 years ago
14

Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of

F across S. For closed surfaces, use the positive (outward) orientation.
F(x, y, z) = xy i + yz j + zx k S is the part of the paraboloid z = 2 − x2 − y2 that lies above the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1,
and has upward orientation
Mathematics
1 answer:
slega [8]3 years ago
6 0
 <span>Let r(x,y) = (x, y, 9 - x^2 - y^2) 

So, dr/dx x dr/dy = (2x, 2y, 1) 

So, integral(S) F * dS 
= integral(x in [0,1], y in [0,1]) (xy, y(9 - x^2 - y^2), x(9 - x^2 - y^2)) * (2x, 2y, 1) dy dx 
= integral(x in [0,1], y in [0,1]) (2x^2y + 18y^2 - 2x^2y^2 - 2y^4 + 9x - x^3 - xy^2) dy dx 
= integral(x in [0,1]) (x^2 + 6 - 2x^2/3 - 2/5 + 9x - x^3 - x/3) dx 
= integral(x in [0,1]) (28/5 + x^2/3 + 26x/3 - x^3) dx 
= 28/5 + 40/9 - 1/4 
= 1763/180 </span>
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A sample of 40 observations is selected from one population with a population standard deviation of 5. The sample mean is 102. A
marin [14]

1) This is a Two tailed Test.

2) Decision rule is; If the p-value is greater than 4% fail to reject H₀.

3) P-value = 0.00968764 and so we reject H₀

<h3>How to state the decision rule in hypothesis testing?</h3>

We are given the hypothesis as;

Null Hypothesis; H₀: m₁ = m₂

Alternative Hypothesis; H₁: m₁ ≠ m₂

1) Since the alternative hypothesis has "not equal to sign", then it is a two tailed test.

2) Since we are told to use significance level as 0.04, then we can say that the decision rule is;

If the p-value is greater than 4% fail to reject H₀.

3) Using a 2-Sample Z-Test online TI calculator gives the test statistic as;

z = 2.5868

4) From z-score calculator, p-value equals 0.00968764. This is less than 0.04 and as such the decision regarding H₀ is to reject H₀.

5) P-value = 0.00968764

Read more about decision rule in Hypothesis Testing at; brainly.com/question/17192140

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3 0
1 year ago
the length of a rectangle is twice its width. the area of the rectangle is 32 square feet. what are the length and width? which
SSSSS [86.1K]
Work shown above!

Length would be 8 feet

Width would be 4 ft

Equation would be either:
Area = 2w^2 or
32 = 2w^2 which is the same thing except area was replaced with it's actual number

4 0
3 years ago
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What is 207/500 simplified
bezimeni [28]
207/500 is already in simplest form
8 0
3 years ago
Find the value of 3y + 4 given that - 2y + 6 = 2.<br> Simplify your answer as much as possible.
Dennis_Churaev [7]

Answer:

10

Step-by-step explanation:

to find the answer for 3y + 4 we have to find the value of y.

we can find that by using the second equation.

-2y+6=2

-2y+6-2 =0 (subtract 2 from both the sided)

4= 2y (we will bring the -2y to the other side of the equation and then subtract the 6-2 to get the 4)

4/2=y  (divide by 2 on both the sides)

∴ y=2

now we will plug in the y of value that we see as -2 into the first equation.

∴ 3y+4 will become

=  3(2)+4

=6+4

=10

hope this helps!!

6 0
2 years ago
Khloe bought 13 chicken wings for $14.30. If Khloe spent $19.80, how many chicken wings did she buy?
Stolb23 [73]
18 chicken wings :)
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have a great day!
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