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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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Task 1:
laiz [17]

Answer:

The toy's maximum height is 10.12\ \text{feet}.

Step-by-step explanation:

The equation that models the toy's height in feet from the ground at t seconds after  he threw it is given by :

h = -2t^2 + 7t + 4 .....(1)

It is required to find the toy's maximum height. For maxima or minima, put

\dfrac{dh}{dt}=0

Plugging the value of t in above equation,

\dfrac{d(-2t^2 + 7t + 4)}{dt}=0\\\\-4t+7=0\\\\t=\dfrac{7}{4}\\\\t=1.75\ s

Now put t = 1.75 s in equation (1) such that,

h = -2(1.75)^2 + 7(1.75) + 4\\\\h=10.12\ \text{feet}

So, the toy's maximum height is 10.12\ \text{feet}.

4 0
3 years ago
B is between A and C. AB = 3x, BC = 2x + 7, AC = 42<br><br> a) X =<br> b)AB =<br> c)BC=
ryzh [129]

Answer: x=7

               ab=21

               bc=14

Step-by-step explanation:

ab=3x

bc=2x±7

ac=42

3x±2x±7=42

5x±7=42

5x=42-7

5x=35

to get the value of x you divide 35 by 5x

35÷5x=7

so the value of x is 7

ab=3x

x=7

3x=7×3x

7×3=21

x=7

2x=7×2x

2×7=14

5 0
3 years ago
What number go were for gretest to least 0.38 0.34 7/20 and 1/5
valentinak56 [21]

Answer:

turn the fractions into decimals

7/20 = 0.35

1/5 = 0.20

the answer is

0.38 then 7/20 then 0.34 then 1/5

3 0
3 years ago
Dr. David Smith lived 1/13 of his life as a child. He spent 4/39 of his life preparing for an outstanding
stich3 [128]

Answer:

40 14/25 years

Step-by-step explanation:

Well, this certainly is fun.

First, to find the fraction of the doctor's life which 13 years represents, subtract the fractions from 1 (and in this case l stands for lifetime):

13 = (1 - (\frac{1}{13} + \frac{4}{39} + \frac{1}{2}))(l)

13 = (\frac{25}{78})(l)

So, multiply this equation by the reciprocal of 25/78 to isolate one of l:

13(\frac{78}{25}) = l

l = 40\frac{14}{25} years

4 0
2 years ago
Consider the following formula used to estimate height, h, of a seedling after w weeks since planting:
svp [43]

Answer:

Option B. w=5h-8

Step-by-step explanation:

we have

h=(\frac{1}{5})w+(\frac{8}{5})

Solve for w

That means ----> isolate the variable w

Multiply by 5 both sides to remove the fraction

5h=w+8

subtract 8 both sides

5h-8=w+8-8

5h-8=w

Rewrite

w=5h-8

4 0
3 years ago
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