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adelina 88 [10]
3 years ago
9

Suppose f⃗ (x,y,z)=⟨x,y,4z⟩f→(x,y,z)=⟨x,y,4z⟩. let w be the solid bounded by the paraboloid z=x2+y 2 z=x2+y2 and the plane z=9.z

=9. let ss be the closed boundary of ww oriented outward. (a) use the divergence theorem to find the flux of f⃗ f→ through s.
Mathematics
1 answer:
Aleonysh [2.5K]3 years ago
5 0
\mathbf F(x,y,z)=\langle x,y,4z\rangle

By the divergence theorem, the surface integral taken over S,

\displaystyle\iint_S\mathbf F\,\mathrm dS

is equivalent to the triple integral of the divergence of \mathbf F over W, the space bounded S,

\displaystyle\iiint_W(\nabla\cdot\mathbf F)\,\mathrm dV

We have

\nabla\cdot\mathbf F=\dfrac{\partial x}{\partial x}+\dfrac{\partial y}{\partial y}+\dfrac{\partial(4z)}{\partial z}=1+1+4=6

The latter integral is then given by

\displaystyle6\iiint_W\mathrm dV=6\int_{|x|\le3}\int_{|y|\le3}\int_{x^2+y^2\le z\le9}\mathrm dz\,\mathrm dy\,\mathrm dx=648
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Bob and Doug are both 100-meter sprinters. Bob's sprint time is normally distributed with a mean of 10.00 seconds and Doug's spr
alexdok [17]

Answer:

The standard deviation (σ) = 0.05

Step-by-step explanation:

The question is to find the standard deviation.

STEEP 1: FIND THE MEAN

(10+9.9) ÷ 2 = 9.95

STEP 2: SQUARE THE DIFFERENCE BETWEEN SPRINT TIME AND MEAN

10-9.95= 0.05

0.05^2 = 0.0025

9.9 - 9.95= -0.0025

-0.0025^2 = 0.0025

STEP 3: FIND THE VARIANCE

0.0025+0.0025= 0.005

0.005/2= 0.0025

STEP 4: FIND THE STANDARD DEVIATION (σ )

√variance

√0.0025 = 0.05

Therefore

σ = 0.05.

From the standard deviation, the percentage probability of the higher value to occurs is

0.05×100= 5%

That means Doug has 95%

And Bob has 5%

3 0
3 years ago
A garrison of 400men had food for 40days.After 10 days,200 more men joined them .How long will the food last now?(Assume that th
mestny [16]

Let x be the amount of food needed for one man for one day. At the beginning, we have enough food for 400 men for 40 days, i.e.

400\cdot 40\cdot x = 16000x

After 10 days, the 400 men will have consumed

400\cdot 10\cdot x = 4000x

food, impliying that the food remaining is

16000x-4000x=12000x

If 200 more men join the garrison, there are now 600 men. Each of them requires x food each day, and there are 12000x units of food remaining. They will last

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6 0
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Twelve toy turtles run a race. Each turtle is numbered from 1 to 13. A turtle can move forward one step whenever their number is
Fofino [41]

The turtle that would most likely win the race is the turtle 7

<h3>How to determine the turtle with the most chance?</h3>

The turtles are given as:

Turtle = 1 to 13

When two dice are rolled and the sum of the outcomes are taken, the sample space is:

<u>Outcome   Frequency</u>

2                    1

3                    2

4                    3

5                   4

6                   5

7                    6

8                    5

9                    4

10                   3

11                    2

12                    1

The outcome 7 has the highest frequency of 6

This means that the turtle 7 has the highest chance of winning the race

Read more about probability at:

brainly.com/question/25870256

#SPJ1

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1 year ago
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