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2 years ago

5

Se the divergence theorem to calculate the surface integral s f · ds; that is, calculate the flux of f across s. f(x, y, z) = x2

sin(y)i + x cos(y)j ? xz sin(y)k, s is the "fat sphere" x8 + y8 + z8 = 125.

1 answer:

pishuonlain [190]2 years ago

8 0

$\mathbf f(x,y,z)=x^2\sin y\,\mathbf i+x\cos y\,\mathbf j-xz \sin y\,\mathbf k$
$\implies\nabla\cdot\mathbf f(x,y,z)=2x\sin y-x\sin y-x\sin y=0$

which means

$\displaystyle\iint_S\mathbf f(x,y,z)\,\mathrm dS=\iiint_R\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV=0$

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A ball on a string moves around a complete circle, once a second, on a frictionless, horizontal table. The tension in the string

ki77a [65]

The tension in the string balances out, and thus equals the centripetal force of the ball

T = mv^2/r
<span>
if it only takes half the time to finish one orbit it has to be moving at twice the original speed. </span>
<span>
And since v is squared T will increase by 4 </span>
<span>
T' = m(2v)^2/r </span>
<span>
T' = 4mv^/r = 4T </span>
<span>
T' = 24.0 N

I hope my answer has come to your help. Have a nice day ahead and may God bless you always!
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5 0

2 years ago

There are 9 students in a service club. The club is making gift baskets for children in a hospital. Each club member donated 4 c

VladimirAG [237]

Answer:

Step-by-step explanation:

Let x represent the number of toys that each club member donated.

There are 9 students in a service club.

If each club member donated 4 children's books for the baskets, it means that the total number of books donated by the club members would be

9 × 4 = 36

If each club member also donated an equal number of toys. It means that the total number of toys donated by the club members would be

9 × x = 9x

A total of 63 items were collected for the baskets. Therefore, the linear equation that you can use to find how many toys each club member donated would be

9x + 36 = 63

4 0

2 years ago

a computer shop charges 20 pesos per hour (or a fraction of an hour) for the first two hours and additional 10 pesos per hour fo

Serhud [2]

Answer:

The equation for the price, as a function of time in hours is:

P(x) = 20*x for 0 ≤ x ≤ 2

P(x) = 40 + 10*(x - 2) for 2 ≤ x

Now, we want to evaluate this function in 40 mins.

we know that 1 hour = 60mins.

Then 40 mins = (40/60) hours = 0.67 hours.

Then we input this in our function, and because this is smaller than 2, we use the first piece of our function:

P(0.67) = 20*0.67 = 13.4

So in 40 mins, the charge will be 13.4 pesos.

7 0

2 years ago

Agent Hunt transferred classified files from the CIA mainframe onto his flash drive. The drive had some files on it before the t

topjm [15]

Answer: The drive was 24.32% full when the transfer began.

Step-by-step explanation:

Given: The rate of transferring file = 4.44 megabytes per second.

After 32 seconds, the amount of data on the drive = 384 megabytes

The amount of transferred data = $32\times4.4=140.8$ megabytes

Therefore, the amount of data in the drive at the beginning is given by :-

$\text{Beginning amount=Amount after 32 seconds -Amount transferred}\\\\\Rightarrrow\ \text{Beginning amount=}384-140.8=243.2$

The drive had a maximum capacity of 1000 megabytes.

$\frac{243.2}{1000}\times100=24.32\%$

Hence, the drive was 24.32% full when the transfer began.

4 0

1 year ago

Read 2 more answers

During a field trip, 60 students are put into equal-sized groups. Describe two ways to interpret 60÷5 60 ÷ 5 in this context. Fi

Afina-wow [57]

The second question:

Consider the division expression $7\frac{1}{2} / 2$ . Select all multiplication equations that correspond to this division expression.

$2 * ? = 7\frac{1}{2}$ $7\frac{1}{2} * ?= 2$ $? * 2 = 7\frac{1}{2}$

$2* 7\frac{1}{2} = ?$ $? * 7\frac{1}{2} = 2$

Answer:

1. See Explanation

2. $2 * ? = 7\frac{1}{2}$ and $? * 2 = 7\frac{1}{2}$

Step-by-step explanation:

Solving (a):

Given

$Students = 60$

$Group = Equal\ Sized$

Required

Interpret $\frac{60}{5}$ in 2 ways

<u>Interpretation 1:</u> Number of groups if there are 5 students in each

<u>Interpretation 2:</u> Number of students in each group if there are 5 groups

<u>Solving the quotient</u>

$Quotient = \frac{60}{5}$

$Quotient = 12$

<u>For Interpretation 1:</u>

The quotient means: 12 groups

<u>For Interpretation 2:</u>

The quotient means: 12 students

Solving (b):

Given

$7\frac{1}{2} / 2$

Required

Select all equivalent multiplication equations

Let ? be the quotient of t $7\frac{1}{2} / 2$

So, we have:

$7\frac{1}{2}/2 = ?$

Multiply through by 2

$2 * 7\frac{1}{2}/2 = ? * 2$

$7\frac{1}{2} = ? * 2$

Rewrite as:

$? * 2 = 7\frac{1}{2}$ --- This is 1 equivalent expression

Apply commutative law of addition:

$2 * ? = 7\frac{1}{2}$ --- This is another equivalent expression

8 0

1 year ago