Answer fast, please!!!

Parameterize this surface by

r (u, v) = 9 cos(u) sin(v) i + 9 sin(u) sin(v) j + 9 cos(v) k

with 0 ≤ u ≤ 2π and 0 ≤ v ≤ arccos(4/9)

See the attached sketch to see how we arrive at the upper limit for v.

Take the normal vector to the surface to be

n = ∂r/∂u × ∂r/∂v

n =  -81 cos(u) sin²(v) i -  81 sin(u) sin²(v) j - 81 sin(v) cos(v) k

which has magnitude

||n|| = 81 sin(v)

Then the surface area is

[tex]\displaystyle \iint_S \|\mathbf n\| \,\mathrm du\,\mathrm dv = 81 \int_0^{2\pi} \int_0^{\arccos(4/9)} \sin(v)\,\mathrm dv\,\mathrm du \\\\ = 162\pi \int_0^{\arccos(4/9)} \sin(v)\,\mathrm dv \\\\ = -162\pi (\cos\left(\arccos\left(\frac49\right) - \cos(0)\right) \\\\ = 162\pi \left(1 - \dfrac49\right) \\\\ = \boxed{90\pi}[/tex]

If you're not familiar with surface integrals, you can instead use what's sometimes called the projection method. Let

z = f(x, y) = √(81 - x ² - y ²)

(where we take the positive square root because we're looking at a part of the top half of the sphere)

Projecting the surface down onto the (x, y)-plane, we see that it casts a "shadow" of a disk with radius √(9² - 4²) = √65. (Use the Pythagorean theorem to solve for the missing side of the triangle in the sketch.)

Then the surface S considered above is hovering over the set in the (x, y)-plane,

D = {(x, y) : x ² + y ² ≤ 65}

The area is then

[tex]\displaystyle \iint_D \sqrt{1 + \left(\dfrac{\partial f}{\partial x}\right)^2 + \left(\dfrac{\partial f}{\partial y}\right)^2} \,\mathrm dx\,\mathrm dy[/tex]

It's easier to compute this integral in polar coordinates, so we take

x = r cos(t )

y = r sin(t )

dx dy = r dr dt

and the region D is given by the set

{(r, t ) : 0 ≤ r ≤ √65 and 0 ≤ t ≤ 2π}

Then the integral would be

[tex]\displaystyle \iint_D \sqrt{1 + \left(\dfrac{\partial f}{\partial x}\right)^2 + \left(\dfrac{\partial f}{\partial y}\right)^2} \,\mathrm dx\,\mathrm dy = \iint_D \sqrt{1 + \frac{x^2+y^2}{81-x^2-y^2}}\,\mathrm dx\,\mathrm dy \\\\ = \iint_D \sqrt{\frac{81}{81-x^2-y^2}}\,\mathrm dx\,\mathrm dy \\\\ = \int_0^{2\pi} \int_0^{\sqrt{65}} r \sqrt{\frac{81}{81-r^2}}\,\mathrm dr\,\mathrm dt[/tex]

Substitute s = 81 - r ² and ds = -2r dr :

[tex]\displaystyle \int_0^{2\pi} \int_0^{\sqrt{65}} r \sqrt{\frac{81}{81-r^2}}\,\mathrm dr\,\mathrm dt = 2\pi \int_0^{\sqrt{65}} r \sqrt{\frac{81}{81-r^2}}\,\mathrm dr \\\\ = -9\pi \int_{81}^{16} \frac{\mathrm ds}{\sqrt s} \\\\ = 9\pi \int_{16}^{81} s^{-1/2}\,\mathrm ds \\\\ = 18\pi \left(\sqrt{81} - \sqrt{16}\right) \\\\ = \boxed{90\pi}[/tex]

9514 1404 393

Answer:

Step-by-step explanation:

The difference in ratio units is 5 - 4 = 1. The difference in actual quantity is 3, so 1 ratio unit must represent 3 students.

There are 5×3 = 15 boys.

There are 4×3 = 12 girls.

9514 1404 393

Answer:

  (a)  -4

Step-by-step explanation:

The picture is fuzzy, but perhaps you want to evaluate ...

  [tex]-1\left|\dfrac{2}{3}-4\right|\div\dfrac{5}{6}=-1\left|-\dfrac{10}{3}\right|\div\dfrac{5}{6}\\\\=-\dfrac{10}{3}\div\dfrac{5}{6}=-\dfrac{20}{6}\div\dfrac{5}{6}=-\dfrac{20}{5}=\boxed{-4}[/tex]

Answer:

6z + 9

Step-by-step explanation:

distribute 3/4 by 8z to get 6z

distribute 3/4 by 12 to get 9

Answer:

$415 at 6% and $1315 at 14%

Step-by-step explanation:

She has x amount at 6%.

She has y amount at 14%.

y = x + 900

0.06x + 0.14y = 209

Since the first equation is already solved for y, we use the substitution method. Substitute x + 900 for y in the second equation and solve for x.

0.06x + 0.14(x + 900) = 209

0.06x + 0.14x + 126 = 209

0.2x = 83

x = 415

y = x + 900

y = 415 + 900

y = 1315

Answer: $415 at 6% and $1315 at 14%

Answer:

7.81

Step-by-step explanation:

Step-by-step explanation:

[tex]distance = \sqrt{(x2 - x1) ^{2} + (y2 - y1) ^{2} } [/tex]

Now, substitute the numbers into the equation,

[tex] \sqrt{(2 + 4) ^{2} +( 5 - 0)^{2} } [/tex]

distance = 7.81

brianlist me??

Step-by-step explanation:

260000*0*54*30

$421200

Answer:

(3, -3.5)

Step-by-step explanation:

Using midpoint formula:

M = (x1 + x2/2 , y1 + y2/2)

By inserting the points you'll find the answer:

M = (5 + 1/2 , -2 + -5/2)

M = (6/2 , -7/2)

M = (3 , -3.5)

Step-by-step explanation:

arithmetic sequence : every new item of the sequence is created by adding a constant term to the previous item - in this case 195.

a1 = 3087 (that's our starting value)

a2 = a1 + 195

a3 = a2 + 195 = a1 + 2×195

an = a1 + (n-1)×195

a)

when he is 45 years old, that is 20 years (and 20 annual increments) plus to our starting value.

so, n = 1+20 = 21

a21 = a1 + 20×195 = 3087 + 20×195 = 6987

so, when he is 45 years old, his monthly salary will be RM6,987

b)

how many years (= how big is n) until he gets 8937 ?

8937 = a1 + (n-1)×195 = 3087 + (n-1)×195 =

= 3087 + n×195 - 195 = 2892 + n×195

6045 = n×195

n = 6045/195 = 31

so, a31 = 8937

and that means, he has to work 30 additional years (31 minus the starting level 1) to earn monthly RM8,937.

that means he will be 25+30 = 55 years old.

no solution,

48x+43=47x+43

     -43         -43

48x=47x

if x= 1

48 is not equal to 1

B

Answer:

B

Step-by-step explanation:

It's impossible to let these 2 equation have same answer!

Answer:

No pictures so can't help ya.

Answer:

8:36

Step-by-step explanation:

if you sharpened 8 pencils out of 44 that means 8 pencils are sharpened and the other 36 aren't

Answer:

the answer is negative two / x= -2

_________

[tex] \: [/tex]

[tex] \rm3(2x - 5) - (2x - 5 ) = 6(4x + 5)[/tex]

[tex] \rm6x - 15 - 2x - 5 = 24x + 30[/tex]

[tex] \rm4x - 20 = 24x + 30[/tex]

[tex] \rm4x - 24x = 30 + 20[/tex]

[tex] \rm - 20x = 50[/tex]

[tex] \rm \: x = \frac{50}{ - 20} [/tex]

[tex] \rm \: x = \boxed{ - 2 \frac{1}{2} }[/tex]

Answer:

$4.61

Step-by-step explanation:

To calculate a tip of 20%, you would perform the following:

$92.18 * 0.20 = $18.436

Similarly, for a tip of 15%:

$92.18 * 0.15 = $13.827

The difference would just be subtracting the two tip amounts from each other!

$18.436 - $13.827 = $4.609

Then you round to the nearest cent.

$4.609 ≈ $4.61

Answer: lotion- semisolid

capsule- solid

suspension- liquid

Step-by-step explanation:

Answer:

[tex]x =[/tex] [tex]-30[/tex]

Step-by-step explanation:

Solve for [tex]x[/tex] by simplifying both sides of the equation, then isolating the variable.

Call me when you want, call me when you need

Call me in the morning, I'll be on the way

Call me when you want, call me when you need

Call me out by your name, I'll be on the way like

Step-by-step explanation:

there are 36 (6×6) possible results and number combinations for 2 dice.

a)

to create a sum of 4 we need one of the following combinations :

1 3

2 2

3 1

so, 3 out of the overall possible 36 possibilities.

and that means the probability is 3/36 = 1/12

b)

to create a sum of 7 we need one of the following combinations :

1 6

2 5

3 4

4 3

5 2

6 1

so, 6 out of the overall possible 36 possibilities.

and that means a probability of 6/36 = 1/6

c)

since the possible outcomes in that regard are only 2 (even and uneven), with equal balance the probability is 1/2.

make it more formal ?

to get an even sum, every possible number on one die can be combined with 3 possibilities on the other.

1 can be combined with 1, 3, 5

2 with 2, 4, 6

3 with 1, 3, 5

4 with 2, 4, 6

5 with 1, 3, 5

6 with 2, 4, 6

these are 6×3 = 18 combinations of of the possible 36.

so, the probability is 18/36 = 1/2

d)

not a 6 ?

so, what does that mean ?

we are looking only at 5 possible outcomes per die.

that is 5×5 = 25 combinations out of the possible 36.

that means that probabilty is 25/36.

e)

not a perfect square ?

we have in the range of the possible sums with 2 dice (2 .. 12) only two perfect squares : 4 and 9

so, the sum must NOT be 4 AND NOT be 9.

so, here it might be easier to count the unwanted cases and then deduct the probability from 1 to express the opposite.

the combinations to get 4 we have already under a)

3 combinations with 3/36=1/12 probability.

the combinations to get 9

1 none

2 none

3 6

4 5

5 4

6 3

so, 4 combinations with a probability of 4/36 = 1/9

therefore, we have (3+4) = 7 cases out of the possible 36 we actually want to avoid.

so, the probability to get any one of the other (desired) combinations is therefore (36-7)/36 = 29/36

The probabilities are:

The probability for a given outcome is given by the quotient between the number of combinations that give that outcome and the total number of combinations.

Here each dice has 6 possible outcomes, so the total number of combinations for the two dice is:

6*6 = 36 combinations.

a) Here we need to count how many combinations add to 4, the notation I will use is:

dice 1   dice 2

1              3

3               1

2               2

There are 3 combinations that add to 4, then the probability of getting a sum equal to 4 is:

P = 3/36 = 0.083

b) Same thing as before, this time we count the combinations that add to 7.

dice 1   dice 2

1               6

6               1

5               2

2               5

4                3

3                4

There are 6 combinations that add to 7, so the probability is:

P = 6/36 = 0.167

c) The possible even numbers are: {2, 4, 6, 8, 10, 12}

A way of doing this, is:

If the first dice is even/odd, then the second also must be even/odd.

Then the probability is just 1/2  = 0.5 (because there are the same number of odd and even numbers in a dice).

d) The sum must not be equal to 6, the combinations that add up to 6 are:

dice 1   dice 2

2            4

4             2

3             3

1              5

 5            1

So 5 combinations add up to 6, then there are 31 combinations that do not add up to 6, this means that the probability of not getting a sum equal to 6 is:

P = 31/36 = 0.861

e) The perfect squares are 4 and 9, we already know that 3 combinations add up to 4, now let's find the combinations that add up to 9.

dice 1   dice 2

6             3

3              6

5              4

4               5

So 4 combinations add up to 9, then there is a total of 7 combinations that give a perfect square, then there are 29 combinations that do not add to a perfect square.

The probability is:

P = 29/36 = 0.806

If you want to learn more about probability, you can read:

https://brainly.com/question/251701

Answer:

The amount is $18548.38 and the interest is $2548.38

Steps for solution:

First you want to use the formula A=P(1+[tex]\frac{r}{n}[/tex])^n*t. A= total amount, P= principle or amount of money deposited, r= annual interest rate, n= number of times compounded per year. and t= time in years. In the problem we have P= $16000, r= 3%, n= 1 and t= 5 years. The first picture is the formula used to find the total amount. After we use the formula A=P+I, since A=18548.38 and P=16000. The second picture represents the interest after 5 years.

[tex]3x - (2x + 1) \\ = 3x - 2x - 1 \\ = x - 1[/tex]

x - 1

Answer: x-1

Step-by-step explanation: in the picture

Step-by-step explanation:

Let's first find the slope

(-5-2)/(5--1) = -7/6

the equation should be

[tex]y = \frac{ - 7}{6} x + c[/tex]

To find c, we replace X with -1 and Y with 2

c= 5/6

So the equation is

[tex]y = \frac{ - 7}{6} x + \frac{5}{6} [/tex]

And if you multiply everything by 6 you get

6y = -7x +5

Answer:

2 2 y = a x 2 + b x + c ; a ≠ 0 2

Step-by-step explanation:

Answer: In this equation, let "x" equal the rate at which the tub will be filled. The tub holds 32 gallons, which will be one-half of the equation. The tub already contains 12 gallons, so this will be half of the other side of the equation. The rate is "x" gallons per minute, and the time it required was 5 minutes, so this would be "5x". Placing all these parts together gives an equation of (32 = 5x + 12) gallons per minute dispensed.