step by step explanation, 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]

Answer:A

Step-by-step explanation:A

Answer:

130º

Step-by-step explanation:

a line is 180º so if one angle is 50 then it's just 180-50

Answer:

it is continues

Step-by-step explanation:

it is continues

1. 75

2. 105

3. 105

4. 75

6. 105

7. 105

8. 75

Answer:

10x - 1

Step-by-step explanation:

(x + 8) - (-9x + 9) = x + 8 + 9x - 9 = (x+9x) + (8-9) = 10x -1

The equivalent Expression is (10x- 1).

An expression in math is a sentence with a minimum of two numbers/variables and at least one math operation in it.

For example,  A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression.

Given:

We have to find the difference when (-9x +9) is subtracted from (x + 8)

so, (x + 8) - (-9x + 9)

= x + 8 + 9x - 9

= (x+9x) + (8-9)

= 10x -1

Hence, the equivalent Expression is (10x- 1).

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Answer:

21. 123    22. 6.86 or 6/ 6/7  23. 90

Step-by-step explanation:

21. (6+4)² + (22+10÷2)

     (10)² + (22 + 5)

        100 + 27

           127

22. (11+42-5) ÷ (11-4)

         48 ÷ 7

        6.85 or 6 6/7

23. (17-3) × (14 - 6) -22

         14 × 8 - 22

         112 - 22

           90

9514 1404 393

Explanation:

Of course, copying the form is the same as following the instructions telling you how to fill in the form.

Line 4 is the sum 5000 +50 = 5050.

Lines 11a and 12 are the difference 757.50 -757.50 = 0.

Answer:

I think there is a typing error it should be 214 ml

Step-by-step explanation:

1 litre = 1000 ml

5 litre= 5000ml

5000- 214= 4786

hope it helps :)

Answer:

I am doiiiiiiinnnnggg just wait

Answer:

7°

Step-by-step explanation:

simple arithmetic duh

Answer:

lol no34532534

Step-by-step explanation:

Using the concept of standard deviation, it is found that:

In a normal distribution, 99.7% of the measures are within 3 standard deviations of the mean.

[tex]48 \pm 3(7)[/tex] and [tex]48 \pm 3(1)[/tex] are both reasonable distributions for the tree heights, thus, it is possible to have standard deviations of 7.5 and 1 feet.

A similar problem is given at https://brainly.com/question/24754716

Answer:

65435675e

Step-by-step explanation:

12456764 br5654365

Answer:

here ya go

Step-by-step explanation:

zeros at x = 1 and x = 5

Answer:

1 1/5

Step-by-step explanation:

3/10 + 9/10

The denominator is the same so we can add the numerators

12/10

Rewriting

10/10 + 2/10

1 2/10

Simplify the fraction

1 1/5

Answer:

1.2 would be the decimal form to answer and in the fraction form it would be

6/5 or in a mixed number fraction 1 1/5

So 1 1/5 is your answer

Please mark me as branliest

Answer:

ดำหเภสยาแไ_ะทบบใืกไภเืวบวมเพนยชตึภ/ภึรื

Answer:

The two digit numbers having sum equal to 8 are: 17,26,35,44,53,62,71,80.

Step-by-step explanation:

Answer:

it is a answer

Step-by-step explanation:

Answer:

x = 10.55cm

Step-by-step explanation:

Sin 29 degrees = 7cm/x

X = 7cm / sin 29

= 10.55 cm

Answer:

x =14.4cm

Step-by-step explanation:

Sin x = opp/hyp

This is because we are given angle look into the triangle and see opp given =7 and need hypotenuse

Sin x = 7 / sin (29)  = 14.4386574 cm = 14.4cm

This is because the opp is the 7 measure.

x = 14.4cm

We can prove the base is less through Pythagoras theorem

simply as c^2-b^2 = a^2

14.4386.....^2 -7^2 = c^2

sqrt 208.47 - sqrt 49 =c^2

c^2 = sqrt 159 = 7.43849023

therefore base = 7.44

To check angle 29 degrees for 3rd proof

cos (29) x  7/x= (x)

= 203 / x

check 203/29 = 7

Given a=7 and ∠α=29°,

b = 12.62833

c = 14.43866 proof

∠β = 61°  

h = 6.12234

area = 44.19917

perimeter = 34.06699

inradius = 2.59484

circumradius = 7.2193

9514 1404 393

Answer:

  $3

Step-by-step explanation:

The cost that hasn't been covered by bake sale proceeds is ...

  $750 -150 = $600

If that cost is divided among 200 students, the amount each student needs to pay is ...

  $600/(200 students) = $3/student

They need to charge $3 per ticket.

Hey there! Your answer is:

7 inches

Explanation:

If Tyler is 5 inches tall, he needs to grow 7 inches to be a foot tall. This is because 12 inches are in 1 foot. We can do a simple subtraction problem to figure this out.

12 inches - 5 inches = 7 inches

Since Tyler is 5 inches tall, we know that if we subtract 12 inches from 5 inches we will get the number of inches he needs to grow.

I hope this answer helps you out! Let me know if you have any questions and have a wonderful day/night!

Answer:

Step-by-step explanation:

the answer is 16.8

Explanation: well for starters you have to do what's in the parenthesis, so 4 times 1.4 is equal to 5.6. so now we add up the equation and get 28, so now we are left with 28-5.6-5.6 which equals 16.8

hoped this helped;)

Answer:

She subtracted the lengths of the diagonal lines instead of adding them.

Step-by-step explanation:

Answer:

[tex]\frac{1}{3} *\frac{1}{2} =\frac{1}{6}[/tex]

Step-by-step explanation:

So the first two balls are black, so the way to change the path is to take two out of six black balls over two out of ten balls, which is 1/3.

If the last one is red then the probability is that if you take one of the four red balls and you take one of the eight balls, you get 1/2.

So the total probability is 1/3 times 1/2 is 1/6.

Answer:

5

Step-by-step explanation:

i say 5 it makes more sens then the other answers

The graph which have slope 4/5 is Graph II.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

We have the graph.

As, we know slope= rise / run

In graph 1 the slope is

Slope= rise/ run

slope= 4/4

slope= 1

In graph 2 the slope is

Slope= rise/ run

Slope = 4/5

In graph 1 the slope is

Slope= rise/ run

Slope= 2/5

Thus, Graph II have slope 4/5.

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============================================================

Explanation:

cos(A) = 0.6 = 6/10 = 3/5

Recall that csc is the reciprocal of sine.

If csc(A) = -1.25, then sin(A) = 1/csc(A) = 1/(-1.25) = -0.8 = -8/10 = -4/5

Then we would have

tan(A) = sin(A)/cos(A)

tan(A) = sin(A) ÷ cos(A)

tan(A) = (-4/5) ÷ (3/5)

tan(A) = (-4/5) * (5/3)

tan(A) = -4/3

Answer:

-4/3

Step-by-step explanation:

Check the solution

Answer:

6/7 is the correct answr

The total amount of money y you spent if you play x games is expressed as y = 1/30x

Given the following

Total amount of AED of coupons at Dubai Expo 2020 = 100 AED

If you spend 30 AED per game, this can be expressed as:

30 AED = 1 game

100 AED = x game

Cross multiply

30 x = 100 * 1

30x = 100

x = 100/30

x = 10/3 games

This shows that 100 AED of coupons is used for 10/3 games

100 AED = 10/3 games

y AED = x games

Cross multiply

100 x = 10/3 y

100xy = 10/3

10 xy = 1/3

30xy = 1

y = 1/30x

Hence the total amount of money y you spent if you play x games is expressed as y = 1/30x

Learn more here: https://brainly.com/question/14107099

Answer:

1/8

Step-by-step explanation:

First convert 1/2 to eighths:

1/2 = 4/8

5/8-4/8= 1/8

Hope this helps! :)