HELPPPPPPPPPPPPPPPPPPPPPPPPPPP

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:

1) 8 3/5

2) Option 3

A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.

The formula for adding two fractions:

= a/b + c/d

= (ad + bc) / cd

The fraction spent altogether on food and clothes is 7/12.

A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

Fraction of earnings spend on food:

= 1/3

Fraction of earnings spend on clothes:

= 1/4

Fraction of total spending on food and clothes.

= 1/3 + 1/4

= (4 + 3) / 12

= 7/12

The formula for adding two fractions:

= a/b + c/d

= (ad + bc) / cd

Fraction of earnings saved after spending on food and clothes.

= 1 - 7/12

= (12 - 7) / 12

= 5/12

Thus,

The fraction spent altogether on food and clothes is 7/12.

Learn more about fractions here:

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Answer:

Step-by-step explanation:

The y-intercept of the equation is -8.

You can test this by making X = 0 and solving algebraically. Similarly, if you make y = 0, you can solve the X value. This means X = 8/5

Co-ordinates (8/5, -8)

9514 1404 393

Answer:

  5.7×10^6 mi

Step-by-step explanation:

(1.9×10^5 mi/s) × (3.0×10^1 s) = 5.7×10^6 mi

_____

Additional comment

When I can see that the product will have a mantissa that has a value greater than 10 or less than 1, I like to adjust the factors so the mantissa of the product comes out in the range 1-10. Here, we could adjust 1.9 to 0.19, or 30 to 3.0. We chose the latter.

Moving the decimal point of 30.0 1 place to the left means we increase the corresponding exponent by 1 (from 0 to 1).  30.0×10^0 = 3.00×10^1

Given :

To find :

Solution :-

The first set is ,

Solving the Quadratic equation ,

Hence ,

The second set is ,

Solving the Quadratic equation ,

Hence ,

Now ,

Since AΠ B is a null set , hence ,

Answer:

-3

Step-by-step explanation:

hope it helps

not 100% sure since you didnt show us an image

we change this number 1.5=15/10=3/1 and 0.5=5/10=1/2

it will show on the number line!

The expression using subtraction to find the distance between the two jellyfish is 0.5 - (-1.5).

The distance between the two Jellyfish is 2.

We have,

The point of A on the number line: -1.5

The point of B on the number line: 0.5

Now,

To find the distance between the two jellyfish.

= B - A

= 0.5 - (-1.5)

= 0.5 + 1.5

= 2

Thus,

The expression using subtraction to find the distance between the two jellyfish is 0.5 - (-1.5).

The distance between the two Jellyfish is 2.

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Cost  $425.00

Markup  200 %

Revenue  $1,275

Profit  $850

To find markup percentage, businesses use the markup percentage formula:

Markup Percentage = (Markup / Cost) x 100% Determine markup. Markup is the difference between selling price and cost:

Markup = Selling Price - Cost. Divide markup by cost. ...

Markup Percentage = (Markup / Cost) Convert to a percentage.

Answer:

2^3 + 5^2 = 34

7^2 - 3^3 = 22

8^2 + (square root) 100 = 74

Step-by-step explanation:

Hope this helps! Lol I couldn't find the square root symbol.

Answer:

180 litres

Step-by-step explanation:

Quart: 1.1 litre

3 quarts used every 1 time its cleaned

cleaned 5 times 1 month

5 x 3=15

12 months in a year 15 x 12 = 180

Answer:

Step-by-step explanation:

Given equation:

Solve for x:

____________

[tex] \: [/tex]

[tex] \frac{x}{2 - 8} = y[/tex]

[tex] \frac{x}{2} = y + 8[/tex]

[tex]x = \bold{2y + 16}[/tex]

Answer:

36-9w or -9w+36

Step-by-step explanation:

Distributive Property - a(b-c) = ab-ac

Using that, we have-

9(4-w) = 9(4) - 9(w) = 36-9w

Answer = 36-9w or -9w+36

Thank you! Please Mark Brainliest! :)

Answer:

36-9w

Step-by-step explanation:

9*4=36

9*w=9w

36-9w

Answer:

4

Step-by-step explanation:

the answer is 4

yep it is because eight cancels out with the other one

Answer:

(8 × 4)/8

so answer=4

Answer:

(n^3)/12

Step-by-step explanation:

1/12 * n^3

= (n^3)/12

Answer:

[tex]\sqrt[3]{\frac{1}{12} }[/tex] * n

Step-by-step explanation:

You want to get the n alone. In order to do that, you need to get rid of the 3rd power. The opposite of a power is a radical. So do:

[tex]\sqrt[3]{\frac{1}{12} }[/tex] * [tex]\sqrt[3]{n^3}[/tex]

This cancels out the n and turns the problem into:

[tex]\sqrt[3]{\frac{1}{12} }[/tex] * [tex]n[/tex]

I can't solve for n since I haven't been given the entire problem (what they're equal to), but you can solve for [tex]\sqrt[3]{\frac{1}{12} }[/tex].

Answer:

One: 58.5

Two 36.6

Step-by-step explanation:

One

20 students * 65 = 1300 This is the total score of all 20 students. They may not all get 65, but 1300 is what their average total is.

20 students * 52 = 1040

The total score of all 40 students was 1300 + 1040 = 2340

The average for the entire class was 2340 / 40 = 58.5

Two

This question is done almost the same way.

Supposes the total number of members is 100. That means that 28 of them are men

28 * 33 = 924     This is the total age for the men

100 - 28 = 72        Out of 100, 72 of the people there are women.

72 * 38 = 2736

The total number of years of all of the members is

924 + 2736 = 3660      

The average age of all members is 3660/100 = 36.6

Why did I pick 100 as the total membership? It is because a percentage is number out of 100. Am I allowed to invent things like that? Sure. I'm just using the definition of a percentage.

The average will make it come out the same.

Answer:

-56

Step-by-step explanation:

Equation = 7x( 3 + x/4)

f(x) = 7x( 3 + x/4)

f(-8) = 7( -8 )( 3+ -8/4 )

f(-8) = -56 ( 3+ ( - 2 ))

f(-8) = -56( 1 )

f(-8) = -56

-Chetan K

Answer:

7x3=21

Step-by-step explanation:

7+7+7=21, 7x3=21

A = 440

answer...

A

=

a

+

b

2

h

=

25

+

19

2

·

20

=

440

Step-by-step explanation:

=2(20)+2(14)

=2⋅20+2(14)

=40+2(14)

=40+2⋅14

=40+28

=40+28

=68

Answer:

Step-by-step explanation:

P = 2L + 2W

P = 2(20) + 2(14)

P = 40 + 28

P = 68//

Answer:

85 km

Step-by-step explanation:

[tex]68^{2} +51^{2} =c^{2}[/tex]

4,624+2,601 = [tex]c^{2}[/tex]

7,225 =[tex]c^{2}[/tex]

Square both side and you get your answer 85km

Answer: The answer is steak's temperature = chicken's temperature since they are both -5.7°C

Step-by-step explanation:

s=9×8/6

s=12.

hope this helps you.

Answer: 12

Step-by-step explanation:

using ratio;

[tex]\frac{6}{9}=\frac{8}{x}[/tex]

[tex]\frac{2}{3}=\frac{8}{x}[/tex]

[tex]x=\frac{(8)(3)}{2}[/tex]

[tex]x=\frac{24}{2}[/tex]

[tex]x=12[/tex]

please give me a brainliest answer

Answer: January, because negative numbers are positive numbers' opposite; so -11.4 < -10.4

Answer:

Step-by-step explanation:

Hi there!

According to the question;

radius (r) = 7

We know,

Circumference (c) = 2πr

                              = 2π * 7

                              = 14π

Therefore the circumference of p is 14π.

Hope it helps!

Answer:

C.

Step-by-step explanation:

Answer:

936.58

Step-by-step explanation:

Answer:

How

Step-by-step explanation:

You want to put picture in

Answer:4,66

Step-by-step explanation: first , we subtracted 1 people . 34,56 - 1,94 = 32,62 . then we divided for seven people . we have : 32,62 : 7 = 4,66 each person