Can someone please help me on this problem I’m struggling

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:

17 units

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

Answer:

Alonso can use 2.1 gigabytes while staying within his budget.

Step-by-step explanation:

53.50 + 3x = 59.80

3x = 59.80 - 53.50

3x = 6.3

x = 6.3 ÷ 3

x = 2.1

Alonso can use 2.1 gigabytes while staying within his budget.

Answer:

x x x and 1 1 1

Step-by-step explanation:

3rd option is the correct answer.

Answer:

Napakadali lang sagutin nyan pre basic mangiba naman dapat Ang sagot ay SAS hopefully all

Vertex form: y = |x - h| + k

Vertex = (h, k)

G(x) was shifted 3 to the right and up 2.

G(x) = |x - 3| + 2

Hope this helps!! :)

The rectangular equation for the curve is [tex]y = \frac{x^{2}}{2} -1[/tex].

In this question, we have a set of parametric equation which must be reduced into a single rectangular equation both by algebraic and trigonometric means, that is to say:

[tex]x = f(\theta), y = g(\theta) \to y = h(x)[/tex]

If we know that [tex]x = 2\cdot \cos \theta[/tex] and [tex]y = \cos 2\theta[/tex], then the rectangular equation is:

[tex]y = \cos 2\theta[/tex]

[tex]y = \cos^{2}\theta - \sin^{2}\theta[/tex]

[tex]y = 2\cdot \cos^{2}\theta -1[/tex]

[tex]\cos \theta = \frac{x}{2}[/tex]

[tex]y = 2\cdot \left(\frac{x}{2} \right)^{2}-1[/tex]

[tex]y = \frac{x^{2}}{2} -1[/tex]

The rectangular equation for the curve is [tex]y = \frac{x^{2}}{2} -1[/tex].

We kindly invite to check this question on parametric equations: https://brainly.com/question/23070611

[tex]p = 2(l + w) = 2.(15 + 12) = 54 cm[/tex]

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

The number of trees that died is an illustration of proportions.

The lowest value of X that is consistent with the belief that the tree died due to mishandling is 1.5

From the question, we have: 1 out of 10 died

This means that, the mean number of trees that died are:

[tex]\mathbf{\bar x =\frac{1}{10}}[/tex]

In 15 trees, the number (n) of trees expected to die is:

[tex]\mathbf{n = \bar x \times 15}[/tex]

So, we have:

[tex]\mathbf{n = \frac{1}{10} \times 15}[/tex]

[tex]\mathbf{n = 1.5}[/tex]

Hence, the lowest value of X is 1.5

Read more about mean and proportions at:

https://brainly.com/question/1139885

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:

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:

D

Step-by-step explanation:

the graphic does not indicate any limitation in any form in any direction.

compared to a default y = x function this function is just shifted a bit. but that does not block x or y from "running" all the way from -infinity to +infinity.

The expected value of this policy to the insurance company is $285.00.

Using this formula

Policy expected value=Insurance policy charges-[(Probability × Claim)+(Probability × Claim)]

Let plug in the formula

Policy expected value=$1,300-{(.0041)($150,000)+(.08)($5,000)]

Policy expected value=$1,300-($615+$$400)

Policy expected value=$1,300-$1,015

Policy expected value=$285.00

Inconclusion the expected value of this policy to the insurance company is $285.00

Learn more here:

https://brainly.com/question/19819099

Answer:

h= 17.67 cm

Step-by-step explanation:

We have,

h=x

b=16 cm

p=7.5cm

Using Pythagoras Theorem,

h^2=p^2+b^2

h=√(7.5^2+16^2)

h=√(56.25+256)

h=√312.25

h=17.6705970471 cm

Hyperbola: y = 1/x

--------------------------------

Shape: open curve with two branches

Domain: Any non-zero real number x < 0, x > 0 or x∈ (-∞, 0) ∪ (0, +∞)

Range: Any non-zero real number y < 0, y > 0 or y∈ (-∞, 0) ∪ (0, +∞)

Locater point: Imaginary point of intersection of asymptotes (0, 0)

Asymptotes: x = 0 and y = 0

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??

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:

Disabilities or Special Needs, Race or Ethnicity

Step-by-step explanation:

these are categories, while the rest are numbers

According to the given data, the categorical (or qualitative) variables are Disabilities or Special Needs, Race or Ethnicity.

A qualitative variable is a categorical variable which is not numerical, it is based on quality that describes the characteristic of an individual.

"In clinical diagnostic and functional development, special needs refers to individuals who require assistance for disabilities that may be medical, mental, or psychological."

"The belief that some races of people are better than others; unfair ways of treating people of different races"

"An ethnic group or an ethnicity is a grouping of people who identify with each other on the basis of shared attributes that distinguish them from other groups."

As we know each discussed variable Disability or Special Needs, Race, and Ethnicity describes the characteristics of an individual. Hence, Disabilities or Special Needs, Race or Ethnicity are the qualitative variables.

To learn more about qualitative variables here

https://brainly.com/question/18296158

#SPJ3

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: lotion- semisolid

capsule- solid

suspension- liquid

Step-by-step explanation:

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

polygon

quadrilateral

triangle

rectangle

hexagon

hexagon

octagon

square or parallelogram

trapezoid

square

heptagon

decagon

gon, gon, the gons mason, what do the gons mean.

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.

Answer:

23/90

Step-by-step explanation:Sorry if it's wrong!!!

Answer:

UWUWUWUUWUWUWUWUUWUWUW

Step-by-step explanation:

UwU OwO

Step-by-step explanation:

260000*0*54*30

$421200