PLEASE PLEASE HELP!!!

Answer:

π/6 [(29)^³/₂ − 1]

81.247

Step-by-step explanation:

Surface area is:

S = ∫∫ √(fₓ² + fᵧ² + 1) dA

The partial derivatives are:

fₓ = -2x

fᵧ = -2y

Substituting:

S = ∫∫ √(4x² + 4y² + 1) dA

To make this easier, we can convert to polar coordinates.

S = ∫∫ √(4r² + 1) dA

S = ∫∫ √(4r² + 1) r dr dθ

S = ⅛ ∫∫ 8r √(4r² + 1) dr dθ

The limits for θ are 0 to 2π.  The minimum of r is 0.  The maximum of r is:

-6 = 1 − x² − y²

-6 = 1 − r²

r² = 7

r = √7

Integrating the first integral:

S = ⅛ ∫ ⅔ (4r² + 1)^³/₂ |₀ᴿ dθ

S = ⅛ ∫ [⅔ (4(7) + 1)^³/₂ − ⅔ (4(0) + 1)^³/₂] dθ

S = ⅛ ∫ [⅔ (29)^³/₂ − ⅔] dθ

S = ¹/₁₂ [(29)^³/₂ − 1] ∫ dθ

Integrating the second integral:

S = ¹/₁₂ [(29)^³/₂ − 1] θ |₀²ᵖⁱ

S = ¹/₁₂ [(29)^³/₂ − 1] (2π − 0)

S = π/6 [(29)^³/₂ − 1]

S ≈ 81.247

The area of a shape is the amount of space it covers.

The surface area is approximately 81.3 unit squares

The given parameters are:

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

[tex]\mathbf{z = -6}[/tex]

Calculate the partial derivatives of [tex]\mathbf{z = 1 - x^2 - y^2}[/tex]

[tex]\mathbf{f_x = -2x}[/tex]

[tex]\mathbf{f_y = -2y}[/tex]

So, the surface area is:

[tex]\mathbf{A = \int\limits^a_b\int\limits^a_b {\sqrt{(f_x^2 + f_y^2 +1 )}} \, dA }[/tex]

So, we have:

[tex]\mathbf{A = \int\limits^a_b\int\limits^a_b {\sqrt{((-2x)^2 + (-2y)^2 +1 )}} \, dA }[/tex]

[tex]\mathbf{A = \int\limits^a_b\int\limits^a_b {\sqrt{(4x^2 + 4y^2 +1 )}} \, dA }[/tex]

Factor out 4

[tex]\mathbf{A = \int\limits^a_b\int\limits^a_b {\sqrt{(4(x^2 + y^2) +1 )}} \, dA }[/tex]

Substitute

[tex]\mathbf{r^2 = x^2 + y^2}\\\mathbf{dA = rdr d\theta}[/tex]

So, we have:

[tex]\mathbf{A = \int\limits^a_b\int\limits^a_b {\sqrt{(4r^2 +1 )}} \, r\ dr\ d\theta }[/tex]

Multiply by 1

[tex]\mathbf{A = \int\limits^a_b\int\limits^a_b {\sqrt{(4r^2 +1 )}} \, r \times 1\ dr\ d\theta }[/tex]

Express 1 as 8/8

[tex]\mathbf{A = \int\limits^a_b\int\limits^a_b {\sqrt{(4r^2 +1 )}} \, r \times \frac{8}{8}\ dr\ d\theta }[/tex]

Rewrite as:

[tex]\mathbf{A =\frac{1}{8} \int\limits^a_b\int\limits^a_b {8r \sqrt{(4r^2 +1 )}}, \ dr\ d\theta }[/tex]

From the question,

[tex]\mathbf{z = -6}[/tex]

So, we have:

[tex]\mathbf{1 - r^2 = -6}[/tex]

Add 6 to both sides

[tex]\mathbf{7 - r^2 = 0}[/tex]

So, we have:

[tex]\mathbf{r^2 = 7}[/tex]

Integrate [tex]\mathbf{A =\frac{1}{8} \int\limits^a_b\int\limits^a_b {8r \sqrt{(4r^2 +1 )}}, \ dr\ d\theta }[/tex]

[tex]\mathbf{A =\frac{1}{8} \int\limits^a_b {\frac{8}{12} (4r^2 +1 )^{\frac 32}}, |\limits^R_0 d\theta }[/tex]

[tex]\mathbf{A =\frac{1}{8} \times \frac{8}{12} \int\limits^a_b { (4r^2 +1 )^{\frac 32}}, |\limits^R_0 d\theta }[/tex]

[tex]\mathbf{A =\frac{1}{12} \int\limits^a_b { (4r^2 +1 )^{\frac 32}}, |\limits^R_0 d\theta }[/tex]

[tex]\mathbf{A =\frac{1}{12} \int\limits^a_b { (4r^2 +1 )^{\frac 32} -(4 \times 0^2 +1 )^{\frac 32} }, d\theta }[/tex]

Substitute [tex]\mathbf{r^2 = 7}[/tex]

[tex]\mathbf{A =\frac{1}{12} \int\limits^a_b { (4\times 7 +1 )^{\frac 32} - 1^{\frac 32}}, d\theta }[/tex]

[tex]\mathbf{A =\frac{1}{12} \int\limits^a_b {29^{\frac 32} - 1}, d\theta }[/tex]

Rewrite as:

[tex]\mathbf{A =\frac{1}{12} (29^{\frac 32} - 1), \int\limits^a_b d\theta }[/tex]

Integrate

[tex]\mathbf{A =\frac{1}{12} (29^{\frac 32} - 1), \times \theta |\limits^{2\pi}_0}[/tex]

So, we have:

[tex]\mathbf{A =\frac{1}{12} (29^{\frac 32} - 1), \times (2\pi - 0) }[/tex]

[tex]\mathbf{A =\frac{1}{12} (29^{\frac 32} - 1), \times 2\pi}[/tex]

Rewrite as:

[tex]\mathbf{A =\frac{2\pi}{12} (29^{\frac 32} - 1)}[/tex]

[tex]\mathbf{A =\frac{\pi}{6} (29^{\frac 32} - 1)}[/tex]

[tex]\mathbf{A =81.3}[/tex]

Hence, the surface area is approximately 81.3 unit squares

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Answer:

Option (4)

Step-by-step explanation:

From the figure attached,

Lines 'c' and 'd' are the parallel lines a transversal line is intersecting these lines.

m∠2 = 124° [Corresponding angles]

m∠7 = 124° [Vertically opposite angles]

m∠2 = m∠3 = 124° [Vertically opposite angles]

Therefore, angles ∠2, ∠7 and ∠3 measure 124°.

Option (4) will be the answer.

Answer:

I'm guessing you convert to decimals?

2-0.666666667x=0.75

Let me know if that is wrong

Stay Safe,

evancorral7

Menjawab:

2k + 5

Penjelasan langkah demi langkah:

Mengingat bahwa:

Pembelian pertama:

Karung beras yang dibeli = 2

Tambahan kg beras yang dibeli = 5kg

Misalkan banyaknya kg dalam satu karung beras = k

Karenanya,

Pembelian pertama + pembelian tambahan

2k + 5

Oleh karena itu, ungkapan aljabar untuk Beras yang dibeli oleh Pak Veri dalam kg:

2k + 5

k diberikan dalam kg

Answer:

Sunday: 50 Monday: 60 Tuesday: 50 Wednesday: 50 Friday: 40 Saturday: 40

Step-by-step explanation:

That's If Its To The Nearest Tenth If This Is What U Wanted I'm Just Doing What The Instructions Told Me

Answer:

The zoo has 43 chickens.

Step-by-step explanation:

I did the math. Teehee ur welcome :)

First one the one that has the blue inside

Answer:

267.25

Step-by-step explanation:

4276/16=267.25

An expression is defined as a set of numbers, variables, and mathematical operations. The value of −b²−2bx²−x when the value of x=-2 is −b²−8b + 4.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The value of the expression −b²−2bx²−x will be,

−b² − 2bx² − x

= − b² − 2b(-2)² − (-2)

= − b² − 8b + 4

Hence, the value of −b²−2bx²−x when the value of x=-2 is −b²−8b + 4.

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Answer:

439.001  439.09  439.1  439.6

Step-by-step explanation:

Step-by-step explanation:

10-2=8 has the difference of 8

The difference of two numbers is obtained using the subtraction operation ; Hence, two numbers whose difference gives a value of 8 are 16 and 8.

There are many possible values where, the value of the two numbers will give a value of 8.

They include;

Therefore, two numbers whose difference gives a value of 8 are 16 and 8.

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Answer:

b=4

Step-by-step explanation:

Since the line has a slope of zero, it's a horizontal line. A horizontal line so have the same y axis bc it passes through the y axis. So in this case the coordinate point is (-2,4) and it has a zero slope so you can assume that b= 4 since it has a zero slope.

Answer: C=4

Got this answer right hit the heart button if this helped or comment and let me know if this helped you : ) have a great day!

Answer:2 then 8

Step-by-step explanation:wowowowowowow

Answer:

I believe it is A 20,

however id wait for another answer to confirm lol

Answer:

B, Up 5 units

Step-by-step explanation:

because of the +

Answer:

7, -3, and -5 are coefficients.

Step-by-step explanation:

Answer:

The leading coefficient is 7

Answer:

46,303

Step-by-step explanation:

12789+9324+9324+1078+12789+999= 46,303

The total number of ice-cream sold was 46,303 as the shop sold 12,789 chocolate and 9,324 cookie dough cones. It sold 1078 more peanut butter cones than cookie dough cones that means 10,402 peanut butter cones and 999 more vanilla than chocolate cones that means 13,788 vanilla cone.

Total refers to an entire or complete amount, and the verb "to total" means to combine two numbers or to destroy something. In mathematics, you add numbers to get the total; the outcome is the total. The result of adding 8 and 8 is 16. A total is the sum of several numbers or the number of items in a group, as determined by addition or counting. Total is referred to as the total or overall sum. The final amount for dinner on a check serves as an illustration of a total.

Here,

number of chocolate cone=12,789

number of cookie dough cone=9,324

peanut butter cone=9,324+1,078=10,402

vanilla cone=12,789+999=13,788

Total sum= number of chocolate cone + number of cookie dough cone+ peanut butter cone+ vanilla cone

=12,789+9,324+10,402+13,788

=46,303 ice-cream cones

The shop sold 12,789 chocolate and 9,324 cookie dough cones, for a total of 46,303 scoops of ice cream. It sold 999 more vanilla than chocolate cones, which translates to 13,788 vanilla cones, and 1078 more peanut butter than cookie dough cones, or 10,402 peanut butter cones.

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Answer:

6

Step-by-step explanation:

Answer:

1,1.5 is the answer

Step-by-step explanation:

Answer:

x = 25

Step-by-step explanation:

Those 2 angles together form a straight line which is equal to 180°. So you can set up an equation:

3x + 18 = 93

-18 -18

3x = 75

Divide both sides by 3

x = 25

Answer:0.00102529049

Step-by-step explanation: Use a calculator >:) EX clap.

Answer:

0.001025290498975

Step-by-step explanation:

Answer:

120-4.50 = 115.10

Step-by-step explanation:

She will have $115.10 left if she buys one mean

The fraction 3/18 is equal to the decimal number [tex]\hat{0.167}[/tex]

An equation is an expression that is used to show the relationship between two or more numbers and variables.

Division is one of the four basic operations of arithmetic. Division is the act of dividing, or separating, a whole into pieces.

Given the expression:

3/18

Dividing gives:

= 0.16666666667

= [tex]\hat{0.167}[/tex]

3/18 is equal to [tex]\hat{0.167}[/tex]

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Answer:

6.2

Step-by-step explanation:

decimals are rational numbers so you could do 6.2

Answer:

1.16

Step-by-step explanation:

you have to divide 14 by 12 since the amount of acres mowed in 12 hours is how much acres she's mowed.

Answer:

all of the above

have a good day keep working

Answer: This is not a function.

Step-by-step explanation: A function CANNOT have a repeating x-value.