If there are 12 eggs in a carton, how many are in 5 cartons?

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

Read more about surface areas at:

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Answer:

267.25

Step-by-step explanation:

4276/16=267.25

Answer:

7, -3, and -5 are coefficients.

Step-by-step explanation:

Answer:

The leading coefficient is 7

Answer:

48 lbs

Step-by-step explanation:

say that the cat weighs x pounds. then the dog weighs 8x pounds. together they weigh 54 pounds. So our equation is x+8x=54. solve for x to get the cat's weight, and you get x=6. The cat weighs 6 lbs. all I need to do now is multiply 6 by 8 so this the dog weighs 8 times as much as the cat. 8•6=48. the dog weighs 48 pounds.

Answer: answer is $23

Step-by-step explanation:

first divide 6.90 by 3

and you should get 2.3

Then you multiply 2.3 by 10

and you should get $23

Answer:

D. 2,5, and 6

Step-by-step explanation:

Because if u mutiply 2*5 = 10 and 2*6 is 12 as 5*6 is 30 and 2*9 is 18 .

= 5x - 25 = -10

= 5x = -10 + 25 ( transposing-25 from LHS to RHS changes -25 to +25 )

= 5x = 15

= x = 15 ÷ 5 ( transposing ×5 from LHS to RHS changes ×5 to ÷5 l

= x = 3

Let us check whether or not we have found out the correct value by keeping 3 in the place of x :

= 5 × 3 - 25 = -10

= 15 - 25 = -10

= -10 = -10

LHS = RHS

We have found out the correct value of x .

Therefore x = 3 .

Answer:

I believe it is A 20,

however id wait for another answer to confirm lol

Answer:

6

Step-by-step explanation:

Answer:

1,1.5 is the answer

Step-by-step explanation:

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.

Learn more about Expression:

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#SPJ2

Answer:

Step-by-step explanation:

1. yes

2. no

3. -10 and 5

4. -6

5. 3x+3

6. 3x+4

7. 14xy^2-3y+7

8. -3y-7x

9. 10x -5

Answer:

1) yes they are if y is alone its just 1y so yes their like terms.

2)no 5xy^2 is different bc the exponent

3)5x-5

4)-6

5)3x+3

6)4+4x

7)14xy^2-3y+7

8)3y-7x

9)10x-5

Step-by-step explanation:

Answer:

It is the portion of the cost based on renting a car for d days

Step-by-step explanation:

Given:

Total cost = 15 + 18d

Total cost = fixed cost + variable cost

Fixed cost are cost that do not change.

Fixed cost = base rate = 15

Variable cost changes during production process. The variable cost in the above varies with the number of days (d)

Therefore, 18d is the portion of the cost based on renting a car for d days.

If you rent the car for 1 day

Total cost = 15 + 18d

= 15 + 18(1)

= 15 + 18

= 33

First one the one that has the blue inside

Answer: n=16

Step-by-step explanation:2(n-7) = 18  

n - 7 = 9  

+7    +7

Answer:

2(x-7) ≥ 18

2x - 7 ≥ 18

     +7    +7

2x ≥ 25

2       2

x ≥ 12.5

Check

2((12.5) -7) ≥ 18

2(5.5) ≥ 18

11 ≥ 18

I think this works

Answer:

He will love the Tea

Step-by-step explanation:

12 divided by 2 is 6

We take 6 ( the liter that he likes ) and multiply it by 15. This gives us 90, exactly what Peggy made.

Answer:

It is just right!

Step-by-step explanation:

12 divided by 2 is 6 . We take 6 and multiply it by 15. This gives us 90, which is exactly what Peggy made.

Answer:

The answer is QR,RS, and ST

Step-by-step explanation:

i hope this helps .

Answer:

4

Step-by-step explanation:

x = 3

Hi there !

3x + 2 = 11

3x = 11 - 2

3x = 9

x = 9/3

x = 3

Good luck !

Answer:

B, Up 5 units

Step-by-step explanation:

because of the +

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:

Is that the question? I don't think it is

Answer: This is not a function.

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

Answer:

all of the above

have a good day keep working

Answer:

y=-3/4x+0

Step-by-step explanation:

Answer: 0.9968

Step-by-step explanation:

Let [tex]\overline{X}[/tex] be the sample mean life of television.

Given: [tex]\mu=138,\ \ \ \sigma^2=324\Rightarrow\ \sigma=\sqrt{324}=18,\ \ \ , n=83[/tex]

The probability that the sample mean would be less than 143.4 months will be :

[tex]P(\overline{X}<143.4)=P(\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}<\dfrac{143.4-138}{\dfrac{18}{\sqrt{83}}})\\\\=P(Z<2.733)=0.9969\ \ \ [\text{By p-value table}][/tex]

hence, the required probability = 0.9968

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:

g = h/f - d/f

Step-by-step explanation:

Answer:

Step-by-step explanation: