Pls help i dont understand :( will give Brainliest + 25 Points

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:

https://brainly.com/question/3621496

Answer:

26

Step-by-step explanation:

Answer:

26

Step-by-step explanation:

Step 1:

Start by setting it up with the divisor 3 on the left side and the dividend 78 on the right side like this:

   3 ⟌ 7 8  

Step 2:

The divisor (3) goes into the first digit of the dividend (7), 2 time(s). Therefore, put 2 on top:

       2    

   3 ⟌ 7 8  

Step 3:

Multiply the divisor by the result in the previous step (3 x 2 = 6) and write that answer below the dividend.

       2    

   3 ⟌ 7 8  

       6    

Step 4:

Subtract the result in the previous step from the first digit of the dividend (7 - 6 = 1) and write the answer below.

       2    

   3 ⟌ 7 8  

     - 6    

       1    

Step 5:

Move down the 2nd digit of the dividend (8) like this:

       2    

   3 ⟌ 7 8  

     - 6    

       1 8  

Step 6:

The divisor (3) goes into the bottom number (18), 6 time(s). Therefore, put 6 on top:

       2 6  

   3 ⟌ 7 8  

     - 6    

       1 8  

Step 7:

Multiply the divisor by the result in the previous step (3 x 6 = 18) and write that answer at the bottom:

       2 6  

   3 ⟌ 7 8  

     - 6    

       1 8  

      1 8  

Step 8:

Subtract the result in the previous step from the number written above it. (18 - 18 = 0) and write the answer at the bottom.

       2 6  

   3 ⟌ 7 8  

     - 6    

       1 8  

     - 1 8  

         0  

Answer:

C

Step-by-step explanation:

well when we multiply to get a common denominator we get 25/30 and 12/30 so the only possible answer is 1/3

Answer:

35:2

Step-by-step explanation:

7000 and 400 are each multiples of 100. 7000÷100=70

400÷100=4

70/4 is left

divide each by 2 as it is the only number that can go both in to 70 and 4

Answer/Step-by-step explanation:

We are given the following coordinates of two points on the line of the graph shown in the question as: A(2, 1) and B(4, 2)

Vertical change from point A = [tex] y_2 - y_1 = 2 - 1 = 1 [/tex]

Horizontal change from point A = [tex] x_2 - x_1 = 4 - 2 = 2 [/tex]

Rate of change = [tex] \frac{y_2 - y_1}{x_2 - x_1} = \frac{1}{2} = 0.5 [/tex]

Answer:

yes

no

Step-by-step explanation:

i hope im correct please give me brainliest and some feedback if im correct or not :)

Answer:

The answer is the first one, I put 5 pounds of birdseed and he ate 5 pounds, leaving you with none, or zero.

Step-by-step explanation:

Answer:

a = 60

Step-by-step explanation:

Since it is a quadrilateral, the sum of interior angles is equal to 360°. Now you have to create an equation to solve this question. To create an equation, you have to add all the interior angles to 360°.

The equation would be 2a°+a°+a°+2a° = 360°.

Then you would simplify it to 6a° = 360.

You would divide 6 on both sides to get to a° = 60.

Therefore, the value of a is 60.

Hope this helped! If not, please let me know! <3

Step-by-step explanation:

[tex] \sf{\dfrac{5( \fbox{41} - 32)}{9} = C}[/tex]

[tex] \sf{\dfrac{5( \fbox{9})}{9} = C}[/tex]

[tex] \sf{ \dfrac{45}{9} = C}[/tex]

[tex] \sf{C = 5 }[/tex]

So,

41° F = [5]°C

Answer:

200,000

Step-by-step explanation:

Answer:

a = 2 hours and 9 minutes

Explanation:

(using fractions)

45 minutes + 1 2/5 hours = 3/4 hours + 7/5 hours = 15/20 + 28/20 = 43/20 = 2 3/20 = 2 9 /60 = 2 hours 9 minutes.

(using decimals)

45 minutes + 1 2/5 hours =

0.75 hours + 1.4 hours = 2.15 hours = 2 hours 9 minutes.

since .15 × 60 = 9 .

Also keep in mind that there are 60 minutes in an hour.

Answer:2 3/20

Step-by-step explanation:

1 2/5 + 45(3/4)

=2 3/20

Answer:

(5a + 0.1b^5)(5a + 0.1b^5)

Step-by-step explanation:

25a^2 − 0.01b^10 =

This follows the pattern: x^2 - y^2 = (x + y)(x - y)

= (5a + 0.1b^5)(5a + 0.1b^5)

Answer:

pretty sure its B

Step-by-step explanation:

hope this helps ;)

Answer:

15 (50*0.3)

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

0.3*50 = 15

Answer:

-6/49

Step-by-step explanation:

this is the answer it is very easy

Answer:

51 cubic units

Step-by-step explanation:

[tex]3x+2y+z=12\\\Rightarrow z=12-3x-2y[/tex]

Now we integrate over volume integral over the range [tex]R = \{(x,y) | 0\le x \le {1}, -{2} \le y \le {4} \}[/tex]

[tex]V=\int_0^1\int_{-2}^4 12-3x-2y dydx\\ =\int_{-2}^4 12y-3yx-y^2|_4^{-2} dx\\ =\int_{0}^1 12\times4-3\times4x-16-[12\times-2-3\times-2x-4]dx\\ =\int_{0}^1 60-18xdx\\ =60x-9x^2|_{0}^1\\ =60-9\\ =51\ \text{cubic units}[/tex]

The volume of the solid is 51 cubic units.

Answer:

x=36

Step-by-step explanation:

2/3x-7=17

2/3x-7+7=17+7

2/3x=24

2/3x(3)=24(3)

2x=72

2x/2=72/2

x=36

Answer:

3

Step-by-step explanation:

Answer:

3 sqrt3

Step-by-step explanation:

AP3X

Answer:

5 > 4.7 > 4 > 350% > 1.22 > -0.5 > -13 > -66

Step-by-step explanation:

Answer:

(a) 0.000061

(b) 0.000061

(c) 0.209

Step-by-step explanation:

An array of 14 bits is equally likely to be 0 or 1.

That is, P (0) = P (1) = 0.50.

(a)

Compute the probability that all bits are 1s as follows:

[tex]P(\text{All bits are 1s})=[P(1)]^{14}[/tex] ∵ the bits are independent

                            [tex]=(0.50)^{14}\\=0.00006103515625\\\approx 0.000061[/tex]

Thus, the probability that all bits are 1s is 0.000061.

(b)

Compute the probability that all bits are 0s as follows:

[tex]P(\text{All bits are 0s})=[P(0)]^{14}[/tex] ∵ the bits are independent

                            [tex]=(0.50)^{14}\\=0.00006103515625\\\approx 0.000061[/tex]

Thus, the probability that all bits are 0s is 0.000061.

(c)

Compute the probability that exactly 7 bits are 1s and 7 bits are 0s as follows:

Define X as the number of bits that 1s.

Then the random variable X will follows a binomial distribution with parameters n = 14 and p = 0.50.

The value of P (X = 7) is:

[tex]P(X=7)={14\choose 7}(0.50)^{7}(1-0.50)^{14-7}[/tex]

               [tex]=\frac{14!}{7!\times 7!}\times (0.50)^{14}\\\\=3432\times 0.000061\\\\=0.209352\\\\\approx 0.209[/tex]

Thus, the probability that exactly 7 bits are 1s and 7 bits are 0s is 0.209.

Answer:

If it is simple interest then it is $24805

If it is a compound interest then it is $25113.38

Step-by-step explanation:

Answer:

380 dollars

Step-by-step explanation:

John earns $437 a week after a 15% pay rise.

Let the initially pay of John be x

x + (15% of x) = 437

x + 0.15x = 437

1.15x = 437

x = \frac{437}{1.15}

1.15

437

x = 380

Answer:

-15

Step-by-step explanation:the

Answer:

his balance will be 51.25 rs.

Step-by-step explanation:

200 - 148.75 = 51.25

Answer:

51.25

Step-by-step explanation:

200-148.75

=51.25

Answer:

7/8

Step-by-step explanation:

3/4+1/8

give common denominators

6/8+1/8

add like terms

7/8.

Answer:

3/4 +1/8=

6/8+1/8=7/8

Answer:

So the answer is gonna be: 33,580.  Hope this help!

Step-by-step explanation:

Answer:

-[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

We can find the slope of the line by using the point slope formula: [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex].

If we plug in your numbers, we get:

[tex]\frac{4-2}{4-8}[/tex], or -[tex]\frac{2}{4}[/tex], or -1/2.