An easy way to determine the slope of a roof is to set one end of a 12-inch level on the roof surface and hold it level. Then take a tape measure or ruler and measure from the other end of the level down to the roof surface. This will give you the slope of the roof.

The slope of the roof shown here is measured with a 12-inch level and a ruler.


What is the slope of the roof in this picture?

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:

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

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:

The zoo has 43 chickens.

Step-by-step explanation:

I did the math. Teehee ur welcome :)

Answer:

267.25

Step-by-step explanation:

4276/16=267.25

First one the one that has the blue inside

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:

B, Up 5 units

Step-by-step explanation:

because of the +

Answer:2 then 8

Step-by-step explanation:wowowowowowow

Answer:

y=-3/4x+0

Step-by-step explanation:

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 .

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:

= 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:

4

Step-by-step explanation:

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:

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:

g = h/f - d/f

Step-by-step explanation:

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.

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:

6

Step-by-step explanation:

Answer:

1,1.5 is the answer

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

Answer:

I believe it is A 20,

however id wait for another answer to confirm lol

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.

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:

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.