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GarryVolchara [31]
2 years ago
5

I need to know the surface area of these

Mathematics
1 answer:
anastassius [24]2 years ago
6 0

9514 1404 393

Answer:

  245 cm²

Step-by-step explanation:

The surface area of a cone is given by ...

  SA = πr(r +s) . . . . where r is the radius, and s is the slant height

Filling in the given values, we have ...

  SA = (3.14)(3 cm)(3 cm +23 cm) = (3.14)(3)(26) cm² ≈ 245 cm²

The surface area of the cone is about 245 cm².

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Simplify the expression: 2/3 (6e+9f-21g)
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Step-by-step explanation:

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3 years ago
Please help me ASAP!
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Answer:

y = 6.5

Step-by-step explanation:

     When triangles are similar, we can set up a proportion to compare the sides. I will have the "left" side on the bottom of the fractions, and the side I am solving for on the top.

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7 0
2 years ago
Beth is knitting mittens and gloves. Each pair must be processed on three machines. Each pair of mittens requires 2 minutes on M
anygoal [31]

Answer:

Two mittens and seven gloves  

Step-by-step explanation:

I presume you are asking how many mittens and how many gloves Beth should knit to produce the most profit.

Let x = the number of mittens and

Let y = the number of gloves

1. Summarize the information in a table

\begin{array}{cccc}&\textbf{Mittens}& \textbf{ Gloves} & \textbf{Minutes Available}\\\text{Machine A} & 2 & 4 & 32\\\text{Machine B} & 2 & 2 & 18\\\text{Machine C} & 4 & 1 & 24\\\text{Unit profit} & $8.00 & $10.00 & \\\end{array}

2. List the constraints

(a) Beth can't make a negative number of mittens, so

x ≥ 0.

(b) Neither can she make a negative number of gloves, so

y ≥ 0.

(c) The total number of minutes on Machine A cannot exceed 32, so

2x + 4y ≤ 32.

(d) The total number of minutes on Machine B cannot exceed 18, so

2x + 2y ≤ 18.

(e) The total number of minutes on Machine C cannot exceed 24, so

4x +   y ≤ 24.

3. Write an equation for the profit

P = 8.00x + 10.00y

4. Graph the constraints to identify the feasible region

See the figure below. The feasible region is the dark green area where all three regions overlap.

5. Determine the points of intersection between the constraints  

(i) Constraints (c) and (d)

\begin{array}{rcr}2x + 4y  & = & 32\\2x + 2y & = & 18\\2y & = & 14\\y & = & \mathbf{7}\\2x + 14 & = & 18\\2x & = &4\\x & = & \mathbf{2}\\\end{array}\\

The lines intersect at (2,7).

(ii) Constraints (c) and (e)

\begin{array}{rcl}2x + 4y  & = & 32\\4x + y & = & 24\\4x + 8y & = & 64\\7y & = & 40\\y & = & \mathbf{\dfrac{40}{7}}\\\\4x + \dfrac{40}{7} & = & 24\\\\4x & = &24 - \dfrac{40}{7}\\\\4x & = & \dfrac{128}{7}\\\\x & = & \mathbf{\dfrac{32}{7}}\\\\\end{array}\\

The lines intersect at (27/7,32/7).

(iii) Constraints (d) and (e)

\begin{array}{rcr}2x + 2y  & = & 18\\4x + y & = & 24\\4x + 4y & = & 36\\3y & = & 12\\y & = & \mathbf{4}\\4x +4 & = & 24\\4x & = &20\\x & = & \mathbf{5}\\\end{array}\\

The lines intersect at (5,4).

6. Determine the x- and y-intercepts of the feasible region

(i) x-intercept

\begin{array}{rcr}4x + y & = & 24\\4x + 0  & = & 24\\x & = & \mathbf{6}\\\end{array}

The x-intercept is at (6,0).

(ii) y-intercept

\begin{array}{rcr}2x + 4y & = &32\\2(0) + 4y & = &32\\4y & = & 32\\y & = & \mathbf{8}\\\end{array}

The y-intercept is at (0,8).

The five black dots are the vertices of the polygon that represents the feasible region.

7. Calculate the maximum profit

Calculate the profit at each of the vertices.

(i) At (0,0)

P = 8.00x + 10.00y = 8.00(0) + 10.00(0) = 0 + 0 = $0

(ii) At (2,7)

P =  8.00(2) + 10.00(7) = 16 + 70 = $86

(iii) At (5,4)

P =  8.00(5) + 10.00(4) = 40 + 40 = $80

(iv) At (6,0)

P =  8.00(6) + 10.00(0) = 48 + 0 = $48

The maximum profit occurs at (2,7)

Thus, Beth should knit two mittens and seven gloves.

 

7 0
3 years ago
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