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shepuryov [24]
2 years ago
13

Find the surface area please. teacher checks soon

Mathematics
1 answer:
Nat2105 [25]2 years ago
7 0

Answer:

Surface Area= 144

Step-by-step explanation:

To find the area of the triangle you would multiply the base times the height and divide it by 2. 9x6/2=27. For one triangle the area is 27. Since there are 4 you would multiply it by 4. 27x4= 108. This will give you 108. Now all you need to do is add the square which is 6x6= 36. 108+36=144.

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Find a formula for the sum of n terms. Use the formula to find the limit as n → [infinity]. lim n → [infinity] n 2 + i n 8 n i =
Masteriza [31]

Complete Question

Find a formula for the sum of n terms.   \sum\limits_{i=1}^n  ( 8 + \frac{i}{n} )(\frac{2}{n} )

Use the formula to find the limit as n \to \infty

 

Answer:

   K_n  =  \frac{n + 73 }{n}

  \lim_{n \to \infty} K_n  =  1

Step-by-step explanation:

     So let assume that

                  K_n  =  \sum\limits_{i=1}^n  ( 8 + \frac{i}{n} )(\frac{2}{n} )

=>             K_n  =  \sum\limits_{i=1}^n  ( \frac{16}{n} + \frac{2i}{n^2} )

=>              K_n  = \frac{2}{n}  \sum\limits_{i=1}^n (8) + \frac{2}{n^2}   \sum\limits_{i=1}^n(i)

Generally  

         \sum\limits_{i=1}^n (k) = \frac{1}{2}  n  (n + 1)

So  

      \sum\limits_{i=1}^n (8) = \frac{1}{2}  * 8*  (8 + 1)

      \sum\limits_{i=1}^n (8) = 36

K_n  = \frac{2}{n}  \sum\limits_{i=1}^n (8) + \frac{2}{n^2}   \sum\limits_{i=1}^n(i)  

and  

  \sum\limits_{i=1}^n (i) = \frac{1}{2}  n  (n + 1)

  Therefore

         K_n  = \frac{72}{n} + \frac{2}{n^2}   *  \frac{1}{2}  n (n + 1 )

         K_n  = \frac{72}{n} +    \frac{1}{n}   (n + 1 )

         K_n  = \frac{72}{n} +   1 +  \frac{1}{n}

        K_n  =  \frac{72 +  1 +  n }{n}

        K_n  =  \frac{n + 73 }{n}

Now  \lim_{n \to \infty} K_n  =  \lim_{n \to \infty} [\frac{n + 73 }{n} ]

=>     \lim_{n \to \infty} [\frac{n + 73 }{n} ]  =    \lim_{n \to \infty} [\frac{n}{n}  +  \frac{73 }{n}  ]

=>     \lim_{n \to \infty} [\frac{n + 73 }{n} ]  =    \lim_{n \to \infty} [1 +  \frac{73 }{n}  ]

=>     \lim_{n \to \infty} [\frac{n + 73 }{n} ]  =    \lim_{n \to \infty} [1 ] + \lim_{n \to \infty}  [\frac{73 }{n}  ]

=>    \lim_{n \to \infty} [\frac{n + 73 }{n} ]  =  1  +  0

Therefore

      \lim_{n \to \infty} K_n  =  1

5 0
3 years ago
You are an engineer for a company that produces shipping boxes. The boxes that are made on one machine are all in the shape of a
Sidana [21]

Answer:

Step-by-step explanation:

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If s is measured in inches, then A = 6x^2 inches^2.

b. Define a formula to determine the volume of a cube-shaped box, V, in terms of its side length, s, (in inches). Preview What are the units for the cube's volume?

The formula for the volume of a cube is V = s^3.  In this case, V is measured in inches^3.

c.  Given the formula for determining the volume of a 4 sphere is V = ar atrs, 3 (This is incorrect; the formula in question, for the volume of a sphere of radius r is V = (4/3)(pi)r^3.           (1) We can solve this formula for r^3, and then for r:

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and so the formula for the radius of a sphere whose volume is 87 inches^3

is

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r = ------------ = ------------------

      ∛(4pi)        ∛(4pi)

(2) The volume of the sphere when r = 5.9 in is:

                                                     4(3.14)      205.38 in³

(4/3)(pi)r^3 = (4/3)(pi)(5.9 in)³  =   --------- = --------------------- = 67.46 in³

                                                         3                 3

         

(3) V = (4/3)(pi)r³    

     Please share the possible answer choices.  Basically, you must find the volume twice:  once for a radius of 4 in and once for a radius of 2 in.  Then subtract the smaller from the larger.  The numerical result is the desired answer.

       

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\bold{ANSWER:}
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