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inna [77]
3 years ago
8

Last year 26 members of a certain club traveled to England, 26 members traveled to France, and 32 members traveled to Italy. Las

t year no members of the club traveled to both England and France, 6 members traveled to both England and Italy, and 11 members traveled to both France and Italy. How many members of the club traveled to at least one of these three countries last year?
A) 52
B) 67
C) 71
D) 73
E) 79
Mathematics
1 answer:
OlgaM077 [116]3 years ago
5 0
A) 52 is the answer
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Please see attachment
Dafna11 [192]

Answer:

a) The value of absolute minimum value = - 0.3536  

b) which is attained at   x = \frac{1}{\sqrt{2} }  

Step-by-step explanation:

<u>Step(i)</u>:-

Given function

                       f(x) = \frac{-x}{2x^{2} +1}     ...(i)

Differentiating equation (i) with respective to 'x'

                     f^{l} = \frac{2x^{2} +1(-1) - (-x) (4x)}{(2x^{2}+1)^{2}  }   ...(ii)

                    f^{l}(x) = \frac{2x^{2}-1}{(2x^{2}+1)^{2}  }

Equating Zero

                   f^{l}(x) = \frac{2x^{2}-1}{(2x^{2}+1)^{2}  } = 0

                 \frac{2x^{2}-1}{(2x^{2}+1)^{2}  } = 0

                2 x^{2}-1 = 0

               2 x^{2} = 1

             x^{2}  = \frac{1}{2}

             x = \frac{-1}{\sqrt{2} }  , x = \frac{1}{\sqrt{2} }

<u><em>Step(ii):</em></u>-

Again Differentiating equation (ii) with respective to 'x'

f^{ll}(x) = \frac{(2x^{2} +1)^{2} (4x) - 2(2x^{2} +1) (4x)(2x^{2}-1) }{(2x^{2}+1)^{4}  }

put

      x = \frac{1}{\sqrt{2} }

f^{ll} (x) > 0

The absolute minimum value at   x = \frac{1}{\sqrt{2} }

<u><em>Step(iii):</em></u>-

The value of absolute minimum value

                         f(x) = \frac{-x}{2x^{2} +1}

                       f(\frac{1}{\sqrt{2} } ) = \frac{-\frac{1}{\sqrt{2} } }{2(\frac{1}{\sqrt{2} } )^{2} +1}

         on calculation we get

The value of absolute minimum value = - 0.3536      

<u><em>Final answer</em></u>:-

a) The value of absolute minimum value = - 0.3536  

b) which is attained at   x = \frac{1}{\sqrt{2} }    

3 0
3 years ago
Multiply. Write the product in simplest form. 6/7 × 6/11 steps and how to. and work
Triss [41]

multiply 6 x 6 to get 36 and 7 x 11 to get 77.

6/7 x 6/11 = 36/77

5 0
3 years ago
Factor x2-3x - 28
AVprozaik [17]

Answer:

x equal to -4 or 7

Step-by-step explanation:

x square - 3 x - 28 equals 0 so for me are you now find factors of 28 that and you add you add or multiply those two factors to get those two factors to give you 28 so now so you know Factor ways to get (open x + 4) Close x (open x - 7) close equal to zero your ex number comes -4 or 7

5 0
3 years ago
I don’t know the answer I just need some points to ask more questions !!! have a good day !!
Vlad [161]

Answer: Ooh, okay. Have fun then I guess.

7 0
3 years ago
francine has a square mosaic that is made from small glass squares. if there are 196 small squares in the mosiac, how many are a
Kruka [31]
There would be 56 becasue you calculate the square root of 196 which is 14 and multiply by 4 
5 0
3 years ago
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