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S_A_V [24]
2 years ago
13

Please enter the missing number: 200, 188, 152, 80, 8, ?

Mathematics
1 answer:
Luba_88 [7]2 years ago
6 0
<span>It appears the next number would be 8. To find this, first divide all the numbers by four so that they are smaller and easier to work with, this leaves us with 50, 47, 38, 20, and 2. Next we would look at the differences which appear to be 3, 9, 18, then 18 again. Again, time to break the numbers down so they are easier to work with, this time by 3 so our numbers are 1, 3, 6 and 6. Now the pattern becomes more apparent. We would multiply the first value by three to get the second value, the second value would be multiplied by two to get the third one an the third value would be multiplied by one to get it, and the fourth value would be multiplied by zero. Using this method, the next number in the pattern would be 8.</span>
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Answer: The greatest number of plates Lenin can prepare = 4

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Given: Lenin is preparing dinner plates. He has 12 pieces of chicken and 16 rolls.

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The number of pieces of chicken in each plate = \dfrac{12}{4}=3

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Herbert plans to use the earnings from his lemonade stand according to the table above, for the first month of operations. If he
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Table is attached below

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It is proved that f_x, f_y exixts at (0,0) but not differentiable there.

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Given function is,

f(x,y)=\frac{9x^2y}{x^4+y^2}; (x,y)\neq (0,0)

  • To show exixtance of f_x(0,0), f_y(0,0) we take,

f_x(0,0)=\lim_{h\to 0}\frac{f(h+0,k+0)-f(0,0)}{h}=\lim_{h\to 0}\frac{\frac{9h^2k}{h^4+k^2}-0}{h}\\\therefore f_x(0,0)=\lim_{h\to 0}\frac{9hk}{h^4+k^2}=\lim_{h\to 0}\frac{9k}{h^3+\frac{k^2}{h}}=0    exists.

And,

f_y(0,0)=\lim_{k\to 0}\frac{f(h,k)-f(0,0)}{k}=\lim_{k\to 0}\frac{9h^2k}{k(h^4+k^2)}=\lim_{k\to 0}\frac{9h^2}{h^4+k^2}=\frac{9}{h^2}   exists.

  • To show f(x,y) is not differentiable at the origin cheaking continuity at origin be such that,

\lim_{(x,y)\to (0,0)}\frac{9x^2y}{x^4+y^2}=\lim_{x\to 0\\ y=mx^2}\frac{9x^2y}{x^4+y^2}=\frac{9x^2\times m x^2}{x^4+m^2x^4}=\frac{9m}{1+m^2}  where m is a variable.

which depends on various values of m, therefore limit does not exists. So f(x,y) is not continuous at (0,0). Hence it is not differentiable at (0,0).

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2 years ago
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