mathmath333
  • mathmath333
Question
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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mathmath333
  • mathmath333
\(\large \color{black}{\begin{align}& x\ \normalsize \text{and }\ y \ \ \text{are non negative integers such that } \hspace{.33em}\\~\\ & 4x+6y=20,\ \normalsize \text{and }\ x^2\leq \dfrac{M}{y^{2/3}} \ \normalsize \text{for all values of }\ x,y. \hspace{.33em}\\~\\ & \normalsize \text{what is the minimum value of M ?} \hspace{.33em}\\~\\ &a.)\ 2^{2/3} \hspace{.33em}\\~\\ &b.)\ 2^{1/3} \hspace{.33em}\\~\\ &c.)\ 2^{4/3} \hspace{.33em}\\~\\ &d.)\ 4^{2/3} \hspace{.33em}\\~\\ \end{align}}\)
ganeshie8
  • ganeshie8
(2, 2) and (5, 0) are the only nonnegative integer solutions of 4x+6y=20
ganeshie8
  • ganeshie8
evaluate \(x^2 y^{2/3}\) at above solutions and pick the max value

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More answers

mathmath333
  • mathmath333
i m getting \(2^{8/3}\) which is not in options
ganeshie8
  • ganeshie8
yeah im getting the same
mathmath333
  • mathmath333
while in the book correct answer is \(\large 2^{4/3}\)
ganeshie8
  • ganeshie8
is \(2^22^{2/3}\) really less than the textbook answer ?
mathmath333
  • mathmath333
lol what do u mean
ganeshie8
  • ganeshie8
(2,2) is a nonnegative integer solution to the given equation, yes ?
mathmath333
  • mathmath333
yes
ganeshie8
  • ganeshie8
\[x^2\leq \dfrac{M}{y^{2/3}}\] plugin \(x=2,y=2\) and \(M=\) your textbook answer
mathmath333
  • mathmath333
\(\large \color{black}{\begin{align}& x^2\leq \dfrac{M}{y^{2/3}}\hspace{.33em}\\~\\ &x^2y^{2/3}\leq M\hspace{.33em}\\~\\ &2^2.2^{2/3}\leq M\hspace{.33em}\\~\\ &2^{2+2/3}\leq M\hspace{.33em}\\~\\ &2^{6/3+2/3}\leq M\hspace{.33em}\\~\\ &2^{8/3}\leq M\hspace{.33em}\\~\\ \end{align}}\) ?
ganeshie8
  • ganeshie8
plugin M = textbook answer
ganeshie8
  • ganeshie8
Is \(2^{8/3} \le 2^{4/3}\) really true ?
mathmath333
  • mathmath333
no
ganeshie8
  • ganeshie8
so can we conclude textbook answer is wrong ?
mathmath333
  • mathmath333
yes
ganeshie8
  • ganeshie8
thats it, spending any more time on this is a waste
mathmath333
  • mathmath333
oh

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