A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

mathmath333

  • one year ago

Question

  • This Question is Closed
  1. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \(\large \color{black}{\begin{align}& x\ \normalsize \text{and }\ y \ \ \text{are non negative integers such that } \hspace{.33em}\\~\\ & 4x+6y=20,\ \normalsize \text{and }\ x^2\leq \dfrac{M}{y^{2/3}} \ \normalsize \text{for all values of }\ x,y. \hspace{.33em}\\~\\ & \normalsize \text{what is the minimum value of M ?} \hspace{.33em}\\~\\ &a.)\ 2^{2/3} \hspace{.33em}\\~\\ &b.)\ 2^{1/3} \hspace{.33em}\\~\\ &c.)\ 2^{4/3} \hspace{.33em}\\~\\ &d.)\ 4^{2/3} \hspace{.33em}\\~\\ \end{align}}\)

  2. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    (2, 2) and (5, 0) are the only nonnegative integer solutions of 4x+6y=20

  3. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    evaluate \(x^2 y^{2/3}\) at above solutions and pick the max value

  4. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i m getting \(2^{8/3}\) which is not in options

  5. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yeah im getting the same

  6. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    while in the book correct answer is \(\large 2^{4/3}\)

  7. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    is \(2^22^{2/3}\) really less than the textbook answer ?

  8. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    lol what do u mean

  9. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    (2,2) is a nonnegative integer solution to the given equation, yes ?

  10. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes

  11. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[x^2\leq \dfrac{M}{y^{2/3}}\] plugin \(x=2,y=2\) and \(M=\) your textbook answer

  12. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \(\large \color{black}{\begin{align}& x^2\leq \dfrac{M}{y^{2/3}}\hspace{.33em}\\~\\ &x^2y^{2/3}\leq M\hspace{.33em}\\~\\ &2^2.2^{2/3}\leq M\hspace{.33em}\\~\\ &2^{2+2/3}\leq M\hspace{.33em}\\~\\ &2^{6/3+2/3}\leq M\hspace{.33em}\\~\\ &2^{8/3}\leq M\hspace{.33em}\\~\\ \end{align}}\) ?

  13. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    plugin M = textbook answer

  14. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Is \(2^{8/3} \le 2^{4/3}\) really true ?

  15. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no

  16. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so can we conclude textbook answer is wrong ?

  17. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes

  18. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    thats it, spending any more time on this is a waste

  19. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    oh

  20. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.