A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

mathmath333

  • one year ago

Find the number of integer solutions

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

    \(\large \color{black}{\begin{align} y\leq 5-|x-1|,\ \ y\geq 0\hspace{.33em}\\~\\ \end{align}}\)

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

    |dw:1434213766900:dw|

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

    looks like 36 point

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

    Yes! Notice that number of points above a point on \(x\) axis, \( k\) is given by: \[5-|x-1| +1\]

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

    so the number of lattice points is \[\sum\limits_{x=-4}^{6}6-|x-1|\]

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

    \[\begin{align} &=1+2+3+4+5+6+5+4+3+2+1\\ &=36 \end{align}\]

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

    how did u find interval \([-4,6]\)

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

    -4, 6 are the x intercepts of \(f(x) = 5-|x-1|\)

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

    we want \(y\ge 0\), so we're finding x intercepts

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

    y did u take here 6, \(\sum\limits_{x=-4}^{6}\fbox{6} -|x-1|\)

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

    |dw:1434214973352:dw|

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

    whats the value of f(x) at x=2 ?

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

    4

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

    and how many lattice points are there above x=2 ?

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

    5

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

    so can we say the number of lattice points above x=2 is given by \(f(x) + 1\) ?

  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 3

    \(f(x)+1 = ?\)

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

    x+1

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

    how ?

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

    sry 6-|x+1|

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

    Yep, that expression gives the number of grid points above \(x=k\) iterating it from x=-4 to x=10 gives the required answer

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

    what is the value of this \(\large \color{black}{\begin{align} \sum\limits_{x=1}^{n} |x|\hspace{.33em}\\~\\ \end{align}}\)

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

    |x| = x because all the numbers that x takes are positive

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

    \[\large \begin{align} \sum\limits_{x=1}^{n} |x|&=|1|+|2|+|3|+\cdots +|n|\\~\\ &=1+2+3+\cdots +n\\~\\ &=n(n+1)/2 \end{align}\]

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

    ok thnx

  27. 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.