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mathmath333
 one year ago
Find the number of integer solutions
mathmath333
 one year ago
Find the number of integer solutions

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mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1\(\large \color{black}{\begin{align} y\leq 5x1,\ \ y\geq 0\hspace{.33em}\\~\\ \end{align}}\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3dw:1434213766900:dw

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1looks like 36 point

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3Yes! Notice that number of points above a point on \(x\) axis, \( k\) is given by: \[5x1 +1\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3so the number of lattice points is \[\sum\limits_{x=4}^{6}6x1\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3\[\begin{align} &=1+2+3+4+5+6+5+4+3+2+1\\ &=36 \end{align}\]

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1how did u find interval \([4,6]\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.34, 6 are the x intercepts of \(f(x) = 5x1\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3we want \(y\ge 0\), so we're finding x intercepts

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1y did u take here 6, \(\sum\limits_{x=4}^{6}\fbox{6} x1\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3dw:1434214973352:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3whats the value of f(x) at x=2 ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3and how many lattice points are there above x=2 ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3so can we say the number of lattice points above x=2 is given by \(f(x) + 1\) ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3Yep, that expression gives the number of grid points above \(x=k\) iterating it from x=4 to x=10 gives the required answer

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1what is the value of this \(\large \color{black}{\begin{align} \sum\limits_{x=1}^{n} x\hspace{.33em}\\~\\ \end{align}}\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3x = x because all the numbers that x takes are positive

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3\[\large \begin{align} \sum\limits_{x=1}^{n} x&=1+2+3+\cdots +n\\~\\ &=1+2+3+\cdots +n\\~\\ &=n(n+1)/2 \end{align}\]
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