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If y<0, find the range of all possible values of y such that \(\lceil{y}\rceil\cdot\lfloor{y}\rfloor=110\). Express your answer using interval notation.

 

 

I got (10,11), but it’s wrong.

 Jun 28, 2018
edited by DanielCai  Jun 28, 2018
edited by DanielCai  Jun 28, 2018

Best Answer 

 #1
avatar+7352 
+2

Any value of  y  in the interval  (10, 11)  will make the equation true, for example....

 

\(\lceil{10.1}\rceil\cdot\lfloor{10.1}\rfloor\,=\,11\cdot10\,=\,110 \)

 

But also, any value of  y  in the interval  (-11, -10)  will make the equation true, for example...

 

\( \lceil{-10.9}\rceil\cdot\lfloor{-10.9}\rfloor\,=\,-10\cdot-11\,=\,110\)

 

Since the problem says  y < 0 ,  the only values of  y  that work are those in the interval  (-11, -10) .

 Jun 28, 2018
 #1
avatar+7352 
+2
Best Answer

Any value of  y  in the interval  (10, 11)  will make the equation true, for example....

 

\(\lceil{10.1}\rceil\cdot\lfloor{10.1}\rfloor\,=\,11\cdot10\,=\,110 \)

 

But also, any value of  y  in the interval  (-11, -10)  will make the equation true, for example...

 

\( \lceil{-10.9}\rceil\cdot\lfloor{-10.9}\rfloor\,=\,-10\cdot-11\,=\,110\)

 

Since the problem says  y < 0 ,  the only values of  y  that work are those in the interval  (-11, -10) .

hectictar Jun 28, 2018

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