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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

#1
+8866
+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
+8866
+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) .

hectictar Jun 28, 2018