+0  
 
0
48
1
avatar+117 

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.

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

Best Answer 

 #1
avatar+7153 
+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
 #1
avatar+7153 
+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

12 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.