1. ## Polynomial inequality

Hi,

I hope someone can help. I'm trying to solve 11b and 11c:

For 11b - I don't understand why the solution is only 0 < 154.75 Celsius. I see other parts of this graph where v > 0, namely on the left-hand side of the y-axis, so I'm curious why this is not included in the solution. For example, I see v > 0, when x < -6.676 and in between -2.42 < x < 3.095 - this is without the 50 Celsius conversion. Can someone please provide clarification on this?

For 11c - I just don't know where to start in order to find this solution, so guidance would be appreciated. The solution is 133.78 degrees celsius to 139.56 degrees celsius.

Sincerely,
Olivia

2. ## Re: Polynomial inequality

For 11b - I don't understand why the solution is only 0 < 154.75 Celsius. I see other parts of this graph where v > 0, namely on the left-hand side of the y-axis, so I'm curious why this is not included in the solution. For example, I see v > 0, when x < -6.676 and in between -2.42 < x < 3.095 - this is without the 50 Celsius conversion. Can someone please provide clarification on this?
the function is a mathematical model for viscosity for realistic temperatures (not all real values of $t$) ... the negative value where $v$ changes from positive to negative is $\approx -334^\circ \, C$ ... fyi, absolute zero is $\approx -273^\circ \, C$.

For 11c - I just don't know where to start in order to find this solution, so guidance would be appreciated. The solution is 133.78 degrees celsius to 139.56 degrees celsius.
graph y=15 and y=20 on the calculator and determine the intersections (see screenshots) ... multiply both x-values by 50

3. ## Re: Polynomial inequality

Hey otownsend.

Hint - Can you find the roots of the function along the derivatives at each root?

4. ## Re: Polynomial inequality

Why isn't anything before 0 not a "realistic temperature"?

5. ## Re: Polynomial inequality

Originally Posted by otownsend
Why isn't anything before 0 not a "realistic temperature"?
I believe he meant anything below $-273^\circ C$ is unrealistic as absolute zero is as cold as is theoretically possible. (even in Canada!)

6. ## Re: Polynomial inequality

Originally Posted by otownsend
Why isn't anything before 0 not a "realistic temperature"?
I didn't say that ... you did. I said the value of $t = -6.676$ was not realistic.

coldest-temperature-recorded-earth-antarctica-guinness-book

What value of $t$ would this correspond to in your given model?

7. ## Re: Polynomial inequality

okay I understand now why -6.676 would not be realistic as this above be below the temperature of absolute zero. So then why doesn't the ranges between -2.42 < x < 3.095 work?

8. ## Re: Polynomial inequality

$-2.42 < t < 3.095$ corresponds to the temperatures between $-121.99^\circ \, C$ and $154.77^\circ \, C$

the question asks for the temperature range where viscosity is positive ... your stated solution gives the upper bound as $154.77^\circ \, C$ (close).

I do not know why the answer cuts it off at zero for the lower bound. Clearly, $-121.99^\circ \, C$ is colder than the lowest temperature ever recorded on Earth.

You'll just have to ask your instructor why the lower bound was zero. Maybe the graph represents a climate where it doesn't get below freezing.

9. ## Re: Polynomial inequality

Okay sounds good. Thanks for your help