Question

The viscosity, v, of a newly manufactured synthetic oil is related to its temperature, t, by the formula, v(t)=t³ +7t²+2t−40, where each unit of t is equivalent to 5∘C. Determine the temperature range of which v>0.

Answer 1

To determine the temperature range for which the viscosity of a synthetic oil is greater than zero, solve the given inequality.

Step-by-step explanation:

The given equation represents the relationship between the viscosity (v) of a synthetic oil and its temperature (t). To determine the temperature range for which v > 0, we need to find the values of t that make v greater than zero.

Let's rewrite the equation:

v(t) = t³ + 7t² + 2t - 40

To find the temperature range, we need to solve the inequality v(t) > 0:

t³ + 7t² + 2t - 40 > 0

There are several methods you can use to solve this inequality, such as factoring, graphing, or using the Rational Root Theorem. Once you find the solutions, you can determine the temperature range for which v > 0.