Question

a)How to use the formula C=5/9(F-32) to find the temperature in degrees Celsius if the temperature is 86 degrees Fahrenheit. What is the temperature in degrees Celsius, b)The high temperature for the day is predicted to be 86°F. Choose the best inequality for the range of temperatures predicted, based on the formula below

Answer 1

$30\text{\degree C}$

Explanation

the formula to convert from a temperature given in ° F into °C is given by:

$\begin{gathered} C=\frac{5}{9}(F-32) \\ \text{where F is the temperature in \degree{}F} \end{gathered}$

so, we need to imput the given temperature ( in ° F) to obtain the temperature in °c

so

Let

$\text{tempetare =86 \degree F}$

now, replace in the formula:

$\begin{gathered} C=\frac{5}{9}(F-32) \\ C=\frac{5}{9}(86-32) \\ C=\frac{5}{9}(54)=\frac{270}{9}=30 \\ C=30\text{ \degree} \end{gathered}$

$30\text{\degree C}$

Step 2

Choose the best inequality for the range of temperatures predicted

so,

as the The high temperature for the day is predicted to be 86°F, in other words, teh temperature is predicted to be 86 °F or less

$\text{temperature}\leq86\text{ \degree{}F}$

so, if we solve for F

$\begin{gathered} C=\frac{5}{9}(F-32) \\ \text{ multiply both sides by 9/5} \\ C\cdot\frac{9}{5}=\frac{9}{5}\cdot\frac{5}{9}(F-32) \\ \frac{9}{5}C=(F-32) \\ \text{add 32 in both sides} \\ \frac{9}{5}C+32=(F-32)+32 \\ \frac{9}{5}C+32=F \end{gathered}$

and F must be smaller or equal than 86, so

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