Q. 54 - Algebra 2

Question

For exercises $\mathbf{53}-\mathbf{55},$ use the following information.

Suppose the temperature $T^o\left(C\right)$ below Earth’s surface is given by $T\left(d\right)=35d+20$, where $\mathbf{d}$ is the depth $\left(\mathbf{km}\right).$

54. Find the depth if the temperature is ${160}^{o}C.$

Step-by-Step Solution

Answer

The depth is 4 at the temperature $T\left(d\right)$ is ${160}^{o}C$.

Step 1. Given information

A linear equation $T\left(d\right)=35d+20$ and temperature is ${160}^{o}C.$

Step 2. To find the temperature at depth of 2 (km)

Substitute the value of the temperature is ${160}^{o}C$ in the given equation.

Now,

$\begin{array}{l}160=35d+20\\ \Rightarrow 160-20=35d\\ \Rightarrow 140=35d\\ \Rightarrow d=\frac{140}{35}\\ \Rightarrow d=\frac{20}{5}\\ \Rightarrow d=4\end{array}$

Step 3. Conclusion

Therefore, the value of depth is 4 at the temperature $T\left(d\right)$ is ${160}^{o}C$. ${90}^{o}C$

Hence, the depth is 4 at the temperature$T\left(d\right)$ is ${160}^{o}C$.