Chapter 6.3, Problem 51HP

To determine

Who among Molly and Cleveland is correct.

Answer to Problem 51HP

Molly is correct.

Explanation of Solution

Given:

  $\text{Molly and Cleveland are graphing y}\le \sqrt{5x+15}.$

  

Calculation:

  $\begin{array}{l}Given\\ y\le \sqrt{5x+15}\\ To\text{ graph the given inequality , first we graph the boundary }y=\sqrt{5x+15}\\ \text{Since the index is 2 , which is even , the radicand should be non-negative}\text{.}\\ \text{⇒}5x+15\ge 0\\ \text{⇒}5x\ge -\mathrm{15.......}[\text{subtract 15 from each side]}\\ \text{⇒}x\ge \frac{-15}{5}\mathrm{.......}[\text{divide each side by 5]}\\ \text{⇒}x\ge -3\\ \text{The domain of the graph is {x|x}\ge \text{-3}}\\ \text{Because in the given inequality, the 'y' value is less than ,}\\ So,\text{ the shaded region should be below the boundary and }\\ \text{within the domain}\text{.}\\ \text{Check for a point in the region below the boundary:}\\ \text{the point (0,0)}\text{.}\\ y\le \sqrt{5x+15}\\ \text{⇒}Left\text{ hand side =0}\\ \text{Right hand side = }\sqrt{0+15}=\sqrt{15}\\ 0\le \sqrt{15}\\ So,\\ \text{the point satisfies the inequality}\text{.}\\ \text{Hence, the shaded region should be below }\\ \text{the boundary}\text{.}\\ Therefore,\\ \text{Molly is correct}\text{.}\end{array}$