Question

We did not find results for: A measure of​ malnutrition, called the​ pelidisi, varies directly as the cube root of a​ person's weight in grams and inversely as the​ person's sitting height in centimeters. A person with a pelidisi below 100 is considered to be​ undernourished, while a pelidisi greater than 100 indicates overfeeding. A person who weighs​ 48,820 g with a sitting height of 78.7 cm has a pelidisi of 100. Find the pelidisi​ (to the nearest whole​ number) of a person whose weight is 54,688 g and whose sitting height is 72.6 cm. Is this individual undernourished or​ overfed?The pelidsi is _____Round to the nearest integer as needed..

Answer 1

$\bf \qquad \qquad \textit{double proportional variation}\\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with \underline{z}} \end{array}\implies y=\cfrac{kx}{z}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------$

$\bf \begin{cases} p=pedalisi\\ w=weight\\ s=\textit{sitting height} \end{cases}\quad \begin{array}{llll} %pelidisi, varies directly as the cube root of a​ person's weight in grams and inversely as the​ person's sitting height in centimeters. \textit{pelidisi varies directly}\\ \textit{as cube root of weight}\\ \textit{and inversely to }\\ \textit{sitting height} \end{array}\implies p=\cfrac{k\sqrt[3]{w}}{s}\\\\ -------------------------------$

$\bf \textit{we know that } \begin{cases} w=48,820\\ s=78.7\\ p=100 \end{cases}\implies 100=\cfrac{k\sqrt[3]{48820}}{78.7} \\\\\\ 100\cdot 78.7=k\sqrt[3]{48820}\implies \cfrac{7870}{\sqrt[3]{48820}}=k \\\\\\ thus\qquad \boxed{p=\cfrac{\frac{7870}{\sqrt[3]{48820}}\sqrt[3]{w}}{s}} \\\\\\ \textit{now, what is \underline{p} when } \begin{cases} w=54,688\\ s=72.6 \end{cases}?\implies p=\cfrac{\frac{7870}{\sqrt[3]{48820}}\sqrt[3]{54688}}{72.6}$

now, if that value is less than 100, then the fellow is "undernourished", otherwise, is overfed.