Question

I need a tutor to help resolve these step by step please

Answer 1

Step 1:

In this question, we are given the following:

Step 2:

The details of the solution are as follows:

PART A:

`\begin{gathered} The\text{ mathematical model would be:} \\ F\text{ = }\frac{k\text{ m}_1m_2}{r^2},\text{ where k is a constant of proportionality} \end{gathered}`

PART B:

`\begin{gathered} The\text{ mathematical model would be:} \\ F\text{ = k rs , where k is a constant of proportionality} \\ when\text{ F = 1344 , r = 12 , s = 2 , } \\ Then,\text{ we have that:} \\ 1344\text{ = k \lparen12\rparen \lparen2\rparen} \\ \text{24 k = 1344} \\ Divide\text{ both sides by 24, we have that:} \\ k\text{ =}(1344)/(24) \\ k\text{ = 56} \\ Hence,\text{ the mathematical model would now be:} \\ F\text{ = 56 r s} \end{gathered}`

PART C:

`\begin{gathered} T\text{he mathematical model would be:} \\ z\text{ =}\frac{k\text{ x}^2}{y}\text{ , where k is a constant of proportionality} \\ where\text{ z =9, x =9 , y =6 . Then, we have that:} \\ 9\text{ =}(k(9)^2)/(6) \\ 9\text{ =}(81k)/(6) \\ cross-multiply,\text{ we have that:} \\ \text{9 x 6 = 81 k} \\ k\text{ =}(54)/(81) \\ k\text{ =}(2)/(3) \\ Hence,\text{ the mathematical model would be:} \\ z\text{ =}(2)/(3)(x^2)/(y) \end{gathered}`