if r various directly as the square of s.and r=200 when s fine r when s=24
Answer (1)
Answer:1. Set up the direct variation equation:The problem states that "r varies directly as the square of s." This can be written as a mathematical equation:\(r=ks^{2}\)where \(k\) is the constant of proportionality. 2. Find the constant of proportionality (k):We are given that \(r=200\) when \(s=10\). Substitute these values into the equation:\(200=k(10)^{2}\)\(200=k\times 100\)To find \(k\), divide both sides by 100:\(k=\frac{200}{100}\)\(k=2\) 3. Write the specific variation equation:Now that we have the value of \(k\), we can write the specific equation relating \(r\) and \(s\):\(r=2s^{2}\) 4. Find r when s = 24:Substitute \(s=24\) into the specific variation equation:\(r=2(24)^{2}\)\(r=2\times 576\)\(r=1152\) Answer:When \(s=24\), \(r=1152\).
