Problem 27
Question
Solve. If \(L\) varies inversely as the square of \(h,\) and \(L=8\) when \(h=3,\) find \(L\) when \(h=2\)
Step-by-Step Solution
Verified Answer
When \(h = 2\), the value of \(L\) is 18.
1Step 1: Set up the inverse variation equation
Since \(L\) varies inversely as the square of \(h\), we can write the relationship as an equation of the form:
\[L = \frac{k}{h^2}\]
where k is the constant of proportionality.
2Step 2: Find the constant of proportionality (k)
We are given the initial values for \(L\) and \(h\) as \(L = 8\) and \(h = 3\). We can substitute these values into our equation to solve for k:
\[8 = \frac{k}{3^2}\]
\[8 = \frac{k}{9}\]
Now, we need to solve for k:
\[k = 8 \cdot 9\]
\[k = 72\]
3Step 3: Find the value of L when h = 2
Now that we have our constant of proportionality, k = 72, we can find the value of \(L\) when \(h = 2\). Substitute the values for k and h back into our equation:
\[L = \frac{72}{2^2}\]
\[L = \frac{72}{4}\]
Now, divide 72 by 4 to find the value of L:
\[L = 18\]
4Step 4: State the final answer
When \(h = 2\), the value of \(L\) is 18.
Other exercises in this chapter
Problem 27
Sketch the graph of \(f(x) .\) Then, graph \(g(x)\) on the same axes using the transformation techniques. $$\begin{array}{l}f(x)=x^{2} \\\g(x)=-x^{2}\end{array}
View solution Problem 27
Let \(f(x)=3 x-7\) and \(g(x)=x^{2}-4 x-9 .\) Find each of the following and simplify. $$f(6)$$
View solution Problem 27
Rewrite function in the form \(f(x)=a(x-h)^{2}+k\) by completing the square. Then, graph the function. Include the intercepts. \(f(x)=x^{2}-2 x-3\)
View solution Problem 28
Let \(f(x)=-x^{2}+10 x+4\) and \(g(x)=x+1 .\) Find a) \((g \circ f)(x)\) b) \(\quad(f \circ g)(x)\) c) \((f \circ g)(-2)\)
View solution