Answer:
16.1 (1 d.p.)
Step-by-step explanation:
The relationship f is inversely proportional to g can be written as:
[tex]f=\dfrac{k}{g}[/tex]
where k is the constant of proportionality.
Given that g = 3 when f = 18, then:
[tex]18 = \dfrac{k}{3}[/tex]
Solve for k:
[tex]\begin{aligned}18\cdot 3& = \dfrac{k}{3}\cdot 3\\\\54&=k\end{aligned}[/tex]
Therefore:
[tex]\boxed{f=\dfrac{54}{g}}[/tex]
The relationship g is directly proportional to h² can be written as:
[tex]g = ph^2[/tex]
where p is the constant of proportionality.
Substitute this into f = 54/g so that we have an equation for f in terms of h:
[tex]f=\dfrac{54}{ph^2}[/tex]
Given that when f = 15, the value of h is 6, then:
[tex]15=\dfrac{54}{p(6^2)}[/tex]
Solve for p:
[tex]\begin{aligned}15&=\dfrac{54}{36p}\\\\540p&=54\\\\p&=\dfrac{54}{540}\\\\p&=0.1\end{aligned}[/tex]
Therefore:
[tex]\boxed{g = 0.1h^2}[/tex]
To find the value of h when g = 26, substitute g = 26 into the equation for g:
[tex]\begin{aligned}g=26 \implies 26&=0.1h^2\\\\\dfrac{26}{0.1}&=h^2\\\\260&=h^2\\\\h&=\sqrt{260}\\\\h&=16.124515496597....\\\\h&=16.1\; \sf (1\;d.p.)\end{aligned}[/tex]
Therefore, the value of h is:
[tex]\Large\boxed{\boxed{h = 16.1\; \sf (1\;d.p.)}}[/tex]
