Respuesta :
Given:
D varies as R and S, and inversely as t.
D=12, R=3, S=20, and t=5
To find:
The value of D when R=15, S=4 and t=8.
Solution:
It is given that D varies as R and S, and inversely as t. So,
[tex]D\propto \dfrac{RS}{t}[/tex]
[tex]D=\dfrac{kRS}{t}[/tex] ...(i)
Where, k is the constant of proportionality.
We have, D=12, R=3, S=20, and t=5. Substituting these values in (i), we get
[tex]12=\dfrac{k(3)(20)}{5}[/tex]
[tex]12=12k[/tex]
[tex]\dfrac{12}{12}=k[/tex]
[tex]1=k[/tex]
Substituting [tex]k=1[/tex] in (i), we get the required equation.
[tex]D=\dfrac{(1)RS}{t}[/tex]
[tex]D=\dfrac{RS}{t}[/tex]
We need to find D when R=15, S=4 and t=8. Substituting R=15, S=4 and t=8 in the above equation, we get
[tex]D=\dfrac{(15)(4)}{8}[/tex]
[tex]D=\dfrac{60}{8}[/tex]
[tex]D=7.5[/tex]
Therefore, the required value of D is 7.5.
