Respuesta :
ANSWER:
a = 1.523
e = 0.09353
STEP-BY-STEP EXPLANATION:
From the statement we can establish the following two equations:
[tex]\begin{gathered} R_p=a\mleft(1-e\mright)\rightarrow a=\frac{R_p}{1-e}\text{ (1)} \\ R_1=a\mleft(1+e\mright)\rightarrow a=\frac{R_a}{1+e}\text{ (2)} \end{gathered}[/tex]We equate both equations and solve for e, like this:
[tex]\begin{gathered} \frac{R_p_{}}{1-e}=\frac{R_a}{1+e} \\ \frac{1.381}{1-e}=\frac{1.666}{1+e} \\ (1.381)\cdot(1+e)=(1.666)\cdot(1-e) \\ 1.381+1.381e=1.666-1.666e \\ 1.666e+1.381e=1.666-1.381 \\ 3.047e=0.285 \\ e=\frac{0.285}{3.047} \\ e=0.09353 \\ \\ \text{now, for a, replacing in (1):} \\ a=\frac{1.381}{1-0.09353} \\ a=1.523 \end{gathered}[/tex]