SOLUTION: Given that the energy(e) varies directly as the resistance(r) and inversely as the square of the distance(d) if e=32/25, r=8 and d=5 a) calculate the constant k b) calculate r w

Algebra ->  Systems-of-equations -> SOLUTION: Given that the energy(e) varies directly as the resistance(r) and inversely as the square of the distance(d) if e=32/25, r=8 and d=5 a) calculate the constant k b) calculate r w      Log On


   

Question 1116932: Given that the energy(e) varies directly as the resistance(r) and inversely as the square of the distance(d) if e=32/25, r=8 and d=5
a) calculate the constant k
b) calculate r when e=16 and d=3
c) calculate d when r=5 and e=5/6
Found 3 solutions by solver91311, KMST, MathTherapy:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




So



The rest is just arithmetic

John

My calculator said it, I believe it, that settles it

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If e varies directly as r and inversely as d%5E2 (the square of d),
the relation is
e=k%2Ar%2A%281%2Fd%5E2%29 or e=kd%2Fr%5E2 , where k is a constant.
You know that when r=8 and d=5 , e=32%2F25 .
Substituting those values into
e=kd%2Fr%5E2 ,
you get
32%2F25=k%2A8%2F5%5E2 ,
which you can solve for k .
32%2F25=k%2A8%2F5%5E2
32%2F25=k%2A8%2F25
32=k%2A8
32%2F8=k
highlight%28k=4%29

Now you know that the relation between e , r and d%5E2 ,
or between e , r and d is
e=4d%2Fr%5E2 .

To calculate r when e=16 and d=3 ,
you substitute the known values into e=4d%2Fr%5E2 ,
and solve for r .
16=4%2A3%2Fr%5E2
r%5E2=4%2A3%2F16
r%5E2=3%2F4 , and as you know r is not a negative number,
r=sqrt%283%2F4%29
highlight%28r=sqrt%283%29%2F2%29 .

When r=5 and e=5%2F6 , substituting into e=4d%2Fr%5E2 gives you
5%2F6=4d%2F5%5E2
5%2F6=4d%2F25
25%2A5%2F%286%2A4%29=d
highlight%28d=125%2F24=5%265%2F24=approximately+5.21%29

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

Given that the energy(e) varies directly as the resistance(r) and inversely as the square of the distance(d) if e=32/25, r=8 and d=5
a) calculate the constant k
b) calculate r when e=16 and d=3
c) calculate d when r=5 and e=5/6
Correct answers: