SOLUTION: the electrical resistance R of a wire varies directly as the length L and inversely as the square of the diameter d obtain an equation. connecting R, L and d if R =27 when 1=3 and

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Question 1134557: the electrical resistance R of a wire varies directly as the length L and inversely as the square of the diameter d obtain an equation. connecting R, L and d if R =27 when 1=3 and d =2, calculate the
(a)value of R. when L=8 and d=3
(b) values of d when .R=16 and L=18
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
The first sentence description using variation constant k should be

R=kL%2Fd%5E2


You can figure out the rest. First need to solve for k.
Note, be careful with your variables. L can be a variable; l should NOT be a variable in typewritten form or through computer and keyboard:

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..., and d if R =27 when 1=3 and d =2, calculate the ,...
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Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +k+ = constant of proportionality
+R+=+k%2AL%2A%281%2Fd%5E2+%29+
+R+=+27+
+L+=+3+
+d+=+2+
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+R%2Ad%5E2+=+k%2AL+
+k+=+%28+R%2Ad%5E2+%29%2FL+
+k+=+%28+27%2A2%5E2+%29%2F3+
+k+=+108%2F3+
+k+=+36+
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(a)
+R+=+36%2A8%2A%28+1%2F3%5E2+%29+
+R+=+36%2A8%2A%28+1%2F9+%29+
+R+=+32+
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(b)
+16+=+36%2A18%2A%28+1%2Fd%5E2+%29+
+d%5E2+=+%28+36%2A18+%29%2F16+
+d%5E2+=+%28+9%2A18+%29%2F4+
+d%5E2+=+%28+9%2A9+%29%2F2+
+d%5E2+=+81%2F2+
+d+=+9%2Fsqrt%282%29+