R is partly constant and partly varies with E when R=530,E=16000 and when R=730,E=3600.
i)find the formula which connects R&E
i)find R when E=1300.
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R = mE + b
case1: R = 530, E = 16000
530 = 16000m + b **
case2: R = 730, E = 3600
730 = 3600m + b ***
subtract *** from **
-200 = 12400m
m = -1/62
back in ***
3600(-1/62) + b = 730
b = 24430/31
R = (-1/62)E + 24430/31
so when E = 1300
R = (-1/62) + 24230/31
= 23780/31 or appr 767
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fined R when E is = 1, 300
To find the formula that connects R and E, we can use the method of "direct variation.”
Direct variation is a relationship between two variables where one variable is a constant multiple of the other. In this case, we can assume that R varies directly with E, meaning R is proportional to E, and we can use the formula:
R = k * E
where k is the constant of variation.
To find the value of k, we can use the given values of R and E:
When R = 530 and E = 16000:
530 = k * 16000
Solving for k: k = 530 / 16000 = 0.033125
Now we have the value of k. The formula that connects R and E is:
R = 0.033125 * E
To find R when E = 1300, we can substitute the value of E into the formula:
R = 0.033125 * 1300
Calculating: R ≈ 43.06375
So, when E = 1300, R is approximately equal to 43.064.