Can someone help me with this circuits question?

Question

A metal wire has a resistance of 10.00 ohms at a temperature of 20 degrees C. If the same wire has a resistance of 10.55 ohms at a temperature of 90 degrees C, what is the resistance of this same wire when its temperature is -20 degrees C?

Answer 1

assumig linear relation.

Resistance (R) directly proportional to temperature (T) given

Let T = RT +C where K abd C are 2 constants

20 =  k10 + C

90 =  k10.55 + C

Solve for k and C

k = 70/.55 = 127.27.. and C = -1252.72

T = 127.27R -1252.72.

At -20 degree

-20 = 127.27R -1252.72

R = 9.685  ohm

Answer 2

∆t = 70C, ∆R = 0.55

Change in R/C = 0.55/70 = 0.00629

new ∆T = 40

new ∆R = 0.00629*40 = 0.25 ohms

New R = 10.00 - .25 = 9.75 ohms

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Answer 3

Since the relationship between temperature and resistance in wire is linear, this is really a simple algebra problem that we'll use the point-slope formula to solve. First, what you have is two coordinates (10, 20) and (10.55, 90). So, the point-slope form of the relation is

y-20 = (70/.55)(x-10), where x is resistance and y is temperature

T-20 = (70/0.55)(R-10) and we are more concerned here with solving for R so: R-10 = (.55/70)(T-20)

R = .55T/70 -1.1/7 + 10 = (.55T + 689)/70

R(-20) = (.55 * (-20) +689)/70 = 9.69 Ohms