Alex needs to determine the power dissipated in a resistor. She measures the current through the resistor to be I=10.0±0.6 A, and its resistance to be R=45.0±2.0 Ω. Assuming her calculations are correct, Alex should find that the uncertainty in power dissipated in the resistor due only to the uncertainty in the current is:

Explanation:

Given that,

Current measure is

i=10±0.6 Amps

And also,

R=45.0±2.0 Ω

Power dissipated by

P=i²R

Then

P=(10±0.6)²(45.0±2.0)

P=10²×45

P=450Watts

Now, calculating the uncertainty

∆P=|P| • √(2(∆i/i)²+(∆R/R)²)

∆P=450√ (2×(0.6/10)²+(2/45)²)

∆P=450√(0.0072+0.001975)

∆P=450√0.009175

∆P=43.1

The uncertainty in power is 43.1

Then,

P=450 ± 43.1 Watts

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west