Assume that X and Y are independent measurements with uncertainties σx = 0.3 and σy = 0.2. Find the uncertainties in the following quantities:

a. 4X

b. X + 2Y

c. 2X – 3Y

Solution 1E

Step1 of 4:

We have an independent variable X with uncertainty .

Let Y be the independent variable with uncertainty.

Here our goal is:

a).We need to find uncertainty of 4X.

b).We need to find uncertainty of X + 2Y.

c).We need to find uncertainty of 2X - 3Y.

Step2 of 4:

a).

Here we have a constant c = 4

Hence, the uncertainty of 4X is 1.2.

Step3 of 4:

b).

Consider,

=

=

=

=

= 0.50

Hence, the uncertainty of X + 2Y is 0.50.

Step4 of 4:

c).

=

=

=

=

= 0.8485

Hence, the uncertainty of 2X - 3Y is 0.8485.