Perform the calculations and determine the absolute and percent relative uncertainty. Express each answer with the correct number of significant figures. To avoid rounding errors, do not round your answers until the very end of your calculations. [8.47(±0.06)]1/3=[8.47(±0.06)]1/3= absolute uncertainty: ±± percent relative uncertainty: ±± %% log[6.56(±0.05)]=log[6.56(±0.05)]= absolute uncertainty: ±± percent relative uncertainty ±± %%

(a). 0.2% (b). 0.4%

Step-by-step explanation:

This is quite straightforward, so let us follow this carefully.

(a) let us consider the expression that was given in the question;

(8.47 + 0.06)1/3 from the binomial expression,

⇒  (x + ∆x)n = xn + nxn-1∆x

So using the stated formula above

(8.47 + 0.06)1/3 = (8.47)1/3+ 1/3(8.47)1-(1/3) (0.06) = 2.038 + 1/3(8.47)(2/3) (0.06)

= 2.038 + 0.005

This gives us the algebric value as x = 2.038

Also, the uncertainity is ∆x = 0.005

Let us calculate the percentage of relative uncertainity;

Relative uncertainity percent is given thus;

⇒ (∆x / x) * 100

= (0.005 / 2.038) * 100 = 0.2%

We have that the relative uncertainity percent is 0.2%

(b). Also we will consider the expression;

log(6.56 + 0.05)

Let us apply the binomial expression to this;

log(6.56 + 0.05) = log(6.56) + ((0.05)2 / 6.56) = 0.817 + 0.003

This makes the algebric value of x = 0.817

and the uncertainity is  ∆x = 0.003

Therefore the Relative uncertainity percent is = (∆x / x) * 100

= (0.003 / 0.817) * 100 = 0.4%

We have the relative uncertainity percent as 0.4%

cheers I hope this helped !!

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions