Answer:
Either, (9+√69)/6 or (9-√69)/6
Step wise:
3x²-9x+1=0-------------------(i)
comparing equation onw with (ax²+bx+c=0), we get,
a=3, b=-9, c=1
now,
using Quadratic Formula,
(-b±√b²-4ac)/2a=x
{-(-9)±√(-9)²-4.3.1}/2.3=x
(9±√81-12)/6=x
(9±√69)/6=x
Taking +(ve) sign Taking -(ve) sign
(9+√69)/6=0 (9-√69)/6=0
∴(9+√69)/6=0 ∴(9-√69)/6=0
[∵They cannot be further solved]
63 I think, you would subtract
Answer:
The sum is 493.4
Step-by-step explanation:
In order to find the value of the sum, you have to apply the geometric series formula, which is:

where i is the starting point, n is the number of terms, a is the first term and r is the common ratio.
The finite geometric series converges to the expression in the right side of the equation. Therefore, you don't need to calculate all the terms. You can use the expression directly.
In this case:
a=40
b= 1.005
n=12 (because the first term is 40 and the last term is 40(1.005)^11 )
Replacing in the formula:

Solving it:
The sum is 493.4
Id say it's choice b top right.
Answer:
The diameter of the hole is 20.04 ± 0.01 cm
The diameter of the piston is 19.92 ± 0.04 cm.
We are given that The clearance is one-half the difference between the diameters.
So, Clearance = 
= 
Uncertainty in the estimate = 
=
So, Clearance with uncertainty is 
Hence the clearance is 0.06 and the uncertainty in the estimate. is 0.025