# Tutor profile: Sandeep J.

## Questions

### Subject: Pre-Calculus

If, log x = 2 and log y = 4, then log(x y^2) = ?

log( x y^2 ) = log x + log (y^2) = log x + 2 log (y) = 2 + 2*4 = 2 + 8 = 10

### Subject: Civil Engineering

If 1 m head of water = 10 kPa and 1 atm = 100 kPa, vapour pressure of water at 20 deg C = 2.5 kPa, at what negative head of water vaporization will start

We know that, Vaporization will start, when vapour pressure > absolute pressure => Absolute pressure = Atmospheric pressure + Pgauge => 2.5 > 100 + (100 *X) [where x = head of water] => 10X <= -97.5 => x <= -9.75 m head of water => -x >= 9.75 m head of water Hence, vaporization will start when negative head of water is greater than 9.75 m Below this, vaporization will not start

### Subject: Algebra

If x3 + y3 = 12 and x + y = 2, then the value of x4+y4 is

We know, x3+y3 = (x2 − xy + y2)×(x + y) Putting given values of (x + y) & x3+y3 12 = ((x+y)2 − 3xy) × 2 = (4 − 3xy) × 2 = 8 − 6xy 6xy = -4 xy = -0.667 x4 + y4 = (x2 + y2)^2 - 2*(xy)^2 = (x2 + y2)^2 - 2*0.444 [Putting value of xy] = ((x + y)^2 - 2xy)^2 - 2*2.25 [Putting values of (x+y) and xy] = (4 - 0.889)^2 - 2*2.25 = 5.18

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