# Tutor profile: Connor S.

## Questions

### Subject: Basic Math

Solve the following problem: (5/3) + (7/2)

(step 1: find a common denominator) denominator 1 * denominator 2 ; 3*2 = 6 (step 2: multiply numerator and denominator to achieve the common denominator) (10/6) + (21/6) (step 3: add) (31/6) (step 4: simplify if possible) answer = 5 1/6.

### Subject: Chemical Engineering

A pipe (stream 1) flows into a reactor carrying 50 kg/hr A, 25 kg/hr B, and 25 kg/hr of an Inert (I). The reaction takes place as 2A + B --> C. Complete the mass balance to find the mass of product C in the effluent (stream 2) of the reactor when the conversion of A is 80%.

(Step 1: mass balance) Mass A (in) + Mass B (in) + Mass I (in) = Mass A (out) + Mass B (out) + Mass C (out) + Mass I (out) (step 2: calculate mass A out from given conversion) 50kg * 80% = 40 kg converted; 50 kg A - 40 kg A converted = 10 kg A in effluent. (Step 3: calculate mass B out from reaction ratios) 40kg converted, 2:1 ratio A:B therefore 20 kg B converted; 25 Kg B - 20 kg B converted = 5 kg B in effluent. (step 4: plug in mass balance) = 50 kg + 25 kg + 25 kg= 10 kg + 5 kg +25 kg + Mass C (out) (step 5: solve for Mass C) Mass C = 60 kg. (step 7: double check answer) 50 kg + 25 kg + 25 kg= 10 kg + 5 kg +25 kg + 60 kg ; 100 kg = 100 kg ; Balance is good.

### Subject: Algebra

Solve the following equation by (a) completing the square and (b) the quadratic equation: x^2 +4x-21=0

(a) (step 1: write equation) x^2+4x-21=0 (step 2: isolate variables) x^2+4x = 21 (step 3: complete the square) x^2+4x+(4/2)^2= 21 + (4/2)^2 (step 4: simplify) x^2+4x+4=25 (step 5: factor variables) (x+2)^2=25 (step 6: solve for x) x = +/-sqrt(25)-2 (step 7: simplify) x = +/- 5 - 2 (step 8: solution) x = 3, -7 (b) (step 1: write equation) x = (-b +/- sqrt(b^2 - 4ac))/2a where a = 1, b=4, c= -21 (step 2: substitute) x = (-4 +/- sqrt(4^2 - 4*(1)*(-21)))/(2*1) (step 3: simplify) x = (-4 +/- sqrt(16+84))/2 (step 4: simplify further) x= (-4 +/- sqrt(100))/2 (step 5: simplify further) x =(-4 +/- 10)/2 (step 6: solve for solution) x = 3, -7

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