This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here's the solution for question 1: Question 1: Solve for T in the equation (1)/(T) = (14)/(5) of 2(1)/(3)(5)/(6) + (2)/(39) × 1(2)/(11) Step 1: Simplify the numerator. First, convert the mixed fractions to improper fractions and perform the multiplication ("of" means multiplication). 1(4)/(5) = (1 × 5 + 4)/(5) = (9)/(5) 2(1)/(3) = (2 × 3 + 1)/(3) = (7)/(3) Numerator: (9)/(5) × (7)/(3) = (3 × 3)/(5) × (7)/(3) = (3 × 7)/(5) = (21)/(5) Step 2: Simplify the denominator. First, perform the multiplication, then the addition. Convert the mixed fraction to an improper fraction: 1(2)/(11) = (1 × 11 + 2)/(11) = (13)/(11) Multiplication term: (2)/(39) × (13)/(11) = (2)/(3 × 13) × (13)/(11) = (2)/(3 × 11) = (2)/(33) Now, add this to (5)/(6): (5)/(6) + (2)/(33) Find the least common multiple (LCM) of 6 and 33, which is 66. (5 × 11)/(6 × 11) + (2 × 2)/(33 × 2) = (55)/(66) + (4)/(66) = (59)/(66) Step 3: Combine the simplified numerator and denominator. Now substitute the simplified numerator and denominator back into the original equation: (1)/(T) = (21)/(5)(59)/(66) To divide by a fraction, multiply by its reciprocal: (1)/(T) = (21)/(5) × (66)/(59) (1)/(T) = (21 × 66)/(5 × 59) (1)/(T) = (1386)/(295) Step 4: Solve for T. To find T, take the reciprocal of both sides of the equation: T = (295)/(1386) The value of T is: (295)/(1386) 3 done, 2 left today. You're making progress.