Q1) the equation is r = √(km/F) the subject of the equation needs to be 'F' as itneeds to be calculated, since the original equation has 'F' in its square root form Both sides should be squared, r² = km/F The subject of the equation should be brought to the left side we can do cross multiplication F = km/r² correct answer is A
Q2) Carla is a client at the firm. the firm charges $46 from Carla. For each share, an amount of $0.15 is traded. There's a fixed cost of 46 and 0.15 per share. Lets call the number of shares as x Therefore Carla's cost is Cost = 46 + 0.15x the bill given to Carla is 109.30 Therefore 109.30 = 46 + 0.15x 0.15x = 109.30 - 46 0.15x = 63.3 x = 63.3/0.15 x = 422 number of shares is 422
Q3) The overhead costs for a day is $3300. For each item it produces, there's a cost of $42 for each item produced. Therefore 3300 is a fixed cost and 42 is a variable cost that increases with the number of items produced. The number of items produced per day is x. then the cost for producing x number of items is 42x The total expenses (E) for the day is E= 3300 + 42x Answer is C
Q4) Density = mass / volume the mass of sun is given as 2.0 x 10³⁰ kg to find the volume of sun, shape of a sphere the following equation is used. V = 4/3 πr³ the radius of sun is 7 x 10⁸ m Therefore, V = 4/3 x 3.14 x (7.0 x 10⁸)³ = (4 x 3.14 x 343 x 10²⁴)/3 = 1.436 x 10²⁷ m³ Then density = 2.0 x 10³⁰ kg / 1.436 x 10²⁷ m³ = 1393 kgm⁻³
