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