1. Finf the width of a rectangle whose area is 36 sq in. And length is 9in.
2. The attraction F of any two masses m1 and m2 foe each other varies directly as the oroduct of the masses and inversely as the square of the distance d between these teo masses. Express the relation as an equation when the distance between the two masses is 3m and m1 is equal to 3 kg, m2 is equal to 4kg and F is equal to 12 N.
w=36/9
F = k(m1)(m2)/d^2
12 = k(3)(4)/9
Thanks Steve
1. To find the width of a rectangle, we can use the formula for the area of a rectangle: Area = length × width.
Given that the area is 36 sq in and the length is 9 in, we can substitute these values into the formula to solve for the width.
Area = length × width
36 sq in = 9 in × width
To find the width, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by the length.
36 sq in ÷ 9 in = width
4 in = width
Therefore, the width of the rectangle is 4 inches.
2. The relationship between the attraction force (F), masses (m1 and m2), and distance (d) can be expressed as:
F ∝ (m1 × m2) / (d^2)
The proportionality symbol (∝) indicates that the force is directly proportional to the product of the masses and inversely proportional to the square of the distance.
In the given scenario, the distance (d) is 3 m, mass 1 (m1) is 3 kg, mass 2 (m2) is 4 kg, and the attraction force (F) is 12 N. We can substitute these values into the equation and solve for the constant of proportionality.
F = k(m1 × m2) / (d^2)
12 N = k(3 kg × 4 kg) / (3 m)^2
12 N = 12 k / 9 m^2
To solve for k, we can rearrange the equation as follows:
k = (12 N × 9 m^2) / (12 kg)
k = 9 N m^2 / kg
Therefore, the equation expressing the relationship between the force (F), masses (m1 and m2), and distance (d) is:
F = (9 N m^2 / kg) × (m1 × m2) / (d^2)