Answer:
\(k = 0.0025 \text{ lb/ft}^{2}\)
Step-by-step explanation:
We are given a proportional relationship between two variables:
- \(a\), the area that some amount of grass seed will cover
- \(p\), the amount of grass seed in pounds
In equation form, this relationship is:
\(a=kp\)
where \(k\) is a constant of proportionality.
We are given the following measurements:
- \(a=4000\text{ ft}^2\)
- \(p=10\text{ lb}\)
We can plug these into the equation to solve for k:
\(10\text{ lb} = k\!\left(4000\text{ ft}^{2}\right)\)
↓ dividing both sides by (4000 ft²)
\(k = \dfrac{10}{4000}\, \dfrac{\text{lb}}{\text{ft}^2}\)
\(\boxed{k = 0.0025 \text{ lb/ft}^{2}}\)
So, the constant of proportionality between weight and area is 0.0025 pounds per square foot.
