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