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A 10-pound bag of grass seed will cover an area of about 4000 square feet. The relationship between pounds (p) of grass seed and area (a) can be written as a = kp. What is the value of k?



Answer :

Intriguing456

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.

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