Question

It is desired to cover a soccer field with grass, whose surface area is (p^{4}-16) square meters, with p a real number greater than 2. If the rolls of grass measure (p-2) meters wide and (p+2) meters long. How many rolls of grass are needed to cover the entire field?

149

likes746 views

Velda

4.5

97 Answers

1. Determine the area of one roll of grass:

\text{Area of one roll} = (p-2) \times (p+2) = p^2 - 4

2. Determine the surface area of the soccer field:

\text{Field area} = p^4 - 16

3. Determine the number of rolls needed:

\text{Number of rolls} = \frac{\text{Field area}}{\text{Area of one roll}} = \frac{p^4 - 16}{p^2 - 4}

4. Simplify the expression:

\frac{p^4 - 16}{p^2 - 4} = \frac{(p^2 - 4)(p^2 + 4)}{p^2 - 4} = p^2 + 4

5. Therefore, the number of rolls needed:

p^2 + 4

2. Determine the surface area of the soccer field:

3. Determine the number of rolls needed:

4. Simplify the expression:

5. Therefore, the number of rolls needed:

Frequently asked questions (FAQs)

What is the number of ways to arrange 7 objects in a row?

+

What is the value of sin(60 degrees) multiplied by tan(45 degrees)?

+

What is the asymptote of the exponential functions f(x) = 10^x and f(x) = e^x?

+

New questions in Mathematics