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
Answer to a math 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?
Velda
4.5110 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 standard deviation of the following set of numbers: 10, 12, 14, 16, 18?
+
Math Question: What is the measure of the third interior angle in a triangle if the other two angles are 45° and 65°?
+
Math question: What is the variance of the numbers 3, 5, 7, 11, and 13?
+
New questions in Mathematics