Sure, let's solve each part of the question step-by-step.
a) Determine the number of trees planted by each student of class [tex]$9^{\text{th}}$[/tex]
Given:
- Total number of trees = 100
- Number of students in class 9th = 10
To determine the number of trees planted by each student, we simply divide the total number of trees by the number of students.
[tex]\[
\text{Trees per student} = \frac{\text{Total number of trees}}{\text{Number of students}} = \frac{100}{10} = 10
\][/tex]
So, each student planted 10 trees.
b) Find the value of [tex]\(p(2) + p(-2) - p(0)\)[/tex] if [tex]\(p(x)\)[/tex] represents plants planted by class 9th students
Given polynomial:
[tex]\[ p(x) = 2x^2 + 3x + 1 \][/tex]
We need to find:
[tex]\[ p(2), p(-2), \text{ and } p(0) \][/tex]
1. Calculate [tex]\( p(2) \)[/tex]:
[tex]\[ p(2) = 2(2)^2 + 3(2) + 1 = 2(4) + 6 + 1 = 8 + 6 + 1 = 15 \][/tex]
2. Calculate [tex]\( p(-2) \)[/tex]:
[tex]\[ p(-2) = 2(-2)^2 + 3(-2) + 1 = 2(4) + (-6) + 1 = 8 - 6 + 1 = 3 \][/tex]
3. Calculate [tex]\( p(0) \)[/tex]:
[tex]\[ p(0) = 2(0)^2 + 3(0) + 1 = 0 + 0 + 1 = 1 \][/tex]
Now, find [tex]\( p(2) + p(-2) - p(0) \)[/tex]:
[tex]\[ p(2) + p(-2) - p(0) = 15 + 3 - 1 = 17 \][/tex]
So, the value is 17.
c) Tell whether the expression [tex]\( \frac{1}{2x} \)[/tex] is a polynomial. If yes, then justify your answer.
A polynomial is an expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
The expression [tex]\( \frac{1}{2x} \)[/tex] involves division by the variable [tex]\( x \)[/tex], which is not permitted in a polynomial. Therefore, [tex]\( \frac{1}{2x} \)[/tex] is not a polynomial.
So, the final answers are:
a) Each student planted 10 trees.
b) [tex]\( p(2) + p(-2) - p(0) = 17 \)[/tex]
c) [tex]\( \frac{1}{2x} \)[/tex] is not a polynomial.
