Sure, let's solve this step by step.
### Question 9: If [tex]\( x \)[/tex] is a positive real number and [tex]\( x^2 - 3 = 3 \)[/tex], then [tex]\( x^4 = \)[/tex] ?
1. Given Equation:
[tex]\[
x^2 - 3 = 3
\][/tex]
2. Solve for [tex]\( x^2 \)[/tex]:
[tex]\[
x^2 - 3 = 3
\][/tex]
[tex]\[
x^2 = 3 + 3
\][/tex]
[tex]\[
x^2 = 6
\][/tex]
3. Calculate [tex]\( x^4 \)[/tex]:
[tex]\[
x^4 = (x^2)^2
\][/tex]
[tex]\[
x^2 = 6
\][/tex]
[tex]\[
(x^2)^2 = 6^2
\][/tex]
[tex]\[
x^4 = 36
\][/tex]
Thus,:
[tex]\(_x^4 = 36_\)[/tex].
### Question 10: Ordinate of all points on [tex]\( y \)[/tex]-axis is:
The ordinate of a point is the y-coordinate of the point. For points on the y-axis, the x-coordinate is zero, but the y-coordinate can be any real number. We are given specific values to consider, and we need to determine if they fit the criteria of being y-coordinates of points that lie on the y-axis:
Given ordinate points:
- [tex]\( 9
\)[/tex]
- [tex]\( 3
\)[/tex]
- [tex]\( 3
\sqrt{3}
\)[/tex]
- [tex]\( \sqrt{3}
\)[/tex]
We observe that for all the listed values, they all represent valid ordinates, as they are real numbers and can each serve as a y-coordinate (ordinate) of a point on the y-axis.
Therefore, the ordinate points can be:
- [tex]\( 9 \)[/tex]
- [tex]\( 3 \)[/tex]
- [tex]\( 3
\sqrt{3}
\)[/tex]
- [tex]\( \sqrt{3}
\)[/tex]
Thus, all the provided coordinate points are valid as ordinates on the y-axis.
### Final Answers:
1. [tex]\( x^4 = 36 \)[/tex]
- (b) is the correct option.
2. Ordinate of all points on [tex]\( y \)[/tex] axis include:
- (a) [tex]\( 9 \)[/tex]
- (b) [tex]\( 3 \)[/tex]
- (c) [tex]\( 3
\sqrt{3}
\)[/tex]
- (d) [tex]\( \sqrt{3}
\)[/tex]
