The relationship between population growth and climate change highlights: a. Rising emissions due to energy consumption and population trends. b. Declining global temperatures in rural areas. c. Increased use of renewable energy. d. Stabilized dependency ratios among youth.

(b) Show that the relation R on the set \( \mathrm{A}=\{1 \), \( 2,3,4,5\} \) given by \( \mathrm{R}=\{(\mathrm{a}, \mathrm{b}):|\mathrm{a}-\mathrm{b}| \) is even \( \} \) is an equivalence relation.

4. ¿Cuál de estas igualdades es correcta? (A) \( \log _{3} 8=2 \) (B) \( \log _{3} 2=8 \) (C) \( \log _{2} 8=3 \) (D) \( \log _{2} 3=8 \) (D)

5. A psychologist is interested in exploring the effect oftutorial support on student academic performance and assign students into two groups. Students in group on the tutorial support and those in groupltwo do not. In this example, what is the a) Dependent variable b) Independent variable c) Control group d) Experimental group

20. If the expression \( \frac{2 i^{2}-3 i}{1-2 i} \) is written in the form \( a+b i \) where a and \( b \) are real numbers and \( i=\sqrt{-1} \), what is the value of a?

(ix) The equation \( \frac{1}{r r} \frac{\partial}{r}\left(r \frac{\partial u}{r r}\right)=\frac{1}{c^{2}} \frac{\partial^{2} u}{\partial t^{2}} \) is one dimensional wave equation in: (a) Cylindrical coordinate (b) Polar coordinate (c) Spherical coordinate (d) None of these