thout using calculator, prove that : \( \tan ^{2} 60^{\circ}-\tan ^{2} 45^{\circ}=4 \sin 30^{\circ} \)

Question 2 \[ \begin{array}{l}5 x+2 y=2 \\ 2 x+y-z=0 \\ 2 x+3 y-z=3\end{array} \] Given the system of equation he value of \( x \) Add your answer

What is the major character in the story? *

Solve. \[ \sqrt{x-7}+\sqrt{x+8}=5 \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution(s) is/are (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There is no solution.

4. Unan cada expresión con el valor de \( a \) que le corresponde para que se verifique la proporción. \( \begin{array}{ll}\text { a. } \frac{7}{4}=\frac{14}{a} & +a=40 \\ \text { b. } \frac{a}{5}=\frac{16}{\sqrt{8}} & +\mathrm{a}=20 \\ \text { c. } \frac{3}{\mathrm{a}}=\frac{21}{7^{2}} & +\mathrm{a}=8 \\ \text { d. } \frac{\sqrt{16}}{3}=\frac{\mathrm{a}}{15} & +\mathrm{a}=9 \\ \text { e. } \frac{0,3}{2,7}=\frac{a}{81} & +\mathrm{a}=7\end{array} \)

Question 4 ( 5 mks\( ) \) i) Suppose that price of a good falls from 20 Shs per unit to 19 Shs per unit in a day. What is the income elasticity of the good in question given the income of the consumer inereased from 400 shs to 700 shs in a day? Suppose the demand function of a good is given as follows; \( \mathrm{Q}=1400-\mathrm{P}^{2} \) when \( \rho=20 \). Derive the price clasticity of demand iii) State the nature of the elasticities in each case above.