Area of quadrilaterals and triangles: word problems

Solve the following:\newline(6×5=30)(6\times5=30)\newlinei) Find the domain and range of the function \newlinef(x)=1x2f(x)=\sqrt{1-x^{2}} Page 4747\newline(ii) Prove that If \newlineff is differentiable at a point \newlineaa in Domf\text{Dom} f, then \newlineff is continuous at \newlineaa\newline(ii) Show that polar coordinates \newlineP(3,0)P(3,0) and \newlineQ(3,π)Q(-3,\pi) represent the same point.\newlineiv) Evaluate \newlinedxx2+3x+4\int\frac{dx}{x^{2}+3x+4}\newlinev) Find point of Inflection of the curve \newlinef(x)=1x2f(x)=\sqrt{1-x^{2}}00 unit 4747 e, \newlinef(x)=1x2f(x)=\sqrt{1-x^{2}}11\newline-vi) Find area of the region bounded by \newlinef(x)=1x2f(x)=\sqrt{1-x^{2}}22, x-axis, f(x)=1x2f(x)=\sqrt{1-x^{2}}33, f(x)=1x2f(x)=\sqrt{1-x^{2}}44\newlineQ.22. Solve the following:\newlinef(x)=1x2f(x)=\sqrt{1-x^{2}}55\newlineH Examine the continuity of \newlinef(x)=1x2f(x)=\sqrt{1-x^{2}}66 at \newlinef(x)=1x2f(x)=\sqrt{1-x^{2}}77 where \newlinef(x)=1x2f(x)=\sqrt{1-x^{2}}88\newlineii) Evaluate \newlinef(x)=1x2f(x)=\sqrt{1-x^{2}}99\newline(iii) Find the area enclosed by the graph of the circle of radius \newlineff00.\newlineiv) Find reduction formula for \newlineff11 and hence find \newlineff22\newlinev) By using substitution \newlineff33 show that \newlineff44
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QUESTION 33\newlineTABLE 11: THE 20202020/20212021 AND 20212021/20222022 MOGALE CITY WATER TARIFF\newline Mogale City  Locae Municipacity  \frac{\text { Mogale City }}{\text { Locae Municipacity }} \newline\begin{tabular}{|c|c|c|}\newline\hline \begin{tabular}{l} \newlineResidential Water Tariff (Excluding \\\newlineVAT)\newline\end{tabular} & \begin{tabular}{l} \newlineMogale City Approved \\\newlineTariffs July (20202020/20212021)\newline\end{tabular} & \begin{tabular}{|l} \newlineMogale City Approved \\\newlineTariffs July (20212021/20222022) \\\newline\end{tabular} \\\newline\hline Approved Indigents (free 6kl 6 \mathbf{k l} ) & R00 & R00 \\\newline\hline 16kl 1-6 \mathrm{kl} & R1717 & \begin{tabular}{l} \newlineR1818 \\\newline\end{tabular} \\\newline\hline 715kl 7-15 \mathrm{kl} & R2222 & R2424 \\\newline\hline 1630kl 16-30 \mathrm{kl} & R28 \mathbf{R} 28 & R2929 \\\newline\hline 3145kl 31-45 \mathrm{kl} & R3232 & \begin{tabular}{|l|l|}\newline\end{tabular} \\\newline\hline 4660kl 46-60 \mathrm{kl} & R3535 & R3737 \\\newline\hline 6161 and Above & R3939 & R4141 \\\newline\hline \multicolumn{33}{|c|}{\begin{tabular}{l} \newlineOther consumers: Government Schools, NGOs and Hospitals per kl (Excluding Private \\\newlineSchools \& Private Hospitals)\newline\end{tabular}} \\\newline\hline 1200kl 1-200 \mathrm{kl} & R2525 & R2626 \\\newline\hline Above 200kl 200 \mathrm{kl} & R4040 & R4343 \\\newline\hline\newline\end{tabular}\newlineSource:\newlinewww.polokwane.gov.za\newline\begin{tabular}{|l|l|r|}\newline\hline 33.22 & Write down the fixed monthly electricity cost for the prepaid system in Rand. & (22) \\\newline\hline 33.33 & \begin{tabular}{l} \newlineIf a household uses 6kl 6 \mathbf{k l} 00 of electricity in a month, how much would they pay \\\newlinefor their electricity consumption, excluding VAT?\newline\end{tabular} & (44) \\\newline\hline & & [99] \\\newline\hline\newline\end{tabular}\newline44\newlineGRAND TOTAL: 5050
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