Volume of a Tank A civil engineering firm is tasked with designing a new water storage tank for a municipal water supply system. The engineers want the tank to have an efficient shape that maximizes storage capacity while minimizing the amount of construction material used. The tank's cross-section will be shaped by revolving the regions bounded by the lines and curves, \( x=\sqrt{2 \sin ^{2} y} \) \( 0 \leq y \leq \frac{\pi}{2}, x=0 \) about the \( y \)-axis. The goal is to determine the volume of the tank that will be created by this revolution around the \( y \)-axis. 4.1 Source: Mafemba, J. (2024) a. Calculate the volume of the solid generated by revolving the regions bounded by the lines and curves mentioned in the scenario above

Which of the following variables are discrete? I. Number of players in a playground II. The speed in miles per hour of cars passing a certain point on a highway III. Academic rank in class IV. Height in inches V. Weight in kilograms A. I and II B. I, II, and III C. IV and V D. I and III

The profit at a lunch bar increased at a steady rate of \( 12 \% \) per year. This year the profit is \( 85,000 \mathrm{vt} \) How many years will it take the profit to exceed \( 400,000 \mathrm{vt} \) ?

Express \( \frac{2 \sqrt{5}}{(\sqrt{3}+2 \sqrt{5})^{2}} \) with a rational denominator

tercice 5. Soit \( n \in \mathbb{N}^{*} \). On définit la relation \( \mathcal{R} \) sur \( \mathbb{C} \) par: \( z \mathcal{R} z^{\prime} \Leftrightarrow z^{n}=z^{\prime n} \) Montrer que \( \mathcal{R} \) est une relation d'équivalence. Soit \( \mathrm{a} \in \mathbb{C}^{*} \). Déterminer la classe d'équivalence de a note \( \mathrm{cl}(\mathrm{a}) \). En déduire les classes \( \mathrm{cl}(1+\mathrm{i}) \) et \( \mathrm{cl}(-1+i \sqrt{3}) \) pour \( \mathrm{n}=3 \) et \( \mathrm{n}=4 \).

General Given a deck of 52 cards What is the probabilty that a card chosen at random will be 1.1 a hearts 1.2 a ten 1.3 a jack of diamonds