A tablet with WiFi costs R10 579. Mark buys a tablet on HP and agrees to pay a deposit of RI 500 and 36 monthly payments of R350. Calculate the total simple interest paid and the rate of simple interest.

Using the definition, calculate the derivative of the function. Then find the values of the derivative as specified. \( g(t)=\frac{9}{t^{4}} ; g^{\prime}(-4), g^{\prime}(2), g^{\prime}(\sqrt{5}) \)

9. En parejas, analicen la siguiente situación y respondan. Pedro inventó un juego, el cual consiste en que cada 20 pasos que avanza al ir del parque a su casa, debe retroceder 2 . A este proceso lo llamó «jugada». Si cada paso de Pedro mide, aproximadamente, 55 cm .

Let \( f(x)=\frac{x}{\ln x} \) for \( x>1 \). (a) Derive expressions for \( f^{\prime}(x) \) and \( f^{\prime \prime}(x) \), simplifying your answers. (b) Obtain the coordinates and nature of the stationary point of the curve \( y=f(x) \). (c) Obtain the coordinates of the point of inflexion.

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

Outside temperature over a day can be modelled using a sine or cosine function. Suppose you know the high temperature for the day is 62 degrees and the low temperature of 42 degrees occurs at 7 AM. Assuming \( t \) is the number of hours since midnight, find an equation for the temperature, \( D \), in terms of \( t \). \( D(t)= \)