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[.) [communications] The amplitudes of a \(n\)-element array are determined by the coefficients of the binomial expansion of $$ (1+x)^{n-1} $$ Find the amplitudes for a 10 -element array.

through a variable load resistor of resistance \(R\), is given by \(I=\frac{10}{5+R}\). Plot the graph of \(I\) versus \(R\) for \(0 \leq R \leq 10\).

dissipated, \(P\), in a resistor of resistance \(R\), is given by $$ P=\frac{V^{2}}{R} $$ where \(V\) is the voltage across the resistor. Plot on the same axes the graphs of \(P\) against \(V\) for \(0 \leq V \leq 5\) and a \(R=1 \Omega\) b \(R=5 \Omega\) c \(R=10 \Omega\), d \(R=20 \Omega\)

across a variable load resistor of resistance \(R\), is given by \(V=\frac{10 R}{5+R}\). Plot the graph of \(V\) versus \(R\) for \(0 \leq R \leq 10\).

Determine the expansion of \(\left(\frac{w}{4}-\frac{x}{3}\right)^{7}\).

[fluid mechanics] The velocity, \(v\), of a fluid through a pipe is given by $$ v=\frac{1}{40}\left(400-x^{2}\right) \quad-20 \leq x \leq 20 $$ where \(x\) is the distance from the central axis. Sketch the graph of \(v\) against \(x\).

The velocity, \(v\), of an object is given by $$ v= \begin{cases}2 t & 0 \leq t \leq 2 \\ 4 & 2

[fluid mechanics] The streamlines of a fluid flow are given by $$ y=3 x+c $$ where \(c\) is a constant. On the same axes, sketch the graphs for \(c=-10,-5,-1,0,1,5\) and 10

[fluid mechanics] The velocity profile, \(v\), of a fluid is given by \(\begin{aligned} v=& 3 x^{2}-x^{3} \\ &(x \text { is between } 0 \text { and } 3) \end{aligned}\) where \(x\) represents distance. Plot the graph of \(v\) against \(x\), considering \(x=0,0.5,1,1.5,2.0,2.5\) and \(3.0\)

An object has an initial velocity of \(20 \mathrm{~m} / \mathrm{s}\) at \(t=0\). For the first 10 seconds it has no acceleration and then it has a constant acceleration of \(a=-5 \mathrm{~m} / \mathrm{s}^{2}\). i Sketch the velocity-time graph for \(0 \leq t \leq 15\) ii At what time \(t\) is the velocity equal to zero?