posted 10 months ago

a) Should you or your friend radio in the fire spotted to your respective fire stations? Justify your answerand include a diagram with your solution. (AP5, CM2)

b) Your friend decides to dispatch a water plane to the fire. Your station is not equipped with waterplanes. At what angle should the plane fly to target the fire accurately? (AP3)

Your friend decides to dispatch a water plane to the fire. Your station is not equipped with water planes. At what angle should the plane fly to target the fire accurately? (AP3)

posted 10 months ago

You make some interesting discoveries. Dating back to 1940, you find out that one of the original large computers was able to perform about 100 operations per second. After examining the data,you see that the speed of computers has multiplied 5-fold about every 7 years.

a) Some of the data is missing. You know that some super computers can now process4 882 812 500 operations per second. How many years have gone by to reach this number of operations? What year would this have occurred in? Show your solution algebraically! (AP5)

b) Do you think this is a realistic model? What limitation(s) may arise with this model? (CM3)

posted 11 months ago

posted 11 months ago

f(x)=n \text { provided that } n \in \mathbf{Z} \text { and } n \leq x<n+1 .

Determine whether or not f is continuous.

posted 11 months ago

a reason for every step that exactly justifies what was done in the step.

posted 11 months ago

. Use the 8- Bit two's compliments to compute the sum of (89) +(-55).

posted 11 months ago

1+3+3^{2}+\ldots .+3^{n}=\frac{3^{n+1}-1}{2}

posted 11 months ago

posted 11 months ago

y^{\prime \prime}+4 y^{\prime}+3 y=65 \cos (2 x)

x^{2} y^{\prime \prime}-4 x y^{\prime}+6 y=x+1

\frac{d^{2} y}{d x^{2}}-2 \frac{d y}{d x}+y=x+e^{x}

\frac{d^{2} y}{d x^{2}}-4 \frac{d y}{d x}+3 y=10 e^{-2 x}

posted 11 months ago

y^{\prime \prime}+\frac{1}{4} y^{\prime}+2 y=0 ; \quad y(0)=0 ; y^{\prime}(0)=2

(a) Find the solution of this initial value problem. Show all detailed steps.

(b) Plot (using MATLAB) y versus t and y versus t on the same plot. Clearly label you rplots and clearly identify the lines for each curve.

(c) Plot y' versus y; that is, plot y(t) and y (t) parametrically with t as parameter. This plot is called the phase plot and the y-y plane is called the phase plane.

(d) Observe that a closed curve in the phase plane corresponds to a periodic solution y(t).What is the direction of motion on the phase plot as t increases (i.e. clockwise or anti-clockwise)?