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Question 44046

posted 10 months ago

During the summer months, British Columbia experiences numerous forest fires. You are working as a fire ranger in the interior of British Columbia and you spot a fire that is 15 km away from your tower. Your friend is working at another tower that is located 20 km from you at an angle of 21°. She can also see the fire.
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)

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Question 44045

posted 10 months ago

As a computer engineer, you are always looking at ways to improve the computing experience. As part of your final paper to submit for your Master's Degree, you do some research about how far computing has come over the years.
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)

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Question 41482

posted 11 months ago

. Let T be a set and B a collection of subsets of T. Show that if every element of T belongs to at least one subset in B and B is closed under finite intersections, then the collection of all unions of sets in B forms a topology on T.

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Question 41481

posted 11 months ago

8. Let ƒ : R → Z be the “floor" function which rounds a real number x down to the nearest integer:
f(x)=n \text { provided that } n \in \mathbf{Z} \text { and } n \leq x<n+1 .
Determine whether or not f is continuous.

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Question 41537

posted 11 months ago

6. Consider the statement for all sets A and B, (A – B) n (A n B) = Ø. Complete the proof begun below in which the given statement is derived algebraically. Be sure to
a reason for every step that exactly justifies what was done in the step.

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Question 41538

posted 11 months ago

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

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Question 41539

posted 11 months ago

Use mathematical induction to prove that for all integers n > 0,
1+3+3^{2}+\ldots .+3^{n}=\frac{3^{n+1}-1}{2}

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Question 41540

posted 11 months ago

9. A sequence b, b,,b3. satisfies the recurrence relation b=bK-1+6 bx-2for every integer k greater than equal to 2, with initial conditions b,=0^b,=3. Find an explicit formula for the sequence.5 marks

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Question 41693

posted 11 months ago

Use method of undetermined coefficients to solve the following non-homogeneous differentialequations.
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}

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Question 41695

posted 11 months ago

The position of a certain undamped spring-mass system satisfies the initial value problem for u(t)):
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)?

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