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Reduce the following PDE to a set of two ODEs by the method of separation of variables and obtain the solution: d/dx(F(x,y)+2x d/dx(F(x,y))=

Calculate support moments for continuous beams.

Interesting Topics for science and engineering capstone project- grade 12

I need just 4 topics

The axle of a heavy duty tractor 120 K W at 600 rpm it acts as a cantilever supporting a load of 280 N located 60 cm from the fixed end. The allowable normal stress Is 137 MPa and the allowable shear stress is 62 MPa. If the axial load is negligible, find the axle diameter. A:52 mm B:50 mm C:56 mm D:54 mm

1. Compress the word PROPERTY_PROPER using arithmetic coding using 64-bit floating point number. Find compression ratio by assuming that originally the characters are represented in 8-bit (A = 65, B=66, ….., Y = 89, Z = 90, _ = 95).

You are in charge of manufacturing two products, namely Moira and Tassel daily. You need resources from A and B for producing both these products.
It requires 30 units of resource A and 5 units of resource B to produce one product of Moira whereas 20 units of resource A and 10 units of resource B are needed to produce one product of Tassel. There are in total 300 units of resource A and 110 units of resource B available.
Each product of Moira gives a profit of RM 6 whereas each product Tassel gives a profit of RM 8.
You would like to know how many of these products need to be produced daily in order to maximize your profit.
i) Write the required Maximum profit equation to maximize the daily production.
ii) Write the necessary inequalities that this maximum equation is subjected to.
iii) Using a graphical method find the maximum number of these products that are needed to be produced daily in order to get maximum profit.

Find the minimum value of w=2r+10s+8t, subject to the following constraints.
r+s+t≥6
s+2t≥8
-r+2s+2t≥4
r,s,t≥0

Compress the word PROPERTY_PROPER using arithmetic coding using 64-bit floating point number. Find compression ratio by assuming that originally the characters are represented in 8-bit (A = 65, B=66, ….., Y = 89, Z = 90, _ = 95).

If the input signal has values as follows
20 38 56 74 92 110 125 145 166 183 202 217 236 256
Show that the output from DPCM coder

(a) Gene Amdahl, an architect of the IMB 360 computers, has defined a model to characterize how well an application makes use of a scalable parallel processor. (i) Explain the Amdal's Law.
[3 marks] (ii) Making use of your answer in Question Q2(a)(i), determine the maximum possible speed up ratio that can be achieved by an application running in a system with FOUR (4) processors (8 cores each) if only 80% of the application can be parallelized. Please sketch the tinting diagram of your solution.
(iii) Your engineer shows that the measured actual speed up ratio of the multi-threaded application is 50% below the calculated answer in Q2(a)(ii). Please advise the necessary steps to be carried out by the engineer to validate the result.