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Interesting Topics for science and engineering capstone project- grade 12

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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.

A start-up company selling magic scientific calculator borrows 40000 at an interest rate of 10% per year and wishes to repay the loan over a 6-year period with annual payments such that the third payment is 2000 greater than the first two. The fourth payment is 1000 greater than the third payment. The fifth payment is 1000 greater than the fourth payment and the sixth is 1000 greater than the fifth payment. Determine the size of the first payment. (Draw the cash flow diagram)
1.You are faced with making a decision on a large capital investment proposal. The capital investment amount is 140000. Estimated annual revenue at the end of each year in the eight year study period is 40000. The estimated annual year-end expenses are 12000 starting in year one. These expenses begin increasing by 500 per year at the end of year five and continue increasing through the end of year eight. Assuming a 40000 market value at the end of year eight and a MARR = 12% per year, answer the following questions. Using FW, determine whether this proposal is acceptable. (Draw the cash flow diagram)
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