Question 4. (6 points) Consider the Taylor Series of sin(x) centered at 0. Then we have a series that converges to sin(2). How many terms are needed to compute the first three decimal places of sin(2) Show and justify for all work ! (Note, you should only need a arithmetic calculator for this question (i.e. a calculator with plus/minus/multiplication/division abilities), and such calculations are best done last.) i

please make everything visible and readable 2.4 Consider the region depicted in the following figure. Find the area of R. 21 3+ f(x) = x 2 1+ g(x) - - 0 1 N 3

roblem 6 A reinforced concrete footing supports a \( 450 \mathrm{~mm} \) square column. GIVEN : Thickness of the footing \( =645 \mathrm{~mm} \) Effective depth of the flexural reinforcement \( =545 \mathrm{~mm} \) Column axial loads: \( \mathrm{DL}=800 \mathrm{KN} \) \( \mathrm{LL}=800 \mathrm{KN} \) \( \mathrm{U}=1.2 \mathrm{DL}+1.6 \mathrm{LL} \) roblem 6 A reinforced concrete footing supports a \( 450 \mathrm{~mm} \) square column. GIVEN : Thickness of the footing \( =645 \mathrm{~mm} \) Effective depth of the flexural reinforcement \( =545 \mathrm{~mm} \) Column axial loads: \( \mathrm{DL}=800 \mathrm{KN} \) \( \mathrm{LL}=800 \mathrm{KN} \) \( \mathrm{U}=1.2 \mathrm{DL}+1.6 \mathrm{LL} \) Materials : Concrete, \( \mathrm{f}_{\mathrm{c}}{ }^{\prime}=24 \mathrm{MPa} \) Steel, \( \mathrm{f}_{\mathrm{y}}=280 \mathrm{MPa} \) Allowable effective soil bearing capacity \( =219.38 \mathrm{kPa} \) Strength reduction factors: \( \quad 0.75 \) for shear \( 0.90 \) for bending 1. Determine the length required for the footing \( (\mathrm{m}) \) if site conditions limits the width of the footing to \( 2.0 \mathrm{~m} \). A. \( 3.65 \) B. \( 2.45 \) C. \( 4.25 \) D. \( 5.20 \) 2. Determine the no. of pcs \( 28 \mathrm{~mm} \phi \) flexural reinforcements along the long dimension of the footing. A. 8 B. 10 C. 12 D. 14 3. Determine the no. of pcs \( 28 \mathrm{~mm} \phi \) reinforcements along the short dimension of the footing over a bandwidth (centered on centerline of the column), the bandwidth having a width equal to the length of the short side of the footing. A. 6 B. 9 C. 11 D. 13 4. Determine the no. of pcs \( 28 \mathrm{~mm} \phi \) reinforcements (per side) along the short dimension of the footing outside the center bandwidth of the footing. A. 2 B. 3 C. 4 D. 5

simplify the answer 12.5-4. Concentration of NaOH Solution in a Triple-Effect Evaporator. A forced-circulation triple-effect evaporator using forward feed is to be used to concentrate a 10 wt% NaOH solution entering at 37.8°C to 50%. The steam used enters at 58.6 kPa gage. The absolute pressure in the vapor space of the third effect is 6.76 kPa. The feed rate is 13 608 kg/h. The heat-transfer coefficients are U1 = 6246, U2 = 3407, and U3 = 2271 W/m2.K. All effects have the same area. Calculate the surface area and steam consumption. Ans. A = 97.3 m². S=5284 kg steam/h 410

Help please A thin walled cylindrical pressure vessel is subjected to an internal pressure which varies from 750 KPa to 3550 KPa continuously. The diameter of the shell is 1.5 m. Find the required thickness of the cylinder wall based on yield point of 480 MPa, net endurance limit of 205 MPa and a factor of safety of 2.5. A camshaft 19 mm. in diameter is mounted on ball bearings and carries a cam midway from the bearings. The follower, which weighs 2.8 KN, is out of adjustment so that impact is produced when it is contacted by the cam. The height h of fall equals 0.254 mm. The shaft is made of AISI C1045 steel. Determine the maximum bending stress in the shaft.

Consider the following diagram: Internet Modem Wireless AP Switch Wireless AP DO Wireless AP Server 2.1 Using a table, compare 4 types of area networks. Consider the size of the network and the transmission media that is most likely to be found in each type of network. (8) 2.2 Based on the information given in 2.1, which type if network is shown in the Consider the following diagram: Internet Modem Wireless AP Switch Wireless AP DO Wireless AP Server 2.1 Using a table, compare 4 types of area networks. Consider the size of the network and the transmission media that is most likely to be found in each type of network. (8) 2.2 Based on the information given in 2.1, which type if network is shown in the diagram? Motivate your (2) answer. 2.3 This network has wireless access points. Compare three modulation techniques, using sketches, that could be used by these access points to transmit data. Use the bit-stream 10000101111. (6)

Biostatistics ESSAY A firm investigates the length of telephone conversations of their office staff. Ten consecutive conversations had lengths, in minutes: 10.7, 9.5, 11.1, 7.8, 11.9, 4.1, 10.0, 9.2, 6.5, 9.2. Derive a 95% confidence interval for the mean conversation length. Test whether the mean length of a conversation is eight minutes.(25 MARKS)