B) For the following points, find the best results of the second derivatives, f"(2), f"(4), f"(6), f"(13) -T x 0 2 4 5 6 7 8 9 11 13 y 10 11 13 15 10 12 10 8 5 4 1 16 000 0-0-0 0-0-0 12h -104 114 5611 12h (12 Marks)

a5f 1- Show that O for the following equation in less than three steps only f (x,y) = = x2 + 5xy + sin x + 7e* aw v2 2- Find when u = -1, v= 2 if w = xy+ In(z), x = dv , y=u+v, z= cos u.

B شعبة a5f 1- Show that O for the following equation in less than three steps only əx²əy3 f (x, y) = x² + 5xy + sin x + 7e* aw v2 2- Find when u = -1, v =2 if w = xy + In(z), x = dv ,y =u+v, z =cos u. и

Determine the particular solution. (2 + 7xy+ 16x²)dx + x2dy = 0 X-1, Y- %3D O 5(y+4x) = *-y In(x) 95(y-4x) = x+y In(x) O 5(x+4y) = *-y In(x) O 5(y+4x) = -y In(y)

Q6:- When a metallic rod is subjected to a tension force of 35kN, its length increases by 9.88 *10-4m. What is the change in length of this rod if the tension force is lowered by AL 30% of its original value? 198,7 400m A O- ALAE PL 35kN D= 30cm DV 35KN Tr T AL=80,44

Question 7 Which is the correct auxiliary equation for the differential equation- = 2- d²y dy dx2 dx A B m²-2=0 (D) m² - 2m=0 Cm² = -2m m² +2=0 E There is no correct answer from among the given choices.

SOALAN 4(b) M QUESTION 4(b) Determine the centroid (x,y and Z) of the component shown in Figure Q4 (b) if R = 14 mm. L 40 mm Z 20 mm 20 mm 12 mm 30 mm OUTY Hik L=ar y=L=4 R Figure Q4(b)/Rajah S4(b) 8=9=4 M UTM wik A=²9= A=4 x=9=%

F1=18 N           X2=8 m F2=18 N           X3=10 m F3=27 N           X4=17 m F4=11 N

85 in Express your answer with the appropriate units. View Available Hint(s) d= Incorrect; Try Again Review your calculations and make sure you round to 2 significant figures in the last step. Part B 5.25 x 10° yr Express your answer with the appropriate units. View Available Hint(s) = Part C 68f-ay Express your answer with the appropriate units. View Available Hint(s) v = Units 85 in Express your answer with the appropriate units. View Available Hint(s) d= Value HA Part B X Incorrect; Try Again Review your calculations and make sure you round to 2 significant figures in the last step. 5.25x10 yr Express your answer with the appropriate units. View Available Hint(s) Part C μA t= Value Units μA 68 ft/day Express your answer with the appropriate units. View Available Hint(s) Value Units ? Units ? c ?

If Froude's law of similitude exists between a model and a prototype then the power ratio P, is A [ 3.5 L P, 1.5 C L³ p,1 L35 p, 3.5 D Correct Option