For questions 4 – 7 consider the function z=9-2x+4y –x² – 4y? 4. The expressions for and are 5. A stationary point for z is 2 6. %3D ôx² ay? дхду 7. The stationary point in no.5 is a(n)
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- Solve the following differential equation: y'"-2y' +y= e*Inx Select one: a. YG.s=C;Xe¯*+Czx²e*+e* Jinx+ xe-* [Inx = C, sinx+ c>cosx+ sinx Inx+cosx /Inx b. YG.S c. None O d. YG.s=C,xe*+czx²e*-e* ] xInx+e* ]x?inx YG.s=Ce*+c2xe* - e* | xlnx+ xe* | Inx е.From the image below, and using the given datum, match the variable expressions to their position coordinates, SA, SB and SC, where s A is for block A, $3 is for pulley B, and so is for pulley C. If an expression does not match any position coordinate, then match it to the "None" option. 1.k-q 2.0 3.p 4. k SA Datum bc SC k ✓ None SB ФВ A Р ⒸOF6 108 polynomial is used to approximate v8, the answer is: dy 13. of the parametric equations x: 2-3t 3+2t and y =- is dx Use the following information for Questions 14 and 15: 1+t 1+t Using the Newton-Raphson method to determine the critical co-ordinate of the graph y=f(x)=(x)*an (*) (in words x to the power of tan (x)), you will be required to determine f'(x) 14. The expression for f'(x) is: The following tools were required in determining an expression for f'(x): Application of the natural logarithm 15. I. II. The product rule III. Implicit differentiation
- The natural exponential function can be expressed by . Determine e2by calculating the sum of the series for:(a) n = 5, (b) n = 15, (c) n = 25For each part create a vector n in which the first element is 0, the incrementis 1, and the last term is 5, 15, or 25. Then use element-by-element calculations to create a vector in which the elements are . Finally, use the MATLAB built-in function sum to add the terms of the series. Compare thevalues obtained in parts (a), (b), and (c) with the value of e2calculated byMATLAB.A magic square is an arrangement of n numbers into n rows and n columns using distinct numbers from 1 up to n² such that the sum in any row, any column or any of the two diagonals is fixed. Consider the 4 by 4 magic square below: aj a5 2 13 a2 10 11 a7 аз6 а4 12 4 15 a6 1 What is the value of a4 ? 07 O 5 O 16 A Moving to the next question prevents changes to this answer. Question 1 of 3> P Type here to search 9:47 PM 29°C 30-Nov-21 backspe E F C shift alt ctriThe values of p and h which renders (makes) the following set of equations dynamically and statically decoupled are, respectively. k,+k2 5 p+4 x1 = 0, X2 7 h+1 + [7h+1 J+e 5 p+4 J+e h= -0.214 and p = -1.76 h = -0.143 and p= -0.8 h = -0.281 and p= -1.2 h = -0.081 and p = -0.536
- QUESTION 4 Solve the following differential equation in Matlab using ode45.m. Use time interval of 0.1 second. (Don't use options in ode45 to change teh tolerance.) do (t) dt - cos = sint 0(0)=0. What is e(t=4.1)? ○ 0.871 -0.212 1.44 1.28 2.01 3.192-the pivot value is the point of the intersection of the row of the leaving variable and the column of the solution. * true falseQ3: Consider evaluation of different temperatures of solar photovoltaic/thermal system (PVT) as shown in Figure 1(a). The following set of differential equations represent energy balance equations to be solve using matrices and eigenvalues using MATLAB: dTglass = -0.75Tgtass + 0.75TpvT (1) dt - 1.187glass – 22Tpyr + 23Twax (2) dt dTwax 12Tglass + 18TpyT – 19 Twax (3) dt Where, Tgtass , TPVT, and Twax, are temperatures illustrated in Figure 1(b). At time t-0 the initial conditions are Tglass = 35 , Tpyr = 33, and Twax = 31 °C. Cold suppty In frem water Tank Glass PVT Espann Nane-PCMPVT Collector Wax Tubes Sterg Tank Nanofluid Heat Exchanger Contalner Tepe Teek oe Pump for drain