Example 1: If u(x, y) = x³y² + x² - 3y + 4 find a²u e) a²u a2u a2u ди and f) дудх ди а) Əx b) c) ду d) дхду ду?

Q: Q:When B1/z=0.5 & B2/Z=0.25, so 15? find I=? TABLE 8.8 Influence Factor I, by Equation (8.11) (Half…

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Q: 2. Test for exactness. If exact, solve. (a) (x² + y²) – 2xyy' = 0 (b) e3º (dr + 3r d0) = 0 (c)…

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Q: A,f, 107.4 mm 0.85/,'b Ca/B =107.4 mm / 0.85

A: Given data,

Q: Find for the following function: dx 1- y = log2 cosh(2x) 2- y = e(x³+1) 3- xy + x²y = 3 at x = 1 4-…

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Q: Table 18.8 , verify that the given solution satisfies the governing differential equation and the…

A: Example 1 Given  Deflection of beam , Y=w24Ei-X4+2LX3-L3X At X=0 Y=w24Ei-04+2L03-L3×0Y=w24Ei0Y=0 At…

Q: Answers: A₂ A3 A4 D: As mm² x1 mm² x₂ 2 X3 mm² mm² X4 mm² xs 2 4 3 5 mm mm mm mm mm Y₁ Y2 Y3 Y4 YS…

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Q: 6ft o = 32° Y = 110 pcf G.W.T 2ft + = 30° Y = 125 pcf 0 = 10° Y = 126 pcf 9ft c = 600 pcf Oft $ = 0°…

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Q: Problem 827 See Figure P-827. 150 Ib/ft, 400 Ib 300 Ib 50 Ib/ft 3 ft 5t 4 ft MATHalino.com 12 ft 12…

A: To find the moments using Three moment equation

Q: 1. Using DIM, solve for: P = 108kN a. Ymu (mm) b. A (rad) Use E = 200 GPa. 165 kN A 1m B 2m 1m CD 2m…

A: Given, E=200Gpa=200 kN/mm2         P=108kN We need to apply Double Integration Method to find out…

Q: Use the conjugate-beam method to determine the slopes at ends A and D and the deflections at points…

A: Solution: Given that; EI is constant E=1800 ksiI=46,000 in4EI=1800×46000=82.8×106 k-in2EI=575×103…

Q: 4. V2+ v7n; if n = 7 5. (금);ifn=2

A: 4. 2+7n ; if n = 7 It is given that the value of n is 7. Therefore, 2+7n=2+7×7=2+49=2+7=9=3

Q: (VB)/2g PA/Y 50m. Ps/y Qa Q1 Elev. 50 m 2 3 120 100 120 0.406m 0.254m 0.203m L 5000m 3000m 3500m…

A: GIven chazy constant then friction factor according to chazyf=8gc2for pipeline 2…

Q: 2. A column having a length of 7 m is to support a dead load of Section Ix (mm) | (10%mm*) (10°mm)…

A: Given data : Length of column L =7 m Dead Load  = 270 KN Live load  = 200 KN Fy = 345 Mpa E = 200…

Q: Determine the forces on member ABC, presenting your answers as shown. Use F as the last two numbers…

A: Equations of equilibrium: Three main equilibrium equations are enough to solve any forces acting on…

Q: H.W. 1 4.0 m 1.6 m 1 m 3.6 m A =? 2 m P = ? 2.0 m T= ? 17.0 m T 1.2 m 7.0 m 0.90 m Z2 3.0 m - B

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Q: O 26.8 kips O 23.2 kips O 25.2 kips O 19.7 kips O 21.2 kins W L₁ B L2 X

A: To find magnitude of vertical reaction at point C

Q: Eliminate the arbitrary constant in the equation x² + y? = r² none O xdx+ydy=0 O 1/2xdx-1/2ydy=0 O…

A: Given :- X2 + Y2 = r2 We have to eliminate arbitrary constant.

Q: Show that Ex 0x dy Ey Ez |x−Vy] E [ay-vox] E : (0x + ay) E [Ex + V€y] 1-v E 1-v² [ey + vex] [€y

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Q: Н, — 19 тт, Gs = 2.51, Pa = 1.73 g/cm3 do = 0 division, Gauge factor = 0.01 (mm/division) Dial Gauge…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: iv) if zx = (y)-1 then zx/zy = а. XZ b. yz с.у?z d.x?z

A: zx=1y z=1xy zx= ∂z∂x = d(1/xy)dx=-1x2y  Zy= dZdy = d(1/xy)dy= -1xy2

Q: Q:When B1/z=0.5 & B2/Z= 1.0 so find 15? I=? TABLE 8.8 Influence Factor I, by Equation (8.11) (Half…

A: B1Z = 0.5B2Z = 1 Calculate I5

Q: 1. Using DIM, solve for: a. Ymax (mm) b. A (rad) Use E = 200 GPa. 165 KN A 1m B 2m 1m P C D 2m 90…

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Q: Find the particular solution of the differential equation dy/dx = (4x^2 - 7x)/(3y^2+2) at x = 1,…

A: Given: dydx=4x2-7x3y2+2 Find particular solution of DE at x=1, y=1.

Q: hemispherical tank of diameter 4 m contains water up to a height of 2.0 m. An orifice of diameter 50…

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Q: D A E Given side B G Assuming that all stations are occupied and al lines are observed, what is the…

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Q: A point moves in a plane according to the equation x = t2 + 2t and y = 2t3 - 6t. Find dy/dx when…

A: Given

Q: 1 Determine dy/dx given y = (2u² – 1)7 if u = x + 2

A: To determine the derivative w.r.t. x.   Given, y=2u2-157, and u=x+12   First we must transform the…

Q: 6500 N 4.5 m– 4.5 m 1.5 m D 2 m E B Q00

A: It is required to find the force in member AB & AC

Q: H, = 19 mm, G, 2.51, Pa 1.73 g/cm d, = 0 division, Gauge factor = 0.01 (mm/division) Dial Gauge Dial…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…

Q: 80 mm 20 mm | 3P glued joint · NA 2 m 2 m 160 mm В 1.0 m 1.0 m -le 20 mm

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Q: EXERCISE 8. Calculate the vector a x b when a = 2i + j - k and b = 3i – 6j + 2k

A: a=2i+j-k b=3i-6j+2k

Q: B K O F 1x. YY KN 7. XY kN 1Y.XX kN

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Q: marks) 0.4 m B Mass2=35kg Mass1=65 kg 0.32 m 0.16 m 0.16 m

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Q: If 7 = (x+1)√x² + y + ² tan¹(3x-y)j and g = y find: 7xcurl 8+ (g.V) at (0.1.4) x+y In(xy + 2)…

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Q: Use the formula k(t) = ||r'(t) x r"(t)|| to find k(t). r(t) = 11 cos(8t.)i+ 11 sin(8t)j + 3tk %3D…

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Q: prces F so zero. 150 N -F 125 mm 30 30 130° 150 N 125mm 100mm 45 30 450 100mm F is not on its line…

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Q: dVdr=π2rh3=π×2×10.5×203=140π

A: Given data: The equation given in the question is as follows: dVdr=(π2rh)/3=π*2*10.5*20/3=140*π

Q: -100 80 9, A3 - 200 1. What is the value of ybar from the 1-1 line 52.69 2. What is the value of…

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Q: * Next Px ? |(-50.6867-37.59+ 103.368 2)× (.37+li65p t1.lk)

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Q: 3. If F(x, y) — Зxу/(x* + 2у?), find (а) F(1, 1) (b) F(-1, 2) (с) F(, 1) (d) F(-1, у) (е) F(х, х?)

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Q: 3. Solve: y" – 2y' + 2y = 0; y(0) = 1, y(1) = 1

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Q: Question 8 (The Fundamental Theorem of Calculus). Caleulate sin z dr. O 31 O-1 0 2n O 14 O 42 O0 O…

A: Given function is ∫03πsinxdx ∫03πsinxdx =-cosx03π   Applying the limits    -cosx03π=-cos3π +cos0…

Q: a = 600 N/cm t= 400 N/cm y 4 T= 400 N/cm a, 692.82 N/cm a, = 692.82 N/cm T= 400 N/cm T 400 N/cm az =…

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Q: What is the general solution of ydx (* + 6y) dy = 0 ? (2) O ry + 6y = C O ry+ 6y = C O xy 6y = C O…

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Q: а. 80 N b. 140 N Determine the force P to move block B of the figure shown. c. 120 N d. 100 N W =…

A: Please refer the attached image for complete solution. THANK YOU.

Q: 30 위 서 25 80 200 1. What is the value of ybar from the 1-1 line [Select) 2. What is the value of…

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Q: 3- Use Euler Method to find value of when У(16) (x2 + y?)dx = (x + y)dy, use h = 0.2 Y(1) = 0 for…

A: For finding the numerical solution of first order differentials equations with initial data we go…

Q: Which of the following equations is variable separable? O a. (3x² – y²)dæ – 2xydy = 0 O b. (x² +…

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Dimensional homogeneity

The term dimensional homogeneity means that in an equation, the dimensions of each term on both sides are equal, which means the dimensions of the left-hand side (LHS) of an equation are similar to the dimensions of the right-hand side (RHS). For a dimensionally homogeneous equation, the powers of fundamental dimensions will be identical on both sides of the equation.