Differentiate the following functions: a) y = (-5x-7)³ b) y = 7-2x² 2x+1

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A: given differential equation  x+ydx+3x+3y-4dy=0 solution let y+x=u differentiate dy=du-dx…

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Q: Question 8: Consider/f = f(p(t)); ƒ is nonlinear function of p(t); derive nonlinear population…

A: The differential equation for non linear population growth model is defined as, 1pdpdt=a-bp where,…

Q: F(x, y) = xi + yj C: r(t) = (9t + 2)i + tj,      0 ≤ t ≤ 1

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Q: we have found the following Wronskians. W = -3x; We want to find functions u₁(x) and u₂(x) such that…

A: W=-e-3x; W1=-e-2x2+ex-1; W2=-e-x2+ex-1; u1'=W1W; u2'=W2W;

Q: Show that (ℤ,∗)?ℎ??? r ∗s = (r +s)−(r ∙ s)??? ??? r,s ∈ ℤ is group using variable r, s and t.

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Q: Solve using Two Phase Method Max Z = 4x1 + 6x2 Subject to 2x1 + x2 > 4 x1 + 3x2 ≥ 4 x1 + x2 ≤ 5 and…

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Q: Find the determinant. w(x³, x²) = = x² ² 2x 3*2 (x²)(3x²) - (2x)(x³) The Wronskian ---Select---…

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Q: Define the binary operator by: ab=a² + b² and by: a b = 8a+ 8b Find the following. When simplifying,…

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Q: What is 1 + (COS ™n) when n = 4? 01 O -1 O2

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Q: Use spherical coordinates to find the mass of the sphere x² + y² + z² = a² with the given density.…

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Q: The following data are recorded for the velocity of an object as a function of time (Table 2). t, s…

A: Note:- Five point central difference formula for first derivative:- f'x = 112 h fx-2h -8fx-h + 8fx+h…

Q: Use Res(f(z). Za) = lim (z-zo)f(2), Res (f(2), za) = (n-1)! im 2-1 (2-zo)" f(2), or Res(f(2), zo) =…

A: Given function is fz=1z2-6z+102   To Find: The residue at each pole of the given function.

Q: (HW) Ex. 3 Solve the systems of ODES and initial value problem = 2y: 3/₂ = 2y₁ y₁ (0)=1. y₂ (0)=0…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: A force of 720 newtons stretches a spring 4 meters. A mass of 45 kilograms is attached to the end of…

A: Given that  F=720 Nx=4 meters  So, the spring constant is k=Fxk=7204k=180 and, mass  m=45 kg

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A: Given y=C1+C2cos(x)+C3sin(x) is the family of functions is the general solution of the differential…

Q: Step 5 We have found the following derivatives of the functions u₁(x) and u₂(x). U₁ = Find the…

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Q: A force of 640 newtons stretches a spring 4 meters. A mass of 40 kilograms is attached to the end of…

A: Given that a force of 640 newtons stretches a spring 4 meters. A mass of 40 kilograms is attached to…

Q: Determine if R is a field an integral domain a unital ring for R=Z/15Z, R=Z/16Z, R=Z/17Z

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Q: Find ||FI|. F(x, y, z) = i +j+k Sketch several representative vectors in the vector field. -5 -5 y y…

A: given vector field F(x, y, z)=i+j+k

Q: If S is an ordered set, then One of the following is true: A) If A is a subset of S and A has an…

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Q: Find the order of growth the following recurrence relations using master of theorem, if applicable.…

A: Solution a: Given T(n)=3Tn2+n2      n>1, T(1)=1 Comparing with T(n)=aTnb+Onklogpn a=3, b=2, n=2,…

Q: Solve the given differential equation by undetermined coefficients. y" - 2y' - 3y = 4e* - 12 y(x) =

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Q: 24. Solve the following integral using substitution method: f8x√2x² - 1dx

A: Sol:- ∫ 8x2x2-1dxTake the constant out:  ∫a·fxdx=a·∫fxdx=8·∫ x2x2-1dxIntegral Substitution…

Q: Solve the given differential equation by undetermined coefficients. y" - 2y' - 3y = 4e* - 12 y(x) =

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Q: 6. Evaluate the following real integrals by residue theorem 3 I=S -24 2 dx 2x (x²+a²) ² ans ? tr 493…

A: 6. To Evaluate: ∫-∞∞dxx2+a22

Q: 1. Evaluate the following real integrals by residue. theorem 3 • I- 88 dx (x²+1)(x² +9) ans tr 12

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Q: x = 7u + 2v y = 7v -0.5 y 8 1.5 (0,0) 2 1.0 (2,7) 0.5 R (0, 1) S (0,0) (7,0) 4 0.5 (1,0) 1.0 6 1.5 u…

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Q: ABCDV is a solid glass pyramid. The base of the pyramid is a square of side 3.2 cm. The vertical…

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Q: Consider the differential equation x²y" 4xy' + 6y=0; x², x³, (0, 0). Verify that the given functions…

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Q: Three players (Arlo, Melvin, Maxine) must divide a cake among them. The cake is divided into three…

A: As per the question we are given a game theory problem with a 3×3 payoff matrix. And we have to…

Q: Given the following: P₁(x) = (63x5 - 70x³ + 15x), Determine P(x). A. P(x) = (231x6-315x+ +105x² - 5)…

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Q: A bridge is to be constructed to pass over a road, and a surveyor is sent to take some measurements…

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Q: Find a linear differential operator that annihilates the given function. (Use D for the different…

A: The annihilator of xn-1 is Dn The annihilator of xn-1sin βx is D2+β2n Now the given function is…

Q: 6. Evaluate the following real integrals by residue theorem 3 211 1 = √² do Cos 0 + 2 sing +3 ans o…

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Q: form a piecewise function by using exponential, quadratic and linear unction. Domain for the…

A: We need to find a piecewise continuous function using exponential, quadratic, and linear functions…

Q: Use (18) in Section 6.4. x²y" + xy' - (x²x² + ²y = 0 (18) Find the general solution of the given…

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Q: Explain what it means for a function to be (1) and give an example of such a function.

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Q: Q.55 Let A E Rmxn, c E Rn and be Rm. Consider the linear programming primal problem (A) crº≥ b yº…

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Q: Name the function of the graph below: -T/5 -4- 3- 2 0 --1- --2- --3- -4 f(t) = 3 cos (5πt) f(t) = 5…

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Q: Evaluate the double line integral S  of the fuinction (x − 2y + z) dS. S: z = 9 − x,  0 ≤ x ≤ 9,  0…

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Q: Solve the given differential equation by undetermined coefficients. y" - 2y' - 3y = 4e* - 12 y(x) =

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Q: 2. Graph the following exponential functions then state the domain and range [Hint: find parent…

A: Given: 2) y=-32x-2+2 To sketch: The graph of given function.

Q: Suppose T: M₂,2→R¹ is a linear transformation whose action is defined by a+5b+3c+2d -a-5b-3c-2d…

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Q: Find the general solution of the given second-order differential equation. y" - 10y' + 26y = 0 y(x)…

A: The solution is given as

Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

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