Use the method of variation of parameters to solve the initial value problem x'=Ax+ f(t), x(a)=x₂ using the following values. 20e³t 6e4t-e-t ·eªt + et 35e³t 6e4t-6e-t - eªt +6e-t A = x(t)= 5 -1 6 -2 f(t) = x(0) =

Q: 3. Use Rolle's Theorem to show that the equation +3x²5x+7=0 has no more than two solutions. (Hint:…

A: Roll's Theorem:  Let  f: [a,b] -> R  be a continuous function on [a,b]  differentiable in (a,b)…

Q: Find the solution of the equation y= 2x -x- 10 in the interval (2, 4] using derivatives. You can use…

A: To solve an equation  f(x)=0 using derivative of function, we can use the formula…

Q: pls

A:

Q: -3z + 4, a < -2 22 - 2, 2-2 18. If f(x) = find f (-2). || A. 10 В. 2 C. -2 D. -6

A: Given function is fx=-3x+4, x&lt;-2x2-2    ,x≥-2.

Q: Suppose a cheetah is dashing due north at a rate of 30 m/s toward a popular watering hole, and a…

A: We need to find x(t),y(t),r(t) in the above question.

Q: X1 - x2 +1 = 0) 1. Solve : x,? + x,² = 4 } with seed values x1(0) = 0.8 and x2(0) = 1.8. Compute up…

A: x1 - x2 + 1 = 0  =&gt;  x1 = x2 - 1  x12 + x22 = 4 =&gt;  x2 = (4 - x12)1/2    x1(0) = 0.8, x2(0) =…

Q: Solve the following IVP: X' = AX + f(t), where 2 -1 A = 3 -2 and X(0) = ( : -3 2 f(t) 10t ||

A: First we need to find the eigenvalues and eigenvectors of a then find the complementary solution of…

Q: Write an equation for a quadratic func 1 and shifted up 9 uni 5' by a factor of O f(z) = 9+ 5(- x)…

A: Graph

Q: 6. If f(x)= V3x + 4 , find (7).

A: Given function is To find inverse function of f , we set y=f(x) and solve for x Therefore,

Q: Find D,y, given y = 3e" (2x – 5)*. D.y = 3e [4(2x– 5)'(2)]+(2r-5)'(3e") = 24e" (2x – 5)' + 3e"…

A:

Q: 6) Suppose that the price of an Iphone (in dollars) is given by 6t p(t): 4 + 3e²/t . = 300 + t+2 t2…

A:

Q: If f(x) = x) = √² (2³ + 72² S 0 then f"(x) = (t³ + 7t² + 5) dt

A:

Q: The position of an object moving along a straight line is given by the equation s = t³9t² + 15t +4…

A:

Q: We define a logical connective as follows: P Q is true when both P and Q are false, and it is false…

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

Q: The windchill index announced during the winter by the weather bureau measures how cold it "feels"…

A:

Q: 10. The y" of y = (2x¹ + 4x³)(3x¹ − x³) is - a. 336x6 +420x5-120x¹ C. b. 336x5 +420x4-120x d. 48x7…

A:

Q: Apply the method of undetermined coefficients to find a particular solution : x'=9x+y+2et…

A: Corresponding coefficients matrix isA=[91−8−2]The characteristics equation of A…

Q: Q3 Find f-(x) for the following : 1- y = Jx-3 2- y = (2x³ + 1)'/5

A: For finding the inverse, we will replace x with y and y with x

Q: 10. If f(x) = 2x³ - 3 x3, then f'(1) is which of the following? (B) -3 (C) -15 (E) 7 (A) 15 (D) -1

A: given function is

Q: 3. ( Solve the IVP explicitly: f df da =re -2x f(0) = -1

A: To solve the IVP explicitly. fdfdx=xe-2x, f0=-1

Q: the cost of producing q units of a good is C(q) = 50q +500, and the firm sells q units at p(q) =…

A: Solution

Q: Solve the DE using the method of variation of parameters: *y" 4ry' + 6y-6a, y(1) –3, y'(1) =2 All…

A: