Use the method of variation of parameters to solve the initial value problem x' = Ax+ f(t), x(a)=x using the following values. [20] 40 A = 5 -6 f(t): x(0)= At 1-et+6e4t 6e-t-6e4t -e¹+eª² 6e-t

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: x' +4x? + x - 6 f(x) =マ+x-4x -4 %3D X' + X 4х

A:

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: 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: During the first 12 hour, the employees of a machine shop prepare the work area for the day’s work.…

A: The machine parts is a function of time ft=10t-12 Cost of producing machine parts Cx=.1x2+25x+200,…

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: 3. Given f(x) = -7x-8-4sin(8)- 3e-6x – 4n² then determine the defining equation of f(x).

A: To determine the defining equation of f(x) from f'(x), we integrate f'(x) with respect to x.

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: Lee Holmes deposited $17,300 in a new savings account at 12% interest compounded semiannually.  At…

A:

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

A:

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: 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: Suppose f(x)=−x2+10x−6 models the per household smoothie consumption, in quarts, in the town of…

A: Given that : fx=-x2+10x-6. Therefore, take first order derivative : f'x=-2x+10. At f'(x)=0 , we get…

Q: dont understand the fourth and fifth row of equation of gh(x) and why the function is invalid?

A: Solution

Q: b A LB≈ b≈ 2 Note: Triangle may not be drawn to scale. Given the triangle above, find the following:…

A: Sol

Q: 1) Suppose you are driving on a straight, level highway without any hills, and your distance away t3…

A: Gas pedal is closest to the floor of the car when the rate of change of distance is 0 or velocity is…

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: Find f(x+h)-f(x) h 2 f(x) = 5x + 14x-13 OA. B. 10x+14+5h 2 10xh + 14h + 14h² C. 10x+14 OD. 5x+6+ 10h

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Q: Find the indicated outputs for f(x) = 4x² - 5x. f(0) = f(-1)= f(2)= h

A:

Q: With f(x) = 3x +1 and h(x) = 2x – 4, find (f o h)(5)

A: