Determine coefficients a and b such that p(x) = ax² + bx + 7 satisfies p(4) = -1 and p(4) = -6. a = b =

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A: 2k2 - 83  - x = 0 We need to calculate the value of k.

Q: If y = 5(1 - e-2x), compute y and show that y = 10 - 2y.

A: To compute y'

Q: 51. y = 3x + (V3 – 5): and y = -J3x + (-/3– s)

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Q: Find A and B such that 2x-1/(x+1)(3x+2) = A/x+1 + B/3x+2

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Q: Show that Y1 = X1/X2 and Y2 = X1 + X2 are independent and that Y2 isχ2(r1 + r2).

A: Given Y1=X1X2Y2=X1+X2

Q: 3 and V₂ = Find A.

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Q: Use initial value Xo = [-2, 1, %3D -0.5] -2X1+ X2 + X3 = 4 Хз — 4 X1 – 2X2 – X3 = -4 X2 + 2X3 = 0

A: We will solve this equation using the gauss-seidel method. so for that first, we use the initial…

Q: find domain V2 + x 65. g(x) 66. g(x) 3 - x 2r2 + x - 1 67. g(x) = V – 6x 68. g(x) = Vx² – 2x – 8

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Q: x't 3x-4 be x²

A: Consider the integral  ∫x3+3x−42x2dx

Q: if y3-3ax2+x3=0 ,then prove that y2+2a2x2y-5=0

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Q: f(x) = x- 2x+4. Find kth)-fx) ん

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Q: Solve this problem using the indeterminate coefficients method: y" +2y' + y = 2cos(2x)+3x+2+3e^x

A: Given: y"+2y'+y=2cos(2x)+3x+2+3ex

Q: 1. Find a result by using variable separation 101 b- y³y+x³=0

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Q: - (10, 7); 5x-6y = 18 m- %3D とーX5=h 5x+16 (01-x)3こレス G

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Q: . Find f 6x5-25x*+8x3 +43x2-8x-12 (3x-11x3+9x2-11x+6)(9x2+12x+16) dx if this can be reduced to…

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Q: If h(z) = 2x2 - 3r +1, what is h(-2)?

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Q: Maximise Z = 5x1 + 6x2 Subject to X1 + x2 0 and integer

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Q: Let h(x) z² –3z+2 -z² –4x+4' what is h' (-5)?

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Q: 2 has a X 2 X

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Q: 2 v2x-x2 XY xydydx 0 0

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Q: Use Cramer's rule find yhe solution of x1: 2x1+X2-3x3=0 4x1+5x2+X3=8 -2x1-x+4x3=2

A: write the matrix D from the given equations  D=21-3451-2-14 calculate the determinant D…

Q: Q 4. (a). Show that fog = 4x² – 1, if ƒ(x) = 4x – 5 and g(x) = x² +1.

A: a. Given: The functions fx=4x-5 and gx=x2+1, To find: f∘g=4x2-1, Formula used: (f∘g)(x)=f(gx).

Q: Find H. A.of g6)= 3x 5x+2x-7 ifany. Justtfy your answ 2x-3

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Q: Solve cquation for X C. 2-xa %3D

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Q: Find solution using graphical method MAX Z = -2x1 - x2 subject to -3x1 - x2 = 0

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Q: x-3x-7 1. C(x+1)*| (2x+3) 6. 3 - In (2x+3)(x+1)** x+1

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Q: Find The valu eo of a and b :for: Fcr): X-2 7 7X d! ax²-bx+3 if 2<x<3 2x -a +b if x3

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Q: Find the 4 - x' -x²(4 – x²) = 2 i5 (4 - x*) + C 3 x²(4 – x²) 5 3 15

A: Please see the solutions below.

Q: 9. Find the general solutions of X' = AX with A =

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Q: 3. Find the coefficient of xy' in (2x + 3y)°.

A: The provided information is we find the coefficient of  x2y7    in (2x+3y)9 Then, (79)*(2x)2*(3y)7…

Q: Find the constant C such that .4 x3 - 3x + 5 < C,

A: x3 - 3 x + 5≤c x∈{0,3}

Q: If V = 4i + 3k and V2 = -2î + ĵ + 5 k. Find V1 - V2

A: Explanation of the solution is given below...

Q: Find J2z Әх у of z = x3 + 5x² у + 6

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Q: if y3 -3ax2 +x3 =0,then prove that y2 + 2a2 x2 y-5=0

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Q: e-7x - 2e3 et f (x) = e- *+16e10* + 2e-4z

A: (a) Consider the provided limit, limx→-∞e-7x-2e3x-exe-x+16e10x+2e-4x Evaluate the provided limit.…

Q: Q4 Find x for all of : 2- y = 3 x(x-2) x+1 1- y = xvInx

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Q: V4-x² x2+y2 4-x² x²+y² xdzdydx + ædzdydx V1-x² 0,

A: The given integral is∫01∫1-x24-x2∫0x2+y2xdzdydx+∫12∫04-x2∫0x2+y2xdzdydxWe have to convert integral…

Q: if y3 -3ax2 +x3 =0,then prove that y2 + 2a2 x2 y-5 =0

A: Given : y^3 - 3ax^2 + x^3 = 0

Q: Investigate the based on linearization 3 x = x₁ - x₁²³²+x₂z xr 394 - 292 6 Ac

A: This is a question of equilibrium and stability.

Q: x-2 ifx<2, 3x 2 if x2 -2

A: Given:-     To find:- Graph the equation

Q: 1. Use the chain-rule and find x and ÿ in terms of x, i, and ä if: а) у3 4x? b) y= 10x3

A: To find y" in terms of x, x', x".

Q: y3-3ax2+x3=0,then

A: Given:  y^3 - 3ax^2 + x^3 = 0

Q: [ 1-x+2x²-q³ -d.x 6. x(x²–1)²

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Q: √2. y=x² - 4x and y=-x² + 2x.

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Q: x) = (V5x – 1, 2х, X = 1 x> 1

A: A function f(x)f(x) is said to be continuous at x=a if x→alimf(x)=f(a) A function is said to be…

Q: max F(x1 ,x2) = x,x3 subject to 6xỉ + 3x = 72

A: Let the given function be  F(x1,x2)=x1x22    ….(1) and  G(x1,x2)=6x12+3x22-72=0    …(2) From…

Q: (x) = x² - 2x - 5 8CX=6x-1 N of G

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Q: f(x) = 2x² – 4x + 2 on [–2,3).

A: answer is in next step

Q: Find (axb) x c if a=i-2j-3k, b=2i +j-k, Q2. c=i+3j-2k.

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Q: Solve by Cramer's rule. X1 i X2¹ 6x1-2x2=4 3x1 + x2 = 10

A: