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

Q: Find: that: fl4) = -8 f'(4)= -8 %3D glx)=r

A: Given: g(x)=x f(x)f(4)=-8f'(4)=-8

Q: (b) ruz – 2yuy + u = eª , for x> 0

A: 1.(b) Given partial differential equation xux-2yuy+u=ex, for x>0 This can be written as…

Q: Find the particular solution for: 3x²y' 5x - 6xy, x 2 when y = 1 %3D

A: This is linear differential equation. We solve it by finding integrating factor.

Q: Show that r: y = 3. 2n

A: Using two sectant theorem,  ∠n=12x-y  Multiply both sides by 2. ⇒2n=x-y .....(1) Using intersecting…

Q: The productivity of a country is given by ​f(x,y)=14.41x0.427y0.573​, where x is the amount of…

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Q: To the reci max z Ax1 +B x2 A=6 s.t. 2x +4x 2 12, B=1 -X1 + 2x2 S 2, X1 20, x2 Free.

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Q: Differentiate implicitly to find 3xy +4y°z-2x = 3

A: Given query is to find the derivative.

Q: Verify that ƒxy = ƒyx, for ƒ(x, y) = 2x3 + 3y2 + 1.

A: To verify that

Q: FInd the implicity differentiate x^2- 4xy + y^2= 4

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Q: Explain how to get y=kx+b from y=x, and how to get y=ax^{2}+bx+c from y=x^{2}

A: Transformation of the function  f(x)+b shift b units upward f(x)-b shift b units downward…

Q: For Vx 3 evaluate y when y = 4. 2

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

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Q: What is the counterexample of x+x>x ?

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Q: Show that y" + ay' = b, wherein a and b are constants, can be reduced to y' =+C₁e-ax using 2…

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Q: Compate the Cantiderivative of fox) = x²+4 xナ4 %3D x³+ax

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Q: Find the general antiderivative of f(x) = 15x-3/5 and check the answer by differentiating. %3D

A: We have to integrate the function

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

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Q: When x = 2s+7t, y=5st and z= 3.x2 – 3, in the form of s and t. express

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Q: 2t + 3 r(t) -, In(t² + 2) t2 +1

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Q: Let a > 9 be a constant. Evaluate 3z2 + 30x + 30 + 4a dz (3x + a)(x² + 6x + 10)

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Q: If x < 0 and y > 0, determine the sign of the realnumber. xy2

A: Given that, x < 0 that is x is negative. y > 0 that is y is positive.

Q: 82z 8. If z = x + y lnxy, show that x- 82z + ミy2 82z 8y2 8x2 δχδν

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Q: Show that y" + ay' = b, wherein a and b are constants, can be reduced to y' =+ C₁e-ax using 2…

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Q: x^2=Axy+By

A: Simple value put

Q: Use the subst ition =x+y=0 4x-3y=0 By Your answer is

A: -x+y=0  ----->14x-3y=0  ----->2from equation1-x+y=0⇒y=xsubstitute y=x in equation 24y-3y=0y=0

Q: Find yll of x³+y²=3 by implicit ditferetlal C1o pants

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Q: Calculate the LOS of y = -x² + 2x + 4 LOS is x = a is b is ,c is

A: We have to find the line of symmetry and values of a, b, c in the given question.

Q: x, prove that y¨= 2(y² +1)(3y² +1).

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Q: What is the correct evaluation of x2 - y2 - z2, when x is equal to -2, y is equal to 3 and z is…

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Q: I Sdve for dy using the four-step rule 2. y = x"- x 5X-3 ソ= 4- 3X

A: We have to solve the problem

Q: The R2 from regressing Y on X is the same as the R2 of regressing X on Y. True or false?

A: For a simple bivariate regression, the linear correlation coefficient and R-square will be the same…

Q: What is the value of x in (2x - jy) + (y - jx) = 1 - j5?

A: We have to find the value of x where 2x-jy+y-jx=1-j5

Q: What is the counterexample of x/x=1

A: Follow the steps.

Q: f(x, y) = 6 – V4 - x2 - y2 is

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Q: Q2) Show that y = 35 x* – 30 x2 +3 satisfies ( 1- x² )y" – 2xy' + 20y = 0 %3D

A: y =35x4 - 30x2 +3 satisfy (1-x2)y" - 2xy' +20y =0 for this wew find  y" and y' y' = 140x3 - 60x y" =…

Q: Using the principles 2y. -3y + y = 5-3" Vn20 where y=1 and y₁=1

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Q: -V4-x² c3-x²-y² xdzdydx, 0. 0, J-5+x²+y²

A: We will find out the required value.

Q: Verify that y = x² – 1 is a solution of (y')* + y² = -1. %3D

A: Given;            y=x2-1 is a solution of y'4+y2=-1 We compute the first derivative.…

Q: Z1 and 22 are supplementary. Z1 = 124° 22 = (2x + 4)* What is the value of x?

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Q: 9-2-y (x² + y² + z*)% dzdydx

A: Given integral is ∫03∫09-x2∫09-x2-y2x2+y2+z212 dz dy dx Take  I= ∫03∫09-x2∫09-x2-y2x2+y2+z212 dz dy…

Q: What is the DE for A(x^2)+Bx+C using elimination of arbitrary constants.

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Q: If x < 0 and y > 0, determine the sign of the realnumber. x2y

A: Given, The real number is x2y.

Q: 6) qyo -x² +2x + S%y +62=0 sty

A: 6)

Q: 9. For Ax) = -4x+2, find (x) when x==1. %3D а. С. 2 b. -2 d. 6

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Q: Verify that * / II 21 ?х ду 224 ду ох - for f(x, y) = 4x4y3 - 6xy5.

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Q: For j(x) = (2x² – 1) (-3x³ + 2x), find j'(0) by applying the product rule. %3D

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Q: Express (2xy + 2x – 1) – (x² – y² – 2y)i in terms of z & z, then simplify. - -

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Q: Мaximize Z = 14x + 21y subject to 2x +3y 0

A: This is the simple problem based on linear programming problems (multiple optimum) which could be…

Q: 04: Show that y = 35x - 30x +3 satisfies (1-x)-2+20y = 0 da

A: We have to show y=35x4-30x2+3 satisfies 1-x2d2ydx2-2xdydx+20y=0

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.