8x + 4y 14 O non-homogeneous 5x + 7y = 6 O homogeneous 3x 5z homogeneous 3y + 2z Onon-homogeneous - 2x 3y + 5z - -4x 4y = non-homogeneous - 2x + 5y homogeneous %3D 7x + 3y + 7z 1 %3D homogeneous 8x + 3y + 7z -3 %3D non-homogeneous 4x + 5y + 5z O O 2.

Q: 0.8 0.6 0.4 0.2 (c) -0.3 -0.2 -0.1 0.1 0.2 0.3 0.3 0.2 0.1 0.2 0.4 0.8 10 -0.1 -0.2 (d) -0.3 x = 0.5…

A: 1.  x=0.5-0.5ty=1-t2 Answer is (b) 2. x=t3-0.7ty=1-t2answer is graph (c)

Q: xp | %3D P O O d. dy -43xcsc(5x)[5cot(5x)– 3ln(4)] xp -43Xcsc(5x)[5cot(5x)+ 3In(4)] Oc. dy %3D xp |…

A: We have to find

Q: 3. Fxz²i + (1 - 3xy)j + yzk, A. xyi + 2yzj - 3yk B. zi + 2xzj - 3yk C. zi + 2zj3xk D. xi + 2yzj-3yk…

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Q: 1. (x+ 2y) dr-3y dy = 0 O x-6xy+8 xy'-3 y c O 3x -8ry + 6 xy'- y = c O x+ 3xy -4 xy' + 3 y c O+3xy-6…

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Q: raluate the integral / V4x4 – 12r2 +7 xdx. A - (4x* – 12r? +7)½ + c 24 B - {(2r²– 3) /4x+– 12x²+7 –…

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Q: 0 2 j, j(0) = 2 0 1. j' y1 2. j' = 1 ý, 7(0) = -1 -1 -0.5 j, j(0) = 1 %3D [0.5 A B 4.j' = y2 -0.5 ý,…

A:

Q: 1. X 8-2y (T, S) 2x+3y = 13 2. 5x-2y =-7 (C, A) X = -2y +1 3. X=-2y-2 (N, K) 2x +5y = -7 4. Y=-19-3x…

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

Q: 1 [2x²y¢&x +xydv) ces (0, 0), (2, 2) ar

A:

Q: 2x4 +3x2 – 1 Rewrite dx as integral of sum of partial fractions. (x³ – 4x² + 5x)? - B + E |dx x+1'…

A: we can reduce into partial fraction

Q: solve each system of equations using matrices (row operations). If the system has no solution, say…

A: Question 39 - x+y = 8x-y = 4Writing this in the form of matrix  AX = B…

Q: Find the derivatives of the functions

A: The derivative of the given function can be found with the help of the one-time differentiation with…

Q: -1 4 -1 1 2 2 5 2 1 y- 3x-1 A. y = -x+3 B. Y-x+3 y - x+3 y - x-1 y- 3x-4 Oc. y--x+4 y= -4x-1 OD. y=…

A:

Q: æ' = 2) 4e x + %3D -4 3 2e er the associated homogeneous system

A: Given, x'=-12-43x+4et2e2. Find eigenvalues corresponding to the matrix A.…

Q: (3x"-1)(3) %3D 3 Y +1 e 3x"-1 s 3x"+xY =4 %3D -) m =4 30 that 3x +1 %3D 3x4+1

A: See the attachment

Q: x + 2y + z + 4w = 3x + 6y + 5z + 12w 11 30 x + 3y – 3z + 2w = -5 бх y - z + w = -9 - 4-6 X, + 2x, -…

A: Gaussian elimination method: This method is used to solve the system of linear equations. It is also…

Q: 4. x' = 3x – y, y' = 5x – 3y; x (0) = 1, y(0) = -1 %3D

A: The given system of the equation is: x'=3x-y,  y'=5x-3y with initial conditions x(0)=1 and y(0)=-1.…

Q: (x² + 2)y" + 3xy' - y = 0 7 23-7 14 a. + 'x' y = a₁ [1 + ²x². b. y = a₁ [x+ ² x ³ - 4 4-4! 8.6! ·] +…

A:

Q: How do I solve by elimination to find the solution of the two equations?

A:

Q: 3 4 gla) - 4 17 3 A) s '(x) 3 A) Yes B) No -2.x + 8 B) f (x) – 3 C) s '(x) – x – 1 2 3) Sl:) – VI+2…

A:

Q: Let y = e2x and y2 = e3x be solutions for a homogeneous DE. Then, %3D is also a solution to the DE.…

A: As per Bartley guidelines we are supposed to answer only one question per post. This post contains…

Q: Evaluate: S 2y+3 (y-1)(³-1) dy ° − In\y − 1| − § (y − 1)³ + ¼ln|y² + y +1| - O √3 ○ – In|₁¹|- (y −…

A: We will use partial fraction decomposition to solve the given integral .

Q: 2x-4 16x-2 15x+3 U R x+5 Find mLZ Find mZV W. V U. 5х -6 6x +9 4x+2 4+7x S. T Find RS Зх- 12 R. X+12

A: TSRQ is a parallelogram, so, (i) the sum of its adjacent angles is 180° &, (ii) its opposite…

Q: تمارین: جد ناتج التكاملات الاتية (1) ( v2x +3 dx (2) ) Ta+3)² dx (3) | (3x* – 4x° + 3) dx V2x + 3 dx…

A:

Q: 7. Given 2x2y" + xy' + 3y = 0 show that 2x2y+2) + (4n + 1)xy"+1) + (2n² – n+ 3)ym) = 0 %3D

A: We use the method of mathematical induction to show the given statement holds (given…

Q: 12x+1 C) (2x+ 1)2 7) If y= then *+2. dy 12x -1 D) (2x+ 1)2 2x12x•5 A) (x+2)2 7 E) (2x+ 1)2 2x B) 22x…

A:

Q: 1. A function f(x, y) is homogeneous of degree 7 in x and y if and only if, 5x'-2y 8x +3y 2. The…

A: Solution ) A function f(x,y) is homogenous of degree 7 in x and y if and only if f (kx , ky )…

Q: (2t - 4 0st<2 (D2 – 1)y =- 12 %3D t22 y(0)=0, y'(O)=1 Find L{y} L (y) = F1) 4 2e-2s 2e-2s %3D -…

A:

Q: Y1 y2 y3 y4 ys Y1| 0.9 0.3 0.4 0.1 0.2 0 1 0.7 V2| 0.2 1 0.8 R, (x, y) = x, 0.3 0.5 0 0.2 R, (y, z)…

A: Given data:                       y1   y2 y3y4 y5R1x,y=x1x2x30.10.2010.70.30.500.210.8010.40.3…

Q: b) X, + X2 - 2 X3 +Xy = a) 5X +2y = 1 3X +2y %3D = 1 Xz - X3 +2 Xy = 1 %3D = 5 X - 5y = 6 c) 2x, +8…

A:

Q: M. -5z + 11 2² - 10z + 21 Iz 61 2 dz Use any of the results in this $ (a) -12ni (b) |z| = 9 33 Book…

A: We have to solve the given problem.

Q: write the augmented matrix associatedwith the given system.

A:

Q: 7. Solve 2 ( 2y^2 + 5xy - 2y + 4) dx + x (2x + 2y - 1) dy = 0

A:

Q: 6 р %3D Differentiate y with respect to x: y = Vx² + x. 2x 2x+1 2x+1 2 3(x2+x)5 В. 3(x²+ x)5 C.…

A:

Q: 2 (4-х2 2 The integral LG. -(x² + y² ) dzdxdy is Vx² +y? -2 J-/4- 2 C[* dzdrdo .3 dzdrd0 2 •T/2 2 p³…

A:

Q: = 0 = 0 - = 0 2. 2y" - Зу' %3D 0 4. 2y" - 7у' + Зу %3D 0 6. у" + 5y' + 5у %3D 0 8. у" — бу' + 13у…

A: Given differential equation has constant cofficient so We can solve by auxillary equation.

Q: Find all the local maxima, local minima, and saddle points of the functions in Exercises 1–10.

A:

Q: 2. S(7x3 – 5 V +18* +x-40 ) dx x3 C 7 x*. 10 x3/2 + 12x³/2 x-39+C x*.10x3/2+12x-3/2.1x-39 C 4. 39 4…

A:

Q: (x+3y – 4) dr + (x +4y – 5) dy = 0 O z+ 3y + In(x + 2y – 3) = C + In(2x + y – 3) = C z-1 In(2z + y –…

A:

Q: Vy = 2 Input Output 1 -2 -0.5 %3D - -1 -1 1 1 Vy = va %3D 2 0.5 3. 0.33 Vy = |a| %3! b. Input Output…

A:

Q: 10. x+y+z +w +t = 1 x + 2y + 3z + 4w + 5t = 0 x+ 3y + 6z + 10w + 15t = 0 x+ 4y + 10z + 20w + 35t = 0…

A: Gauss Elimination method The corresponding augmented matrix is given as…

Q: Expand (y-3x)*. A y +12y x + 54y*x² + 108y²x³ +81x* B y+4y x+ 6y*x² + 4y²x³ + x* y - 12y x + 54y*x²…

A:

Q: 2x +1 4. g(x)%3D x-1 1-4u 5. h(u) = 1+3u 6. H(s) =avs+

A:

Q: 1 be the standard integrating factor to y' + p(x) y = q(x). If y, =7 x2+19 x+ 19 is one of its…

A: Given: The equation is: y'+pxy=qx The standard integrating factor is: μx=1x And, solution is…

Q: 2,2 2 (xy +x)dx = (x'y+x+y+1)dy O In(x² – 1) =y² – 2y + 4ln|c(y +1)| In(x² +1) =y² - 2y +…

A:

Q: 2x4 + 3x2 – 1 Rewrite dx as integral of sum of partial fractions. (x³ – 4x² + 5x)? C(2x- 4) +D E(2x…

A:

Q: |1 X x21 |1 X YZ| 1 Y XZ = 1 Y Y2 1 Z XY Z 72

A:

Q: b) y = -x -1 -u) 4 = 3x +5 -ài) a) 2x +3 %3D y = 4x -) -ài, Bub ci) from il cis from ei) Sub = 4n -…

A:

Q: The solution of associated homogeneous equation of +6 a п -2 +n2 +2" with a =9 , a, =10 and a =32 is…

A: The solution is given as

Q: (x + 3y – 4)dx + (2x + 6y – 3)dy = 0 %3D O 3x + 6y - 5ln(x + 3y - 4) = C %3D O3x - 6y + 5ln (x + 3y…

A: We will find out the required general solution.

Q: arctan 2x 41. Differentiate y = x2{2x-(1+4x²) arctan 2x] (1+4x²) а. _x²[2x-(1+4x²) arctan 2x]…

A: We have to solve

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related. 

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.