1. If (x and jy) = 3 + j8, find x and y.

Q: 6x2+7y2=C satisfies 6x+7yy' given the inital condition y=4 when x=6 what is C.

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Q: If T(x, y, z) = x² – y² + 4xz represents the temperature at the point (x, y, z), in which direction…

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Q: T(x,y, z) = x² + 2y² + z

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Q: Evaluate ſſs 3y dS where S is the portion of y^2 + z^2 = 4 between x = 3 and x = 3 - z. %3D

A: The surface is ∬S 3y dS=∬S1 3y dS+∬S2 3y dS + ∬S3 3y dS

Q: 4. f(x, y) = 10x²y* – 6xy2 + 10x2; fx(x, y), fy(x, y) %3D -

A: Consider the given function as fx,y=10x2y4-6xy2+10x2

Q: Consider the following IVP: y"-3y'+2y = e*; y(0) = 0, y'(0) = 0 Find the general solution.

A: We solve the given DE  y"-3y'+2y=e3t.......(1) y(0)=y'(0)=0......(2)

Q: Consider the following IVP: y"- y = 4cos t; y(0) = 0, y'(0) = 1   Find the general solution.

A: The given differential equation is: y''-y=4cost So, we can also write as: D2-1y=4cost So, the…

Q: 1.Solve the given problem W = f(x, y, z) = 3x²y+ yz² + 2z³ fxis equal to ? fyis equal to ? fzis…

A: Follow next step

Q: Find the general Solution of DES: x yy'= x +3y

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Q: 03. Find se and *. If f(x,y) = 2e* + Iny² ,and x = 2t + r2, y = ; %3D at r+1

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Q: Let z=xIn(x²+y²-e)-235xy, x=te, y=est. If the value of oz when s=2 and t=1 is equal to Ae?+Be", then…

A: Here, the given functions are: z=x lnx2+y2-e4-235xy, x=t es, y=est so, z is a function of x and y…

Q: [d] If xz = yz and z - 0 then x = y

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Q: Find.: if dy æ*y+æz – yz² = 7. - -2y: 2yz-z C. E. None of the others. /Geen van die ander nie. 비 비…

A: Given; x4y+xz-yz2=7

Q: 1. If (x and jy) = 3 + j8, find x and y. x = 2.40 and y = 1.67

A: According to policy we are allowed to do one question. Image is attached with solution.

Q: - Employ Picard's method to obtain y (0-1) of the equation ay = x +y, given that Y, =0 when x, = 0.

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Q: Solve the following first-order linear DE's. a) y' + 2y = x³e-2x b) y sin2x 7 +: y c) x²y' +3y = x?

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Q: 7. Show that y(t) = c,e¬# +czte¬2# is a solution to y" +4y/ +4y = 0. Determine the constants c and…

A: The given equation is y"+4y'+4y=0. A second order linear, homogeneous ordinary differntial…

Q: - If y = e3x and y = e-3x , prove that: - %3D d²y 9y = 0 dx2

A: Given: y=e3x⇒dydx=ddxe3x⇒dydx=3e3xNow,d2ydx2=ddxdydx       =ddx3e3x       =3ddxe3x       =33e3x…

Q: 2 show that V(x, y) = x 'f (2x+y) is the general Solution of : Xav dx 2x du ду = V

A: We can show given function is a solution of the given equation .

Q: Ifx' +y +z -2aņz =1, then show that V1-x dy 1- y V1-:

A: We have to use the given condition x2+y2+z2-2xyz=1 to find this.

Q: For x,y E [0,1], prove that xy(1-x-y)≤1/27

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Q: #32 Find y' if Yu X-T + X.J9+ =XY

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Q: 4- compute dw dw дх' ду at the point (-2,3) if w = (2x + 3y - 1) ²

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Q: (8) If w = 5x2 + 2y2, x -3s +t, and y s - 4t. %3D aw and at aw Find as

A: w=5x2+2y2,   x=-3s+t,  y=s-4t

Q: (b) If z = 9t²e 4, find dz dt 4

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Compute |// a² d.x dy dz, where E = {(x, y, 2) : x² + y? < 1,0 < z < 1}.

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Q: 3- Suppose that s(x)dx 5. Find A- B- S V3 f(2)dz D-

A: Definite Integral of function f(x) in the interval of [1, 2] is 5. The function remains the same for…

Q: f (z,y, z) = x² + y² + 2² subject to zyz = 4

A: Given: fx,y,z=x2+y2+z2 subject to xyz=4 Let gx,y,z=xyz-4 Using Lagrange Multiplier fx=λgx, fy=λgy,…

Q: Eliminate the Arbitrary Constant(s): 1. y = c,x2 + C2xe* 2. Iny = c, + C2x

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Q: Find the general/particular solution of the follow 1. xy' - y = 2x Inx 2. (1+ x)y' +y = vx 3. t+2y =…

A: The general solution of the differential equations

Q: Give a particular solution for y" – 2y' + y = ex 1+x2

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Q: (4) (b) 10tsin(5t²- n/4)dt (4) (c) S 12(x³ + 2)ex¹+8x dx

A: We have to evaluate the integrals.

Q: Find the general Solution of DES x y = xy +y

A: Given:    x2y' = xy + y2

Q: If u = ₁+₂y+z, where a₁, A2, A3 al constants and J²u J²u J²u น a +a+a = 1. Show that + + = U. მ2 მყ2…

A: This question is based on Partial diffrentiation.

Q: (2 fi = f(x²+xyz, y² +22= Prove that (y²-2x) ou 2ZX) then ne (²h-x) he 18

A: Concept: Partial derivative : The partial derivative is similar to the normal derivative except in…

Q: (T^2-x)dt-tdx =0 when t=1 x=5 Ans,: x=1/3t^2 + 14/3t please show solution

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Q: 11, If PQ = OR, JK = 3x + 23 and LM = 9x- 19, find PK. %3D %3D %3D K J R. %S'

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Q: Find the value of x and KL if K is between J and L. JK = 2x, KL=x+2, and JL = 5x - 10.

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Q: 1 Q4- If you have 1 then x ... And y = %3D x+iy 1+2i

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Q: Prove that the general solution to L(y)=(x) is y=Yh+Yp

A: Definitions:  yh is a homogeneous solution so, for any yh, Lyh=0.  yp is a particular solution so,…

Q: 3. If (x, y, z) = xy²z find grad 6 at (2,−1,3).

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Q: If f(x, y) = xe³y + 4xy, then is given by: dydx 3xe3y + 4 3e3y + 4 xe3y + 4 3 e3y + 4 3

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Q: ( a) 2.xdV where E = {(x, y,z) |0 < y < 2, 0 <xs/4- y² ,0 < z< y } E

A: As per Bartleby's answering guidelines, we are supposed to answer one question if more than one has…

Q: Show that y=x² is asolution to: xy- 3xy'+4y=0, and then use reduction of order to find a second…

A: Linearly independent solutions of the differential equation

Q: 48xyz < (3x + 2y)(y+ z)(3x + 2z) for every x, y, z E [0, +∞[.

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Q: if y' - y =2x Then, d'y -24y prove that dx (3y –1)

A: Given that: y3-y=2x

Q: . Solve the following problem (a) Y'(t) = XY(t) + 1, (b) Y'(t) = \Y(t)+t, Y(0) = 1. Y(0) = 3.

A: In this question, we will solve the given linear first order differential equations.

Q: ='i+(2xz - y)j XZ and (2, 1, 3) is

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Q: If z = u2 v3 w4 , u = t2 , v = 5t − 8 and w = t3 + t, find dz/dt

A: Given,           z = u2v3w4 , u = t2 , v = 5t − 8 and w = t3 + t

Q: (D) If y/(t) + 2y(t) + Só v{r) dr = u(t - 1)

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Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.