The position of x = -1 + 2t, y = 3 + 3t is:   a. [-1, 2] b. [2, 3] c. [3, 3] d. [-1, 3]

Q: If (x, y)= x²y+e* , find; d. y е. b. $, с. Ф Q.4 (1)

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Q: If f(x, y) = 5y² – 7xy+ 14x, then is given by: - dy? O -4 O 17 O 10 O -10

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Q: Evaluate p(x² + y²)5/2 dA, where D = {(x, y) E R² | 0 < y < 1, - V1- y² < a < 0}.

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Q: Find for w = , x = 0', y =r+ 0, z = r – 0 2r2 27 2r 272

A: Given query is to find the derivative.

Q: Solve for x, where u = (1, −1, 2), v = (0, 2, 3), and w = (0, 1, 1). 5u − 2x = 3v + w

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Q: Given f(x, y) = 12/8x* + 6y + 2xy°, find fa(x, y) = f,(x, y) =

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Q: If f(x, y) = 3x² + 2e*Y, find the following. a²f (a) a2f ду дх (b) azf Әх ду (c) a²f ay2 (d) %3D

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Q: f(r, y) : = V3x? + 4y? fz(3, – 2) =|

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Q: Show that for all formulas Y, Þ,0 € S(P), (y = 4) = -(4 ^ ¬b).

A: We need to prove that, φ⇒ψ≡¬φ∧¬ψ Now, constructing the truth table, φ ψ φ⇒ψ T T T T F F F T…

Q: f(x,y)=ylnxsinx, find fxxxxxy(π,1). Keep your answer to 3 significant digits.

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Q: If y varies jointly as x and z when x = 5, y = 80, and z = 8, what is y when x = 16 and z = 2?

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Q: For w = 8x4 + y4 − 2xy2, find ∂2w/∂x2 and ∂2w/∂y2 at the points where ∂w/∂x = ∂w/∂y = 0. And draw…

A: Treat x as a constant for derivative w.r.t y and vise versa.

Q: The value of | ysin(xy)dA, where R=[1,2]×[0,1]will be.

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Q: 3.2 find fxxy: flxiy) Bx*t 2€y?+ qxy!

A: when differentiate with x then y should be constant and when differentiate with y then x should be…

Q: Find x and y in terms of a and b.

A: Given equations are: ax+by=0⇒ax=-by⇒axa=-bya      (dividing both sides by a)⇒x=-bya   ...(1)x+y=1…

Q: Find (a) ∣AT∣, (b) ∣A3∣, (c) ∣ATA∣, and (d) ∣5A∣.

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Q: - Given that (x- pXx-5)%3Dx-qx+15, find the value of p and q.

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Q: R= { (x, y) : y 2r+1}

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: f(x, y) = 3x – 2y x² + 2 + 2y? = 275

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Q: Find the stion 2) y"+@°y= 0, y(0) = A, y'(0) = B.

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

Q: iS (2) = (x + ay² – 2xy) + i(bx² – y + 2xy) is anal ytic, then the values ofa and b is

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Q: Express ow/ds in terms of r and s if w = x² + y², x=r-S, y=r+s A) 4s B) 4r C) 4sr O O

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Q: Given f(x, y) 4x + xy? - 2y4, find %3D fa(x, y) =

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Q: Evaluate y ds, C: x = t², y = t, - 1<t < 9 |3D (325)-(5)를 1 12

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Q: For the DE y = xy², y(0) = - 1. Then, y(2) = Blank 1

A: The differential equation y'=xy2, y(0)=-1

Q: Given f(x, y) = - 5a4 – 4x²y³ + 6y°, find - fa(x, y) = fy(x, y) = %3D fez(x, y) =

A: As per our guidelines we are suppose to solve only first three sub-parts of a question. Kindly…

Q: find the point p such that v=pq has the components (5,-7,-4)

A: find the point p such that v=pq has the components (5,-7,-4)

Q: Given P(x) = 3x + 4y² and R(x) = -7x² + 4xy- 3y², find A. 10x - 4xy + 7y B. -4x - 4xy+ 7y C. 4x -…

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Q: For f(x, y) = (x²y – 8y)°, find. a) fa (x, y) b) fy (x, y)

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Q: I. If f(x, y) = x² – y² + 4xy – 7x + 10, find (a) f(2, 1) (c) f(x + h, y) (b) f(-3, 5) (d) f(x, y +…

A: topic - functions note : As per bartleby guidelines, we are supposed to answer only first three…

Q: Given f(x, y) = 4x³y², evaluate f(1,y) and fy(x,2).

A: We are given a function: f(x,y) = 4 x3y2 We need to find the partial derivative of the given…

Q: For w = 8x^4 + y^4 − 2xy^2, find ∂2w/∂x2 and ∂2w/∂y2 at the points where ∂w/∂x = ∂w/∂y = 0 and draw…

A: Given w=8x4+y4-2xy2.We need to find ∂w2∂y2 and ∂w2∂x2 at the points where ∂w∂x=∂w∂y=0.

Q: as instructed, to find à second sO Y2(X). 9y"- 24y' + 16y = 0; Y1=e4x/3

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Q: If f(x, y) = C, CE R, find y" d²y dx²¹

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Q: Find d?y/d?x from x=t2-3t+4 and y=t2 +4t -5.

A: The parametric equations are x = t2-3t+4 y = t2+4t-5 To evaluate: The expression of d2ydx2 Formula…

Q: Evaluate | (r + y)ds, c : x 3t, y = - 3t + 3, for 0 <t< 3.

A: Given: ∫C(x+y)ds, C: x=3t, y=-3t+3, for 0≤t≤3

Q: Find x and y in terms of a and b. ax + by = - 5 bx + ay = - 5 %3D

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Q: Find and a and дхду f(x,y) = x2 - y2 + 6xy + 4x – 8y + 2 a. b. f(x, y) = e*y + xy

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Q: Given that y = (2e - 6x +5), show that

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Q: if (y+ 4)² = x + 2, then + 2, then dy

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Q: Find C so that y(x)=C(1-x2) a.  y(2)=1 b.  y(1)=2

A: To find the value of C so that y(x)=C(1-x2)...(1) with the given initial conditions.

Q: as Find w = 1° + 2y? I = r - s; y=r+2s2

A: Given:w=x3+2y2x=r-sy=r+2s

Q: y ds, C: x = t², y = t, – 2 <t < 3

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Q: If = =x - xy + 3y and (x, y) changes from (3. - 1) to (2.96, - 0.95), compute the values of A: and…

A: Given that            z = x2 - xy + 3y2 and (x,y) changes from (3,-1) to (2.96, -0.95). We have to…

Q: Find the point (Xo, Yo) on the line 4x + 6y = 12 that is closest to the origin. (Xo, Yo) =

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Q: (Q)WUse T.Cx) =1 and Ticx)= X, to find TEcks and 万(x)

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Q: If B = x'ya, + (2x² + y)a, – (y – 2)a,, find - (a) V. B (b) V X B (c) V (V - B) (d) V x V X B

A: Gradient and divergence

Q: For the DE y' = xy², y(0) = - 1. Then, y(2) = Blank 1

A: topic - differential equations answer is -1/3

Q: Q3) draw and find Df and Rf for y |x2 - 1|

A: We have to draw the graph and find the domain and range for f

Q: Find r'(t), r"(t), r'(t) · r"(t),

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Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.