5. If y varies indirectly with z, find the missing value of y in (12, 5) and (– 4, y). O - 15 60 O - 20 O -3

Q: (1) If x²y – xy? + x² + y? = 0, find y' (2) If x² – xy + y? = 3, find y' and y". (3) If x³y – xy3 =…

A: Since you have asked multiple  questions , we will solve the first three questions. If you want to…

Q: Express ∂w/∂r and ∂w/∂s in terms of r and s if w = x2 + y2, x = r - s, y = r + s.

A:

Q: Please draw and make a short explanation about of this pmf : p(y) = 1/(y+1) for y = 0, 1, ..., 6.

A: Given : Equation : p(y) = 1/(y+1) defined for y = 0,1,2,3,4,5,6 The following graph is obtained

Q: E. If T:(x, y) -→ (x + 2, y), then T²:(x, y) → (_²_, _?_).

A: Given: Tx,y→x+2, y To determine: T2x,y→?,?

Q: the relationship between income and consumption, where x is income and y is consumption; Y=4+0.5*X.…

A: According to the provided information, the relationship between income and consumption, Y = 4+0.5*X…

Q: Which of the following statements is TRUE? Select one: O a. If a variable is said to be integrated…

A: Option c and d

Q: If z = x + iy, z/3 – a – ib and * = 2 (a' -b'), then a is equal а b y to

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Q: -1 2 What valuls e a, b, c,d that that mwhe this - 1 - 5 5 consitents - 2 A xc B --- ~

A: We have to check whether given system is consistent or not?

Q: If the first line has the form Ax + By + C = 0 and the second line has the form Dx + Ey + F = 0 and…

A: The first line is of the form Ax+By+C=0and the second line is of the form Dx+Ey+F=0 As the first…

Q: 5. By Chain Rule , evaluate a. y' for y = u? + 4u and u = 4x3

A: This question is related to Differentiation, We will solve it using given information.

Q: 3) u = y f( ise XU, + yu, t zu. = ?

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Q: are two points find d.c's of OP, QO and PQ where O If p(2, 3, 6), Q(3,4, 5) is the origin.

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Q: Find Duf at P. 2 + 2. 5,3 4 f(x, y, z) = 6x³y°z*; P(1, – 2, 1); u = Duf i

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Q: 2 =x* x*y, x = s + 2t - u, y = stu; when s = 4, t = 1, u = 2 as' at' du az du

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Q: 4 - If w = x + 2y + z? , x =, y= r2 + In(s) , and z = 2r aw find at the point (r, s) = (-8,4). as…

A: See the attachment

Q: In order to investigate whether a particular medicine has the side effect of raising blood pressure,…

A: The confidence interval is the interval in which the population parameter is likely to fall. For…

Q: Show that if x', y are the deviation of the variables from their means, then x Yi r=1. Σ 2N - Ox Oy…

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Q: 2. We showed in class that EL (: - T)(y: – 9) can be written as a linear combination of ys: B1 = Gi…

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Q: Find x, y, and z to t 1.

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Q: 1. Suppose W (x, Y, z) = 20z In y – 13x"y3 + 5xz?, (a) Find (b) Find (c) Find OW (d) Find

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Q: 6) Given that h(x,y) = e**y® _ ¥² Find hxx, hxy, hyy, hyx

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Q: 1 If (x, y)= find f, and f,. Vx? x²+y²

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Q: Q#9) find the clamped cubic spline that interpolates the data ( 1,-1), (3,22), ƒ'(1) = 0, ƒ'(3) = 24

A: Given data is 1,−1, 3,22, f'1=0 and f'3=24. We have to find the clamped cubic spline the…

Q: then Suppose A= G ) and B= ( ) and A is similar to B= M 'AM where M- as O a o, -0 Oba, -1 Oca, -3…

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Q: If x2 + y2 = 2st − 10 and 2xy = s2 − t2, find ∂x/∂s, ∂x/∂t, ∂y/∂s, ∂y/∂t at(x, y, s, t) = (4, 2, 5,…

A: If x2+ y2 = 2st − 10 and 2xy = s2 − t2,To  find∂x∂s,∂x∂t,∂y∂s,∂y∂t at (x, y, s, t) = (4, 2, 5, 3).

Q: 4 - If w = x + 2y + z? , y = r2 + In(s), and z = 2r = X find at the point (r, s) = (-8,4). %3D

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Q: 23 { , si (x, y) # (0,0) b) g(x, y) = 2x2 + y² , si (x, y) = (0, 0)

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Q: Find speed and acceleration at a point (C,D), if distance of a particle is given by S = 2t^3− 3t^2…

A: The acceleration of an object is the rate of change of its velocity. The velocity of an object is…

Q: 8. % = () Given that u = and w = calculate the values of x and y if 2u = v - w. %3D

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Q: 3-VE For dz, z = 2+vz

A: Given,             ∫3-z2+zdz

Q: 1 8. Find y', y" and y"" for y = 3

A: Solution:Giveny=1x+3x2+2x3To findy',y'' and y'''

Q: MSAB MSError < 0.5, while Fo.95,1,8 = e) If by means of a calculation, you find out that 5.318, how…

A: Given information: MSABMSError&lt;0.50F0.95,1,8=5.318

Q: If = 2 z-x'y and A = 2x'î-3 yzj +x z'k, find A.V and A xV4 at the point ( 1,-1,1).

A: given ϕ=2z-x3y and A=2xi^-3yzj^+z2 k^ find at the point 1,-1,1 1) A·∇ϕ 2) A×∇ϕ

Q: 15. In AXYZ, if ZX =ZZ, XY = 13x – 21, YZ = 8x – 6, and XZ = x + 4, find x and the measure of each…

A: given: in ∆XYZ, ∠X≅∠Z XY=13x-21YZ=8x-6XZ=x+4 we have to find x and the measure of each side. that is…

Q: 11. If mVQ = (y + 7)', mQR= (x + 11)', mRS = (3y)', and mST = 65', find the values of x and y. %3D S…

A: According to the Bartleby guidelines only one question can be solved at one time, post the remaining…

Q: B/ If Ø = (x³y²z) and A = 2xzi - 3y2j+ 3xy²k Find a(A) at ду дх the point (2, -1, 3)?

A: When partial derivative is done with respect a specific variable, then other variables are treated…

Q: 3 4 If f(x, y) = x3 + 5x?y + y3 and u = calculate Du?f(3, 1). 5' 5

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Q: 13. If T:(x, y)– (x – 1, y + 6), then T':(x, y) → (__, .

A: GivenT(x,y)=(x-1,y+6)To findT-1(x,y)

Q: Suppose C varies interversely as/ with m^2, and C=72 when m=4. Find C when M=12.

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Q: If E?uz = x² and h = 1, then find ux. %3D

A: The objective is to find ux. Given information is: E2ux=x2, and h=1.

Q: 15. In AXYZ, if ZX = Z , XY = 13r - 21, YZ = 8r – 6, and XZ = x + 4, find x and the measure of each…

A: Solve 15

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

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Q: 10. If z = 2 i, find z6. 2 A. i В. —i С. 1 D. –1 6 cis 90° 11. If z = find |7]. 2 cis 45° А. 4 В. 2…

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Q: 31. *7/2 csc t cot t dt

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Q: 1 4. If S(x,y)= find f, and f,. + y³

A: Since you have asked multiple question, as per our guidelines we are supposed to answer only one…

Q: 5. If y = In(x + y), find y' at the point (x, y) = (e – 1,1).

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Q: a) b) Compute E(X|y), Var(X) and Var(Y). Hence, deduce the value of p= Corr(X,Y).

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Q: Q,3 Evaluate [II, xyz dxdydz, 3 < x S-2,0 < y S 1,0 S zs-

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Q: 5. Find fx, fy, and fz given x®y? f(x, у, 2) z4 %3D

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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.