Make r the subject 1/r = 1/r1+1/r2

Q: Y Find det A 1SA - TAI = T.

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Q: a²f af af and əx' əy :f(x, y) = (x+ y)(2x + y)² Compute se дхду

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Q: Evaluate ff, x² In(y + 1) dA where R = [0,1] x [0,1].

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Q: 1. Point P 9. QR 2. PQ 10. Point A 3. TR 11. TQR 4. CR 12. TQRC A 5. SR 13. Point B R.

A: Given a circle with parts

Q: If Q : R" → R is

A: (a) Given, if Q : ℝn→ ℝ is a quadratic form

Q: Let a A = d e h i and -3a -3b -3c B = g h i d e f Given that det(A)=1/15, what is det( B¬l)? Answer:

A: Just I have used the property of determinant of a matrix. (1) if two rows of determinant are…

Q: Given the relation 1 1 1 с х C y Make y the subject.

A:

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: calculate r(t) and T(t), and evaluate T(1).  r(t) = (et, t2)

A: rt=et, t2 Differentiating with respect to t, we get r't=detdt,  dt2dt=et,  2t Now,…

Q: , (х, у) (0,0) x+y f(x.y)%3D (х, у) (0,0)

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Q: I need help w both parts of question 1

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Q: Let X b(n,-) and E(x) = E(2– 6x) find n.

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Q: Given F(r, s, t) =-r(8s³ +t³), compute: Frst

A: Given  Fr, s, t=-r 8s3+t3

Q: The line that passes through the points (2,0), (0,1) is x+2y = c, where c = 1. O True False

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Q: Consider the problem min 12 s. t. 1+ r2| <1, IEX R.

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Q: Evaluate o y dæ – x*dy,

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Q: Name the preimage of R'. T' T V' R' R Your answer: O T O V O R

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Q: U + 2ru, =0 IER, t> 0, u(x,0) =e=.

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: Evaluate ſc(x – y) ds over the path C: F(t) = 4tỉ + 3tj for 0 <t< 2.

A: Given: The curve C: r→t=4ti→+3tj→ for 0≤t≤2 To Evaluate: The integral∫Cx-yds

Q: If ř = xî + yj + zk. Show that (i) Vř = (ii) v r3

A: Given, r→=xi^+yj^+zk^. (i) r=r→=xi+yj+zk=x2+y2+z2 Now, ∇r=∂r∂xi+∂r∂yj+∂r∂zk.…

Q: Find when r = 2 and s = 0, if: as z = xy² – x – y x = y = ers 1+s

A: Here given that z=xy2-x-y, x=r1+s,y=ers So, ∂z∂s=∂z∂x∂x∂s+∂z∂y∂y∂s        =y2-1-r(1+s)2+2xy-1ersr

Q: Given u(x,t)=(1/t)e^(x^2\4t), compute: uxx

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Q: Let X ~ NB(r, p). Show that E(X*) =-E(Y – 1)*-1 where Y ~ NB(r+1, p). а. b. Use this result to find…

A: It is given that:

Q: f({x, y))) for all c e R and all (x, y) E R?

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Q: DS tan %) c(x) ax

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Q: a. In R?, let C be the line segment from (-1,2) to (0, 4), and let F = (x + 2,-xy). Evaluate S, F ·…

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Q: Obtain (i) P (X 1)

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Q: Consider the relationship R C N x N, R(x, y) holds iff (/æ /T) E N. True or False R is irreflexive…

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Q: Find x E R that satisfies -2 , – 02 + 2 vz U2 det = x det + – ö4 2 0 + 03 U3

A: The key concept to solve the given problem is that : The determinant of a matrix remains unchanged…

Q: dæ is equivalent to Using the substitution u = x + 1 Vx + 1 1 -du 1/2 du du -1/2 du - 1) /u2

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Q: - show that; L-1[e¬v$] = e %3D 2tynt

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Q: (c) Show that |(−1,1)| = |R|, where (−1, 1) = {x € R : −1 < x < 1}.

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Q: Determine that; 2+ni/ mi/a = (1+ i) i. 2+7 ii. eiy+2ni+x = ez

A: As per the instruction, we will be solving only the first question. For (a), (i),…

Q: R and r are defined by E(r, – 5)(y – T) Sry VS., Syy SSR R2 r = SST' (1) Show R? = r².

A: If y = a+bx is the linear equation  Correlation attempts to measure the strength of the relationship…

Q: du ди Find and ds u = x• e'¨: u =x•e" ;x = In(s·t) , y = } , = = s² + ? . 2 ,==s² + t

A: According to the problem, we have

Q: PART C dy 12. Show that dx 2 for the relation %3D V%3D10, x, y X. # 0. y

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Q: -v-S vdu G) - S -r lee) dx 2 (보라2) 2 (x²t2) - x2 2 (R?+2) ㅜ 2 (x? qz) - (x? $2) z (? t2) In Ix? tz…

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Q: (b) Evaluate at the point (s, t) = (1, 2). Əsət

A: As per requirement, we we solve part b) only Given function is z=fst-3,s2+t3 f1-1,9=3, f2-1,9=7,…

Q: Find the value of X and Y in given that; -5 1 6 R = - 1 S = 3R + S = 4 y -1 8 3. 2. 2.

A: We want to find the value of x and y.

Q: Show that || Ar +b|3 cTx +d f(x) = {x |c"x +d > 0}, where A E RmXn, bE Rm, c€ R" and d e R.

A: As per the instruction, we will be solving part (b) of 3.23. We are given the function…

Q: I, y ds S:Z=X 0くxく」 こ>Rつo

A: Solve the following

Q: make v the subject 1/f=1/u+1/v

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Q: Let R=[0,1]x[0,1]. xy3 dA= R.

A: Let's find.

Q: Vy E R Ja E R [ (x² + y² + 1)ª+y+1 = 1] O True O False

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Q: ue of a and c are and

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Q: differentiate. a) g(t)こ3-2t St +1 c) H(u)= (u-JJ) (utro) d) FLt)- モ-3 %3D

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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.