Find the family of orthogonal trageclarnes fo he for

Q: Given: Parallelogram LIFE Prove: Z1 and ZF are supplementary ZF and ZE are supplementary ZE and ZL…

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Q: For z € C, define Tz: CC by Tz(u) = zu. Characterize those z for which Tz is normal, self-adjoint,…

A: Given that: For z∈C, Define Tz:C→C by Tzu=zu. The objective is to verify the given statement. Now…

Q: show that }I f,lm) Ck-m) 2.

A: For, ∑m=0kf1mf2k-m, substitute k-m=n or m=k-n: ∑m=0kf1mf2k-m=∑k-n=0kf1k-nf2k-k-n…

Q: Consider j1,ỹ2, ỹ,ER° and that ỹ,+y;+ÿ;=0. For Î=span{ÿ, ,ÿ and Y=span{ÿ2, ÿ}, show that Ý=Ỹ.

A: Given y1→, y2→, y3→∈ℝ5 such that y1→+y2→+y3→=0. Let Y^=spany1→,y2→ and Y~=spany2→,y3→. To show…

Q: find the funotion with hejp of a indegral meau value betw een 4,1] of g(x)=\xl-2

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Q: 5) Let à = psin(4)ū, + p² Ug Evaluate f Ã. dl given that L is the contour of the following figure.

A: Let A→=ρsinϕu→ρ+ρ2u→ϕ we have to evaluate ∮A→.dl→

Q: Determine the coterminal angle of 0 that is in the interval [0, 27) -29T 0 = 4

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Q: hat is the orthogonality assumption in OLS, taking Y = a + bX as odel, and the error term is e? (e…

A: Assumptions The covariance between X and the error term should be zero. Cov(x,e) = 0

Q: Prove (t, to) = A(t)Þ(t, t,)

A: The variables of function t and to are independent variables.

Q: Find the midpoint OF the line seament given the FOllowing endpaints:(s,2)and(-u,1)

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Q: S. Use the theorems and given information to show that r

A: The figure is as shown below : Given, ∠4 = (13x-4)o, ∠8 = (9x+16)o and x=5

Q: 3. Find all the fixed points and classify cach of them: f(r,u) ryev,

A: Solution:- Fx,y=xye-x2-y2 Put Fx=0 and Fy=0 Fx=e-x2-y2y-2x2=0and Fy=y-2y2 e-x2-y2=0 So,  0,0,12,12,…

Q: Find the d. c. of from definition.

A: Introduction :

Q: find the values of c that satisfy Rolle's Theorem

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Q: Csc? %3D 2cotx

A: csc2x2cotx=csc2x

Q: Start with [ao, bo] and use the false position method to compute Co.C1,C2 and c3. Use

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Q: The area bounded by the curve y = 7x and the lines z= 2 and =9 above the z-aris is O 539.00 square…

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Q: ome 9/ for Find The domain Dp and Rag Re De fallowing fandinse,

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Q: Find a mat rix P such that 0 3 P OA. OB. O 1 P = C. OD. P. OE

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Q: Show that f: R → R defined as f(a) = 3a³- 4 is a one to one %3D iuicuon.

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Q: Consider in the following figure: CB = 4CN, NA =5NX and M the midpoint of the AB side. Let CN=u and…

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Q: F(p), then prove that

A: simple use of integral transformation

Q: For z ∈C, define Tz: C →C by Tz(u) = zu. Characterize those z for which Tz is normal, self-adjoint,…

A: Firstly, find out Tz*.

Q: ) Let à = psin(4)u, + p² Ug %3D Evaluate $ Ã. dl given that L is the contour of the following…

A: Given, A→=ρsinϕup→+ρ2uϕ→ The given diagram can be drawn as,

Q: Use the figure. 7. K If NL = 3, KL = 12, and KJ = 16, find KP. %3D %3D %3D P.

A: From the given figure, it is observed that: PN is parallel to JL i.e., PN∥JL Also, NL=3, KL=12 and…

Q: dual of c, is isometric to l'.

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Q: Which rec tor lield s are not conservative %3D O F(ay)= (3x² - 4 y 4y=-2x> r.

A: Note : As per authoring guidelines, when multiple subparts are posted, then only first three…

Q: f (て) be a top. space 3.ト X-Tab, cidiel (xて) be top space %3D %3D et A= {bj. FindO A Tb,d] %3D 2.…

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Q: (a) Let r(t) = ti+tej+fk. Find ((1),4 × (?),1) - (1)a tuj

A: First we find out first derivative of r(t) with respect to 't' then find out 2nd derivative and then…

Q: Show that fi(r) = rª and f2(r) = r² +1 are orthogonal on the interval [–1, 1).

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Q: Let, T: R' → R';T(x, y,z) = (x+ y+ z,2y + z,2y +3z) Find the dimension of KerT and ImT

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Q: Use the diagram shown. В C 主 G 丰 Which is a needed step to prove that AABF EAEDG

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Q: et whose A = T be standard matsix teans bormaton is the lineas 2. 3. Does maps R3 onto R4? s Ta one…

A: Given that T is a linear transformation whose standard matrix is given by A=203032005000. We have to…

Q: b- Let X₁, X2,... X (a) Find a comp (b) Find the UM

A: Solution:   (a):

Q: Prove the following: %3D

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Q: These figures are congruent. What is mE?

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Q: Use the diagram to answer the following question. Which parts must be congruent to prove APQR APSR…

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Q: Show that the dyfferential equatian IS exact x(スt5in t) do + cast -2tu) abe +x² dt-

A: We will show that the given differential equation is exact.

Q: In the figure alongside, D is mid-point of BC. If 2CG = AC and BA//DE, prove that 3DF = FG. %3D

A: Consider the given triangle. Given that D is the mid point of BC. Hence, BD=DC. Also, the lines…

Q: b) Show that the following wo matricegane orthogonal tker A =-V3 -2VTO 3/T15 15 E/NTS

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Q: Consider the following coordinates. W(1,8), X (7,8), Y(4, 5), and Z(1,2) Select all methods you…

A: Given : W(1,8), X(7,8), Y(4,5) and Z(1,2) To find : All methods to prove triangle WYZ  is congruent…

Q: Prove that Srxdr = 2[, , da, r × dr =

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Q: Let z = 2 - 3xy?+ x². Zay %3D Zyy

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Q: For what values of aare u and v orthogonal?

A: Consider the given vectors  u=11-2  and  v=a-12 Write the vectors in row form u=1,1,-2  and…

Q: Make the first sir rows of the triangle for (), for q = 3. %3D

A: We have to make the first six rows of the tringle for nmq for q=3.

Q: Given: APQR has a right 2Q. M is the midpoint of PR. Prove: MP = MQ = MR

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Q: (f) Find the length of the projection of i onto ū.

A: Given

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.