Letx, y, and z be positive real numbers. Show that: xyz(x+ y+z)sr°y+ y°z+z°x

Q: Find f, and f, and evaluate each at the given point. y' f(x, y) = e*y2, (In 4, 2) %3D

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Q: If f = xi + yj + zk, l7I = r,and i=, then show that grad () =

A: 1. Gradf=(dfdxi^ + dfdyj^ + dfdzk^ )      2.  dxndx = n xn-1 3. r = x2+ y2 +z2

Q: In the figure at the right, WY bisects UV atY and UY bisects TW at X. For each situation, find the…

A: The figure is given as shown below: WY bisects UV at Y UY bisects TW at X We have to solve the…

Q: GIVEN: PS and LT are altitudes T. to sides LM and PM, respectively. XLPT = 4SLP. PROVE: PS = LT. W.…

A: Given that      PS and LT are altitudes to sides LM and PM respectively.     ∠LPT ≅ ∠SLP Here we…

Q: If C is the z-axis from the origin to the point (0,0, 2), then So(3j – 3k) - d - dr |

A: If C is the z‐axis from the origin to the point 0, 0, 2, then ∫C 3j→-3k→.dr→=?

Q: Find a positive angle less than 2n that is coterminal with the given angle. 19T 4

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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: In the diagram shown below segments TU and QS perpendicularly bisect each other at point R. Which of…

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Q: Solve for x if AT is an angle bisector. B. (5x+7 (3x+23) A Segments in AS

A: We have to find x

Q: in the figure below, allbllcand B is the midpoint of AC and E is the midpoint of DF. If B = 2x + 3y,…

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Q: 0(x. y) y= Vuv , then find 2. If x=, at (1,1) O(u.v)

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Q: 9. Given: E is the midpoint of AB and CD Prove: Δ4ΕC ΔΒED

A: In the given figure - E is the mid point of AB and CD. Then,AE = BECE = DE

Q: Find the points on the cone z? = x² + y? that are closest to the point (3,2,0)

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Q: du If u = x²y³ + z* where x = p+ 3p², y = peP, and z = p sin(p), find dp

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Q: AX and DY are altitudes oftwo similar triangles AABC and ADEF. Prove that AX:DY= AB : DE.

A: To prove AX/DY=AB/DE

Q: If z = In /x? + y? , find x- X +y В. 1 С. D. Vx? + y? A.

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Q: Find the points on the cone 22 = x2 + y? that are closest to the point (1,3,0)

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Q: if x? + y? = 4 then prove that = d'y dx %3D

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Q: suppos e Fx (x)= 2% , o<x<77, and 72 y = sing . find fyld) and Fyly) .

A: We are given a PDE in variable x as : fx(x) = 2x/π2 And we have to calculate the PDE : fy(y) w.r.t…

Q: Q: If the point (x, y) is equi distant from the points (a+ b,b-a) and (a-b,b+a). Prove that bx = ay.

A: Use given conditions to prove bx=ay

Q: Let r,s,t,u be the roots of the equation x* + Ax + Bx + Cx +D = 0. Prove that, if rs = tu, then A D=…

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Q: If Fu,y, z) = xzi + xyzj =ý k, find v.È %3D ........

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Q: For what value(s) of h will y be in Span{v1, v2, v3} if Vi = V2 = and y = V3 = 3 h

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Q: The norm of the set {cosh(i nn x},n E N, –-2<x<2 in the Hermitian sense is:

A: Given,                  cosi nπx, n∈ ℕ, -2≤x≤2

Q: Given f(x,y,z) = sin (3xy) + 3xyz°. Find fxzy(3,2,2). %3D

A: Given that: f(x, y,z)=sin(3xy)+3xyz3

Q: If z = u sin(u?) and u = Vt, find ) If z = x² + y², x = u+ v² and y = u² – v, find and

A: Given: (a) z = u sin ( u2 )  (b) z = x2 + y2  , x and y values given

Q: Let z = e*y, where x = Vuv and y = . Find in terms of u and v.

A: Change the z in the terms of u and v and the differentiate.

Q: Let z=x+iy  Let w=a+ib

A: To prove the equality of the two given angles

Q: If u = x²zî + yz?j – xyk and 0 = x²yz then find the value of u. (To)

A: Consider a function fx,y,z. The gradient of the function can be defined as, ∇→f=∂f∂xi^+∂f∂yj^+∂f∂zk^…

Q: Ifx.y,z are real numbers satisfying the equation 25(9x + y) +9:*–15(5xy + yz + 3:x)= 0 then prove…

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Q: as instructed, to find a second solution y,(x).

A: Given, the differential equation                x2y''-5xy'+9y=0;        y1=x3

Q: In AYZX, the midpoints of ZX and YX are M and N, respectively. The intersection of YM and ZN is G.…

A: M and N are the mid points of the side ZX¯ and YX¯, respectively. The measure of side YG is 22.

Q: Given: ZW and ZY are right angles WX = XY Prove: AXWZ EAXYZ

A: GIVEN:- LW=LY=90 WX=XY

Q: YZ is the base of an isosceles triangle; XA || YZ Z1 = 2 Given: Prove: A 2

A: Given: YZ is the base of an isosceles triangle XYZ. YZ is parallel to XA as shown in the given…

Q: Given: ZR and W are right angles, T bisects SV Prove: V

A: Box 1 Given Box 2 Angle R is congurent to Angle W Box 3 ST= TV

Q: キIND THE SOLUTIONS to THE DEFF ERENTIAL EQUATI ON y'= x? tyZ %3D メY

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Q: If z=x+iy where x and y are real, find the real and imaginary parts of:- Z+1

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Q: Let v=i+6j and w=i+3j. Find an exact number c so that w−cv is perpendicular to v.

A: The given vectors are    v = i + 6j w =  i + 3j

Q: Given: B and D are midpoints of the sides AC and CF, BD = DE Prove: BD || AF. (Use two-column…

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Q: Determine C, and C, so that y(x) = C, e²* + C,e* + 2sinx will satisfy the conditions y(0) = and…

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Q: If f(x,y,z)=exp(3x)cos(-4yz), find Vf. %3D

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Q: If z xy? +x°y, find zZxxy and Zyxy %3D

A: On doing partial differentiation we will get

Q: ue of a and c are and

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Q: Find the length of each segment. W X Y -5 5. WX 6. WY Wx= WY = MAXE 7. Points A, B, and C are…

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Q: 4. The diagonals of parallelogram WXYZ intersect at D. Which statements must be true? Select all…

A: To Determine: The diagonals of parallelogram WXYZ intersect at D.Which statements must be true?…

Q: If p is the length of the perpendicular from the origin to the X y 1 1 line += 1, then prove that +…

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Q: Given: E is the midpoint of AB and CD Prove: ΔΑEC - ΔΒED C

A: Given that: E is the mid point of AB and CD

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.