Show that if n is a positive integer, then k+4 n(3n +7) k(k +1)(k+2)¯ 2(n+1)(n+2) k=1

Q: o He are going to invest $100,000 in account that Pains 7.5% 00000 at निगाननी interest for 4 S4…

A: Let us solve the compound interest  problem in the next steps.

Q: 1 L(5x)sin dx dx+ J, (5x – 15)sin| 1.5 1.5 1.5

A: We will use integration by parts here  ∫u.v dx=u∫v dx -∫dudx∫v dxdx

Q: + 2x - + (1 – y²) - dx²y Show that the equation dx2 dy? 2 + y² < 1, parabolic on the boundary is…

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Q: Solve the system +x2 +3x3 1 | 3x1 +2x2 -3x3 3 x2 +s 3.

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Q: find the talor Palynomial Pa), Contered ot co tor

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Q: d'r =-32k, fferential equation: dt2 dr = 8i +8 j, r(0)=100k. dt %3D tial conditions: It=0

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Q: The eqmivalance cluss f the element o is denuled by [o] , Thuy bý defination. %3D - {zez |…

A: We have to explain the steps.

Q: Prove 0 + 1 + 2 + 3 + ...+ n = (n(n + 1))/2

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Q: You want to purchase a house in 10 years. You estimate the cost will be $184,500.00. You want to…

A: Cost of house = $184,500.00 Down payment = 20% = 20% of 184500.00 = 20×(1/100)×184500.00 =…

Q: Sketch a continuous graph with the following conditions f'(x) 0 if (-4, 4) • f"(x) > 0 if (-0o, –1)…

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Q: s function h(x), we have

A: Repeated

Q: Let the region R be the area enclosed by the function f(x) = 2x and g(x) = 3x. If the region R is…

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Q: Sx, ifx 1 f(x) = Show that f is R- integrable.

A: R- integrable function

Q: what notation is use to distinguish the sequence?

A: Notation of sequence is as follows:

Q: equa cions (where no initial values are given, find the general solution). (a) y" – 2y' + y -8 cos…

A: We have to find the general solution of the differential equation y''-2y'+y=-8cosx+8sinx .

Q: Convert using a shortcut: 11100011011two to base ten.

A: 11100011011two= (1×210+1×29+1×28+0×27+0×26+0×25+ 1×24+1×23+0×22+1×21+1×20)ten…

Q: f6) = #(1-|). f(x) -L < x < L

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Q: 24. Let f be an arithmetical function (not ne multiplicative arithmetical function g s S fl(k,n)) =…

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Q: (b) Evaluate the given trigonometric integral sin r dx (x² + 1)(x² + 9)

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Q: Describe the graph of the equation. r = 10 sin 17ri+ 10 cos 17t j O Itis a circle of radius 10 in…

A: Solution :-

Q: Our aim is to write gcd(200,113) as linear combination of 200 and 113, Below is the table related to…

A: See answer below.

Q: Find the Sof (x, y,z)dV A. Q = {(x, y, z)|(x+y² +z 4 and z = x+y, f(x,y2) = x+y} B. Q= {(x, y, z) (x…

A: We will use the basic knowledge of integral calculus to answer this question correctly and…

Q: Give the following system (M). x = 2(mod 13) x = 1(mod 14) x = 3(mod 15) x = 2(mod 16) Which among…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: A population of middle school students contains 160 sixth graders, 180 seventh graders, and 140…

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Q: A 13ft ladder rests against a vertical wall. If the bottom of the ladder is sliding away from the…

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Q: 2. (а) . State whether the divergence of the vector field shown below is on average positive,…

A: consider the two vector fields. At any particular point, the amount flowing in is the same as the…

Q: Use the method for solving Bernoulli equations to solve the following differential equation. dx X…

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Q: Q2 Calculate the power series solution of the differential equation of y' – y = e* up to the five…

A: Powers series solution of the differential equation

Q: Find the g.c.d. in Z [i] of 2 and 3+ 5i.

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Q: 17. prove that Edln H(n/d)7 and σ(n ) σ(n) Σ %3D

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Q: Solve the following differential equation y"+2y'+y=x-1 Select one: -2x +x-3 O a. YG.S=…

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Q: Find the product of the two matrices. Give me two answers at each number letter for the A.B and B.A…

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Q: Grinsen banmutation (92 3) 965)(1 487) O Expruss as a puoduct of diejoint cycles O what or der of…

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Q: Civen tz f(x,y) = J 36-9x=y

A: If the graph of z=f(x,y) is sliced by a plane: z=c, then the two dimensional cross-section obtained…

Q: paper 2 4. INDICES AND SURL 2019 N FUNCTIONS + INDICES AND SURDS Q2 Do not use a calculator in this…

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Q: 4) Jamila runs a grocery store that sells bulk coffee bean blends by the pound. She wishes to mix 40…

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Q: Let S be the quadric with equation 36x² – 4y² – 9z² – 36r = 0. (a) Classify the graph of S. (b)…

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Q: in R°sketch the graph of the cylinder x = (y – 2)?

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Q: 3260° j2 (1 + j) 2430° 2 1 Evaluate j5

A: Let us find the determinant

Q: 7. Calculate the area of the portion of the sphere x +y +z2 = 49 between z= 2 and z=V2. 2 %3D OA.…

A: Surface area of the surface given by z=f(x,y)  A=∫∫D1+fx2+fy2dA where  D is projection of surface on…

Q: [1 2 3] 1. Let A = |1 1 2 Lo 1 2] a) Find A-1. 1 0 0 1 -1 1 3. Given A = |1 -1 1 lo 1 0 -1] b) Write…

A: To find  The inverse of the given matrix A.

Q: b) Tshepile Wool Company (DWC) operates a large farm on which sheep are raised. The farm manager…

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Q: Q) Fit a second-degree parabola for the following :data 4 3 2 1 0 x 6 5 4 3 1 Y Using Y=a+bX+cX2 Y=…

A: The regression analysis is done to fit a dataset into an equation. A graphing utility can be used to…

Q: The equation 21x = 49 (mod 77) has: O no solution modulo 77 O only 7 non-congruent solutions modulo…

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Q: Let C denote the unit circle centered at the origin in C. 1 + z + z°* dz, 2πί Then where the…

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Q: 3. An object exhibits simple harmonic motion with a time period of 0.94 s, a maximum acceleration of…

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Q: 22) Defermine oue tuer tue serieg ntl (-1) conditHonelly Σ conneryes n=1 or obsolutely. or alinery…

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Q: Let n be a positive integer. Which among the following statements is true? n + 1 and n + 2 are…

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Q: Find the product of the two matrices. Give me two answers at each number letter for the A.B and B.A…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: f (1, 2) = 3 and the derivative of the function f in the i + j direction at the point (1, 2) is 0.7.…

A: Given that f1,2=3 and derivative of the function f in the i+j direction at the point 1,2 is 0.7. We…