e is commatative that the scaler product Prove between ?- 2î -8ĵ - 2k and b= it 51-3k

Q: . neN' K Ë i n(n +1) لكل 2 j=1

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Q: Write a in the form a = arT + aN N at t-0 for R(t) = t?i + (t +); + (t - }c")k

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Q: a) 1 -dr+ 1 dr = In a, find the exact value of a. Given that V16+9x? V9+4x?

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Q: Describe the error in using the Pythagorean Theorem c2 a2+b2 10 x2 x2%D x2 =7 x =V776 %3D X 27.9 The…

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Q: 10e? dz by residue theorem, where C'is the contour z| = 2 1:4 + 52ª Evaluate

A: Complex integration

Q: aF1 F. dr = -3 in D, use Green's Theorem to determine Jc, aF2 Referring to the figure, suppose that…

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Q: sy? is a real part z = x+ iy is a ce action v is

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Q: Determine constants a, b, c and d that will produce a quadrature formula f (x) dæ z af (-1)+bf (1) +…

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Q: & 28 root f x+ px'+ q* + rz0 One 3. equals the roob . Prove that px + 9x + r=0 * the ts other sm 3 +…

A: Given that, One root of polynomial x3+px2+qx+r=0 equals the sum of the two other roots. We need to…

Q: 2 x 9 = +9 dy %3D

A: As per our guidelines only one question can be solved. The solution is given below for the 1st…

Q: In r e) I/1+ (In z)² dr

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Q: 6e dz by residue theorem, where C is the contour |2| = 2 Evaluate 524 + 25z

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Q: 5. Find which of the following quadrature formulas are of the interpolatory type. Show your…

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Q: Q2: Let XN B(4, 0). Let H, : 0 = and H : 0 = . Using the definition of BCR, find (1) a BCR of size a…

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Q: Evaluate the t resiake theerem 2 allowing real infegrals by dX ans : こ。(X+a?)2 493 • I= F ans 8…

A: Our guidelines we are supposed to answer only one question. Kindly repost other question as the next…

Q: c) Show thiat det a q² -k-1)(61)-) I <a<b %3D

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Q: tane de sece 4 Q10 3 7 a) 2-2 b) (2 1) c) 24-2 d) (2 -1) 1/3 1/5 5/4

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Q: 8 A baker determined the annual profit in dollars from selling pies using p(n) = 52n-0.05m %3D where…

A: Given : Pn=52n-0.05n2

Q: e) Use (; a²p Find the value of Vm at which both of these deriva- T to find aVm tives are zero.

A: I will present e bit for u in the last step....inorder to show u the steps clearly of e bit , I have…

Q: Q3/ Find length of the cardioid r-a@3from 0 = 0 to 0 = n %3D

A: The equation of the cardioid is r=aθ3. The length of the cardioid is given by the formula,…

Q: Using Simpson's rule with n=2, I(x³ + 1) dx = Select one: а. 22.1 b. 22 c. 22.2 16 d. 22.01

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Q: Prove this equation by deriving F(x, t) =X(x) Y(y). Please show full steps OF OF 2. +2x- =D0 Ditebak…

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Q: y"+9y=7e^x find general solution

A: Here given  y''+9y=7ex or D2+9y=7ex Thus First, find the complementary solution as Put D=m and…

Q: Find the length of the curve. x = 4r°, y = 6t, 0sts V8 < = 3 The length of the curve x = 4t°, y 6t…

A: Givenx=4t3  y=6t2   where t∈[0,8 ].

Q: (10n + 19)° (12n – 4)°

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Q: help proving this  (m−n)(p−q) = (mp+nq)−(mq+np)

A: consider LHS= (m-n)(p-q)= m×p+m×(-q)-n×(p)-n×(-q)=mp -mq-np+(nq)

Q: A PQR is similar to A XYZ. Drag the answer into the box to match each part of A PQR with the…

A: We have given ∆PQR  and ∆XYZ are similar.

Q: 2 HA=A-tj + (t – 1)k, B = 271 + 6Ak, find (a) (A - B) dr %3D

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Q: B) Find real numbers x, y, z for the identity below 2xi + 2yj- 2i + 3j + 2k = 3i -j+ zk

A: (2x-2)i+(2y+3)j+2k=3i-j+zk On comparing both sides

Q: Find the I-coordinate e a Hhe ocal monimeno 07 local makimum of 7 qunction n 7ux)=e? (2x²+3x), x ER

A: Second derivative test : Suppose f is continuous  and differentiable function at x=a where f'a=0 and…

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Q: Please find cross product c=a x b, where a= and b =. For c=16i+0j+?k, please enter the missing k…

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Q: s+2 Use Convolution theorem to find L-1 'G2+4s+13)².

A: We will find out the required value.

Q: Q2. (a) Find the overlapping area of two equations also give its geometrical representation u + p =n…

A: Given functions are                                                       u2+v2=nu2+v-n2=1n=482…

Q: d K, d1 + d. +... + K, 2 n K, K, 1 n

A: Let d=d1+d2+....+dn From Cauchy Schwarz inequality , we have- d1k12+d2k22+.....+dnkn2…

Q: Write a in the form a = arT + aN N at t-0 for R(t) = t2i + %3D (t+r) + ( -r°*

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Q: Let a - ci +j and b- 9i + 12j. Find c so that the a %3D Round your answers to four decimal places…

A: Use dot product

Q: Q3/ Find length of the cardioid r=a03from 0 = 0 to 0 = t %3D

A: By using length formula we find the length of given cardioid as follows :

Q: 4 +V5 B X- (4 + V5)cm. AX is The diagram shows a trapezium ABCD in which AD = 7 cm and AB =…

A: In trapezium ABCD, AD=7cmAB=4+5cmAX⊥DCDX=2cmXC=xcm Area of trapezium ABCD=155+2cm2 We will find an…

Q: 6e? Evaluate dz by residue theorem, 9z4 + 45z3 where C'is the contour z = 2

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Q: 2e Evaluate dz by residue theorem, where Cis the contour 2 = 2 c 9z4+45z3

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Q: a) (dx pcG) V ZxqG))3x (pG) V96), Pore this bis the converse of t he implication above correct!

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Q: et a be a real number. Evaluate 3 (ax° + 1) dx 256a + 4 7 256a

A: Here we have to evaluate;  I=∫-22αx6+1dx

Q: Q2. (a) Find the overlapping area of two equations also give its geometrical representation: u? + v?…

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Q: Use the algebraic definition to find ix w if i = 2i + 2j – 3k and w -2i +j- 3k. - %3D i x w =

A: Given: v=2i+2j-3k And, w=-2i+j-3k

Q: (b) Find the concavity, point of inflection, of f(u) = eln) Where n is 482. Also explain it…

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Q: C. Prove the Converse of the Hinge Theorem. Given: AB = DE, BC = EF, and AC > DF Prove: m1 > m/2

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Q: Prove: If r + 1, then n-1 I – 1 j=0

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Q: Determine la solución general de 2 y"- 3 y' +4 y = 0.

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Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.