8. What is the sum of all the roots of the equation | y+ 2 2 + 3y+ = 4? y y A) -5 В) —4 C) -3 D) -2

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A: Given the system of equation is AX=0 where

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Q: 2. Solve the following Cauchy problem: Uu = Uzz -0 0, u(x,0) = x – a², u(x,0) = 4x, -00 <x < 0. %3D

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Q: 2. Cuven that 7, = -2 +ui, Z= -2i + 3 and E, - |-i. Gvaluate the followshng %3D 2 | 국 2

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Q: #S. A is a 3x3 triangular matrnx with all = 2, azz= 3, ag3=4, I will represent the 3x3 idontily…

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Q: 2. Show that c(x, t) = solves 1 ac(x, t) 2 ax ac(x, 1) ar

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Q: In rhombus R S T V RSTV, R S = 4 x − 2 RS=4x−2 and S T = 3 x + 3 ST=3x+3. Find the length of T V ‾…

A: The given dimensions of rhombus  RS=4x−2 ST=3x+3

Q: A natural cubic spline is defined by Sa,(x-1)' +b,(x-1)² +c, (x - 1) + d, S(x) =- if 0sxs1 (x- 1)' +…

A: Step:-1 Since, we know for cubic spline S(x)=S0x=a0x3+b0x2+c0x3+d0…

Q: 1. Use the Intermediate Value Theorem to prove that the equation 3x - 4x? = 3 is solvable on the…

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Q: (b) In(2x2 + у — 23) %3D х

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Q: prove using the IVT. √c +√c + 2 = 3 has a solution.

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Q: 6. Use the Side-Splitter Theorem to find z given that NQ is parallel to OP. 2.5 5 M O 4 3

A: We have to find out

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Q: Find the values of a, b, c, d, e, f, g and h such that ax, S(x) = { 6(x – 2)³ + c(x – 2)² + d(x – 2)…

A: GivenS(x)=ax3,0≤x≤2b(x-2)3+c(x-2)2+d(x-2)+e,2≤x≤3f(x-3)3+g(x-3)+h,3≤x≤4such that S(x) is a natural…

Q: b) By using De Moivre theorem, calculate in the form of a + bi: 4. i) (VZ – iv2)* | ii) (1– i)6

A: Given (2-i2)4 &amp;   (1-i)6

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A: Given  4y'' + y' = 8y

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Q: 2 Prove that the triangles are Similar. 3. 12 18 1.5 F 12 -A ABC~A DEF by SSS~ -AABC~AEDF by SSS~…

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Q: 12) Show that D- d-del is shortest distance betueen a x- by +c2.of ; and ax+by tcz= dz?

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Q: If x,y,z are real numbers satisfying the equation 25 (9x* +y° )+9z²-15(5xy+yz+ 3zx )=0 then prove…

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Q: Sketch the set of points satisfying: |z - 1 + 2i| = |z + 3 + i|

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Q: In R', the point (1, 1, 1) does not belong to the cylinder x + y = 2. Select one: True O False

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Q: W Given: OWXYZ with diagonals WY and XZ Prove: 21 = 22 2

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Q: 3. Prove that R² is Hausdorff. Is R²T3? Is R² T4?

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: Let S,(x) = 2x³ – 3x² + 3x – 4, 0<x < 1, S,(x) = x³ + b,x² + c,x + d,1 sxs 2. Find b,, C1, d, that…

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Q: (4+38)-(9 -J2) Rectangular ?

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Q: Use the inclusion-exclusion principle to find the number of solutions to the equation x + y + z =…

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Q: If u, v are given unequal numbers anu (un-1+ Pn-1), vn = V (u –1 Vn-1), where n2 2 , %3D Un %3D 2…

A: Given

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Q: The formula in cell C2 is = A$2. Auto fill is used by dragging C2's auto fill box across to D2, E2,…

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Q: Prove that dv du 2 – u? + v² 18

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Q: 3. y" + 7y' + 12y = 2e5* у(о) %3 о, у'(о) %3D2

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Q: The distance from (7,-8, 5) to yZ-plane is OA. 138 O B. 5 OC.8 OD. 89 O E. 7

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Q: 2- (a) Using [X, P] = ih, show that [X, PJ = 2ih& and [&, Þ³1= 2ihP. (b) Show that [, p2 = 2in(in +…

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Q: ven: AABC = AYXZ, MZXYZ = 75°, MLACB = 65°, AB = 10 cm and XZ = 12 cm. your complete solution. of…

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Q: consider Cea) y'= */x . Classify this eg natiun wi th resput neous. For each tu erch entegory,…

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Q: Sketch the solid described by the given inequalities. Oses n/2, r szs4

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Q: 2. In OABCD, ZA = x, ZB = 2x +60. ZD = Draw a sketch to help you.

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Q: I. Solve using De Moivre's Theorem. Given that z is not real number and z = 1, show that w = z-1 z+1

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Q: Find w a + bi = Jz, where a and b are real numbers. VE %3D 24+10i

A: It is given that w=z, where z=24+10i. Let w=a+ib where a and b are real numbers. w=z Substitute…