olve the following Initial Value Problem: y" + y-6y 0, y(0) = 2 y (0) = -1. and %3D %3D %3D

Q: [a, b, ci] [a2 b2 c2] A, = [d2 e2 2] a3 bz C3 Az = \ds es fal If A, = and are any 2 x 3 matrices,…

A: Here we have to prove the given operations.

Q: Which of the following yields the value 3187 (8r+7y)dudy (8r+7y)dydr (8r+7)dudy O none of the oices

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Q: In x²/25+ x² dx , we let x=5sine. A True

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Q: Let r(t) = (t', 1- t, 4t). Calculate the derivative of r(t) - a(t) at t= 4, assuming that a(4) = (9,…

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Q: +1

A: I have stated the used formula in the solution

Q: Q5) Find volume of body bounded by z? + y? + x? = 9.

A: Let's find.

Q: Evaluate fs 2°ds O a. 2*(sln2 - 1) (In2)2 O b. 2(słn2 - 1) (In2)2 O C. 25 - 1) In2 O d. 2° (+ 1) +1)…

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Q: Solve the D.E dy – (2x/1- y2)dx = 0

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Q: 3. Given the functions f (x) = a? - 4, g (x) = Va+ 4, and h (a) = %3D %3D | x + 2 find the DOMAIN of…

A: Domain is the set of all values  for which the function is defined.

Q: Q2) Convert the polar functionr= tan20 to cartesian.

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Q: Find the speed at the given value of t: r(t) = (e4, -9,4t-1),t = 4

A: We know that V(t)=r'(t)Here r(t)=<et-4,-9,4t-1>Differentiate…

Q: Find the volume of the solid that results when the shaded region is Y = x revolved about the…

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Q: Evaluate the following integral using Trigonometric Substitutions Method: 1- x dx y =

A: Let's find.

Q: A particle is moving in space and its position at time t is given by r(t) 4(cos t)i+ 4(sin t)j+ /²k,…

A: Given problem:-

Q: x2 – 125 lim x→-5+ x2 + 4x – 5

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Q: Evaluate the following integral using Trigonometric Substitutions Method: 1- x dx y =

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Q: There are 150 students in the marching band, and 30 of them play the trumpet. Which number line…

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Q: x- 2 For the function f(x) = x-5 a. the graph of the function is until x = 2 only. O b. the graph of…

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Q: 3 3 25x ? 2 7x3 3 16х5 dx 5

A: use property of integral to solve this.

Q: 4 r4-y Evaluate triple integral , S S dz dy dx -2

A: We have to evaluate the triple integral  ∫-22∫x24∫04-ydz dy dx.

Q: Describe the largest set S on which it is correct to say that f is continuous хx* + ху — 5 а. f(х,…

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Q: Q4) Find plane area inside the polar function r = 2 and outside polar function r = 2 sin (* + 0) in…

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Q: Give the VALUE only. No need to include the unit. * A chemical manufacturer sells sulfuric acid in…

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Q: 10re", a 0 (a) Identify all critical numbers of f. (b) Determine the extreme values of f on [-2, 2].…

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Q: 1-y -x. dy at the point (0,1) given the curve dx Find the value of 1+y

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Q: 6.x'y 10. lim (х, у) — (0, о) 2.х* + y*

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Q: 4. Find the area of the region that lies under the graph of f over the given interval. a. f(x) = 2 -…

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Q: a. Neither I nor II

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Q: Ob.2 amom +C Evaluate +Vrdx Oa.5 2 5 3 2 Oc 2 wn +C Od 3 +C 2/3

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Q: Q14. The value of lim et3 -x tan x-cos x x2 is? -

A: use l hospital rule for solving for the integral.

Q: To find the distance across a river, a surveyor choose points A and B, which are 232 m apart on one…

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Q: Differentiate the following function and factor fully. g(x) = (2x – 1)*(2 – 3x)“ |

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Q: Cha invests Php5,000 in an investment that earns 6% per annum. How many complete years does it take…

A: Given Cha invested(P)= Php5,000Rate of interest (R)=0.06Time (t)=?Amount (A)=Php 10,000We know that…

Q: Problem 1: Evaluate the following definite integrals. Sx(x2 + 1)V4- 2x2 – x dx -dx

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Q: find the rational number represented by the repeating decimal. 0.451141414

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Q: 3 -1 3 0 Given F = show that: 19. –F" = (-F)" 20. (F")" = F m 2.

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Q: Helene invests Php 5,000 in an investment that earns 6% per annum. How many complete years doe it…

A: Topic = Algebra

Q: Which of the following is the general solution of the differential equation y" - 36 y=0 ? O…

A: y''-36y=0auxillary equation is given bym2-36=0(m+6)(m-6)=0m=-6,6m1=6 , m2=-6

Q: Determine the slope of the tangent to the curve y – 3.xy +2x =4 at the point (3, 2).

A: curve :  y2-3xy+2x2=4differentiating w.r.t…

Q: e1/n n2 n=1

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Q: A line with positive slope passing through (-1, 1) and intersects the parabola y = x² at the point P…

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Q: (x – y)dr + xdy = 0.

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Evaluate: / y6 sech(e7hny) tanh (e 7Iny) dy A) -sech(y?) +C 7

A: We know that    elnx=  x we use above result to determine the integral

Q: How/ Find the General solution for dhe following O e %3D

A: The given differential equation is;  e2x(dy+2ydx)-x2dx=0. Repost the next questions.

Q: Which of the following limits has a value 0? In x I. lim II. lim X-0 e* Neither I nor II. O l only…

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Q: 12x 3 3 15 12 x4

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Q: dz ins- , if we let y=Vz+4, then the new integral becomes z+4 -2 у-2 True B False

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Q: a. f(x) = 4x + 11 find:f'(-2) %3D b. f(x) = 2x2 - 5x – 3 find: f'(2) %3D

A: derivative

Q: Q4) Find plane area inside the polar function r = 2sin E- 0) and outside r= sin -0) in first…

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Q: sec'x tan?x dx, can be evaluated by using trigonometric transformation. A) True B) False

A: Let's find.