Prove that (ij) d dx² (log √√g).

Q: 4X у - 16 y = 19.2 е + 600 бос Х , усо) =ўс - о -ЧХ 4X 4X Ans. Y= 22e +he +2,4хе - X Че

A: Given,            y''-16y=19.2e4x+60ex; y(0)=y'(0)=0

Q: Use the Composite Trapezoidal rule with h = approximate the improper integral 1 sin 2x dx to

A: Given,        ∫01sin2xx3dx=

Q: Solve the following ODES by Inverse Operator method. 3 -X 2X (D²³+1) y = 3 +2²² +5 ex -X Ans: y = ₁…

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Q: Find the solution of the initial value problem 4y" - 5y + y = 0, y(0) = 4, y'(0) Then determine the…

A: The given initial value problem is ; 4y" - 5y' + y = 0 ,   y(0) = 4,  y'(0) = 14 (i) We have to find…

Q: Let A € Mnxn (R), & be the standard basis for R", and B = {₁,...,n} be another basis for R". If P is…

A: Given, a matrixA∈Mn×n(ℝ). Given, ε as the standard basis ofℝn and  β={v1,v2,...,vn} as another basis…

Q: Define the binary operator by: a ob = 5a + 5b Find each of the following: a. 4 3 = b. 808= c. 304 =…

A: Given a binary operation "∘" defined by a∘b=5a+5b. a We have to find the 4∘3 Use a∘b=5a+5b…

Q: Why we say lie to our own self

A: question- why we say lie to our self? answer 1) To avoid getting punishment. 2) To project another…

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Maximize…

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Q: A. Match the following differential equations and their type. The differential equations may be…

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Q: (a) The function f(t) is defined as f(t)= t (i) Sketch a graph off (t) for 0≤ t ≤ 2π Ⅱ-2 π T 1 2…

A: Ii) The graph of the function is shown below.

Q: An area is bounded by the curve x ^ 2 + 10y - 1600 = 0 and the x-axis . Find the moment of inertia…

A: 1st we need to identify the region R bounded by given curve and x-axis .  Then for moment of inertia…

Q: Prove the following by mathematical induction. V4 ≤NEN, 2n<n!.

A: We have to prove ∀ 4⩽n∈ℕ,  2n&lt;n! using mathematical induction.

Q: The function y = log2x is transformed into the graph of y = log(x + 2) - 3. a) Describe (in a…

A: The function y = log2x is transformed into the graph of y = log2(x + 2) - 3. a) We have to describe…

Q: z^2(p^2+q^2)=x^2+y^2

A: Given partial differential equation is z2p2+q2=x2+y2. We have to find the complete integral of the…

Q: Finding the Solution of the Differential Equation (2x + 5)² y¹¹+3(2x+5)y'-5y=0

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Q: 9. C wants to see all eight directions, he travels clockwise and he moves from one direction to…

A: Given: C wants to see all eight directions. He travels clockwise and he moves from one direction to…

Q: explain

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Q: Margaret Hillman invested $8,000 at 1.4% compounded quarterly for one year. Find the future value…

A: The future value of an amount P invested at a rate of r% compounded for a period of n times is given…

Q: Consider the equation f(x) = x³ – 2x² − 11x + 12 on the interval [1.78, 8.25]. (a) Find the minimum…

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Q: The diagram below shows the graph of f(x) and its first and second derivatives. By using the graph…

A: As per the question we are given the plot of three curves denoting as : Curve A Curve B Curve C…

Q: Given a relation matrix, write the relation R in set and determine whether it is reflexive,…

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Q: Given n ≥ 3 circles on the plane, satisfying • Each two circles intersect at exactly 2 points; . No…

A: Given: for n≥3 circles on the plane, every two circles intersect at exactly two points and No three…

Q: Find the area between the curves. x = -5, x=2, y = 3x, y = x² - 4

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Q: 3. Prove by contradiction, that if x and y are odd integers, then there is no integers z such that…

A: solution : let x and y are odd integers . Therefore , we can write x=2m+1 and y=2n+1 for some…

Q: Q2) Evaluate the following integral (use Integration by Parts) cos³ u+5 Su².- 1-sin² u du

A: Introduction: The method of integration by parts is the process to integrate a function that is in…

Q: Determine the Taylor series about the point X for the given function and value of x- f(x)= In (1 +…

A: We find required Taylor series.

Q: Suppose that y^-1= 7x ^-2/6z^-1 Which equivalent to y? A. 6x^2/7z B. 7x^2/6z C. 7z/6x^2 D. 6z/7x^2

A: I have given the answer in the next step. Hope you understand that

Q: When estimating distances from a table of velocity data, it is not necessary that the time intervals…

A: Let us solve the given problem in the next steps.

Q: (a) y || 8 x = 2, y = 0; (b) y = 7-x², y = 3; about the line x = -2. about the x-axis.

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Q: #4 for the function f(x) = 2x²-3x³-7x state a) degree (even or odd) b) name of polynomial type sign…

A: # as per the guidelines we are entitled to solve maximum three subparts at a time, please resubmit…

Q: Show your complete step-by-step solution. Differential Equation: 2ss" + (s')² = 0 General Solution:…

A: The solution of the differential equation is defined as the function that satisfies the differential…

Q: Let V denote the inner product space of real 2 by 2 matrices endowed with the inner product (A, B) =…

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Q: Question 3. Find the solution of tx' - x = t²√√x when x(1)=0

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Q: Problem 2 Write the sentence with variables p, q, r and connectors, A, V for the following two truth…

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Q: Hi I will upvote if right! Please determine if these are linear or nonlinear. Thanks! y(t) = pi-x…

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Q: x³y" - 6xy +12y = 20x¹, x > 0, y(1) = y(1) = 5, y"(1) = 14

A: We have to solve x3y'''-6xy'+12y=20x4, x&gt;0, y(1)=83, y'(1)=503, y''(1)=14

Q: Let A(x) represent the area bounded by the graph, the horizontal axis, and the vertical lines at t =…

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Q: S&L Financial buys and sells securities expecting to earn profits on short-term differences in…

A: Trading securities are recorded in the books at their fair market values. Cost of Coca-Cola bonds =…

Q: -t 9-y" + 2y +y = 3e¯t

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Q: Define the binary operator # by: a#b = the smaller value of a or b.; Find each of the following: a.…

A: Here , a#b is defined as smaller value of a or b

Q: A spherical vector field is given by F(r,0,0)=2r cos(0) êr + 3r sin(0) ê +0(π- 0) ê. i) Compute the…

A: It is given that Fr,θ,ϕ=2rcosθe^r+3rsinθe^θ+θπ-θe^ϕ. Thus, F1=2rcosθ, F2=3rsinθ, and F3=θπ-θ.

Q: By power series method, Solve the following ODES & xý - (x+2) y = - 2x² - 2x Ans: y=c₂x²³e²+2 x хе

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Q: Find all sollutions in integers of 34x+8y=6

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Q: Find the Wronskian of two solutions of the differential equation t²y" - t(t-3)y' + (t− 2)y =0…

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Q: Solve the initial value problem y = 8eºt + 8eºt ○ y = eºt ○ y=e" + eº ○ y = 8te9 ○ y = teº ○ y =…

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Q: Minimize: Z = 3X₁ + 5X₂ + 5X3 + 4X Subject to: 8X₁ + 2X4 ≤ 100 4X2 + 3X3 = 90 X₁ > Q

A: The given LPP is  Minimize Z=3X1+5X2+5X3+4X4subject to 8X1+2X4≤1004X2+3X3=90X1,X2,X3,X4≥0 Add the…

Q: 5. Vn EN, Prove the following by mathematical induction. Σ(2n-1)² = n(2n − 1)(2n +1) 3 i=1

A: Let p(n) be the statement,   ∑i=0n(2i-1)2=n(2n-1)(2n+1)3

Q: Solve the following ODES by Undetermined Coeff D Ş 17 4X y - 16 y = 19.2 € + 60e, y(a) = ý (0) 1 -4X…

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Q: Solve the following ODES by Inverse Operator method 1.2 ý - 2y +y = e sinx X X X Ans: y = ce+c₂xe -…

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Q: Q5. Given f(x): (R, ||) → (R, ||) 3x + 2 if x > 2 f(x) = 5r−1 if x < 2 (a) Let {n} = {2} be a…

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