Find f by solving the initial-value problem. f(x) = f'(x) = 9x² - 8x, f(3) = 54

Q: Theorem: The Chain Rule If m(x) = E[I(x)] is a composite function, then provided that E' [I(x)] and…

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Q: Find the transformation matrix for the following figure: B'(-5,3) A(-5,0) C(-3,0) B(-5,-3) A(-3,-3)

A: Given the triangle A(−3,−3),B(−5,−3),C(−3,−6).We need to find the transformation matrix so that we…

Q: Find the maximum rate of change of f(x, y, z) = x+y/z at the point (1, -3, 5) and the direction in…

A: We will find the maximum rate of change and the direction.

Q: 3) Find the laurent series expansion for : a) z² sin ½, 02 12-2711 >0 iii) 0< 12-1\<1 2+32 d) +24 ,…

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Q: 1. Find a matrix A such that the linear system d/dt( x(t)) = −7x+2y d/dt (y(t))= −1x−8y is given by…

A: dtd​(x(t)y(t)​)=A(x(t)y(t)​)dtd​(x(t)y(t)​)=A(x(t)y(t)​)Explanation:1. To find matrix  A , we…

Q: 8. The Pinewood company produces cakes & pastriess. The company has 25 pounds of flour and 16 pounds…

A: The Pinewood company produces cakes &amp; pastries.The company has 25 pounds of flour and 16 pounds…

Q: The derivative of the [Select] of two functions is the first times the derivative of the second,…

A: Consider that have two functions f(x) and g(x). The product rule states…

Q: A natural cubic spline S(x) on the interval 0≤x≤2 is defined by S(x) | S (x) 0≤x≤1 = |S₁₂ (x) 1≤x≤2…

A: The answer is explained is belowExplanation:Step 1: Step 2:

Q: 2 3 2 4. y'+=y=—y² {y x X 2 2 } 3+cx²

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Q: 1. A pencil cup with a capacity of 16 in.³ is to be constructed in the shape of a rectangular box…

A: The volume of the cup is Material of the sides cost and the material of the base is .The  base is…

Q: Consider the ODES x²y" - 2xy + (x²+2)y = 0, x²y" - 2xy' + (x² + 2)y = x sin(x) Verify that y₁ =…

A: The ODE given is:x2y″−2xy′+(x2+2)y=0First, we need to find the first and second derivatives of…

Q: Solve for r to two decimal places. 2=e²r (Do not round until the final answer. Then round to the…

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Q: The equation e² = 10(x² - 1) has two positive roots and one negative root. (a) Find all three roots…

A: Attached solution Explanation:To find the roots of the equation  correct to two decimal places, we…

Q: 5. Express in exponential form. a) log5 625 = 4 b) log16 4: = c) loga c = b 2

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Q: Let -6 -3 M = 3 -6 Find formulas for the entries of Mn, where n is a positive integer. (Your…

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Q: 9. An investment of $15,000 earns 2.5% interest, compounded monthly. a) How much will the investment…

A: So, the investment will be worth $16,370.1439 after 3.5 years.

Q: Please answer these question using manual solution thank you

A: The first question asks what the inverse Laplace transform of (F(s)=e^{-2s}/(s+1)) is. The answer is…

Q: practice problems. Need help with prep. For f(x,y,z) = x^2 + y^2 + 3z^2 - 6z,  find all points on…

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Q: Clonex Labs, Incorporated, uses the weighted-average method in its process costing system. The…

A: The equivalent units of production for October are:Materials: 426,440 unitsConversion: 422,280…

Q: (a) Find the inverse of the matrix. Show your work. 2 4 -4 A = 0 -1 2 -1 2 1 (b) Use the inverse…

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Q: Ram Roy's firm has developed the following supply, demand, cost, and inventory data. Supply…

A: The table for the available supply :PeriodRegular time OvertimeSubcontract Demand…

Q: Construct a series solution to the following initial value problem: x(7x+3) y" 15x y' + 3y=28x2,…

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Q: xApproximate the integral |42 1/(x-1)2 dx using cavalieri-simpsons rul, and taking n=6. Compare your…

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Q: Assume that for every positive integer i, A₁ = (-i, i), that is the set of real numbers x with -i <…

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Q: The Question 7 If G is a group, isomorphisms from G to itself are called automorphisms set of…

A: We have to show that the set of all automorphisms of a group forms a group under composition.

Q: Determine the solution explicitly of the following differential equation x(y^2) y' -(y^3) =1

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Q: Let [1 A = 3 1 2 0 1 2 2 Find all vectors in the null space of A. 1013

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Q: For the remaining questions, consider the following problem description: An oil company is…

A: An oil company is considering exploring new well sites.They want to find the least-cost selection of…

Q: A3 Find the half-range Fourier cosine series expansion for the function f(x) = x(Lx), for 0 < x < L.…

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Q: Find the inverse Laplace transforms: Y(s)=(2s+3)/((s+5)^2+4)

A: 2e−5t(4cos(2t)−7sin(2t))​Explanation:

Q: Let G be a graph with vertex set VG and edge set EG. Let VC VG and E C EG. Is there always a…

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Q: A French institutional investor wishes to decrease its exposure to Taiwan. It is interested in…

A: Number of shares to be purchased = 20000Price per share in Taiwan dollar (TWD) = 150.35-150.75here…

Q: Find the B-coordinate vector up for b, relative to the basis ẞ for R² with B= b 7

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Q: Continuous Prove that f(x) = sin(x) is at X., where x is any real number.

A: Given function is continuous.Explanation: Let f(x)=sinx Let x0 be any real number. We know that A…

Q: 2. Provide a graphical (one combined) solution for the system of linear inequalities below: 3 y + t…

A: See explanation for the graphical solution.Explanation:i. 3"&gt;y+(73​)t&gt;3Solve the inequality…

Q: Question 1: (a) Consider the n-point Newton-Cotes quadrature rule n [^ f(x)dx ~ Σ wif(xi). i=1 (1)…

A: The solutions have been attached below.Explanation:Approach to solving the question: Detailed…

Q: An angle with an initial ray pointing in the 3-o'clock direction measures radians (where 0 ≤ 0 < 2).…

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Q: Suppose that S is a vector space that is a subspace of the space of functions from R to R.…

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Q: Given the following integral I(n) = f₁₁(1-2)" dr. We want to ultimately show that 22n+1 (n!)2 I(n) =…

A: The given integral is .We need to evaluate  and .

Q: x2x41 is a valid inequality O True O False

A: Given that:

Q: Solving A = Pet for P, we obtain P = Ae which is the present value of the amount A due in t years if…

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Q: Label the following as TRUE or FALSE, according to Euclid's Elements. a. 5 is parts of 45. b. A…

A: a. TRUEAccording to Euclid's Elements, one number is said to be a part of another number if it…

Q: determine whether each vector belongs to Null A where A=[1,-2,-1,0;0,1,3,-2;-2,3,-1,2]…

A: Since the result of AB  is not the zero vector, the vector B does not belong to the null space of…

Q: Please Solve this question using advance math and differential equation, pls solve manually, i need…

A: Q1-. 5 ROOTSQ2. 2+j30Q3.4Q4.some detail is missing may be initial condition.  However…

Q: Verify Stokes' Theorem for the given vector field and surface, oriented with an upward - pointing…

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Q: Reflexive. • Anti-reflexive. • Symmetric. • Anti-symmetric. Justify all your answers. Transitive. •…

A: Let's consider a few examples of elements inside the relation R, where (a,b)∈ R if and only if…

Q: - Let z = f(x, y) = x² — y. - Form implicit equation for the level curves (contours) at z = -2, -1,…

A: We need to find the implicit equations for the leve curves at .Remember that a level curve of the…

Q: Following an exponential distribution, the average lifespan of a smartphone battery is 2.3 years.…

A: Following an exponential distribution, the average lifespan of a smartphone battery is 2.3 years.…

Q: Calculate the numbers a,b and c, knowing that the line (y=2x-3) is an oblique asymptote of the…

A: For the function  the oblique asymptote is We have to find the value of  and

Q: 2+32 d) z²+24 , 0212/24

A: According to question answer guidelines we only solve one question at a time, here I am solving…