Why is (subtracting two positive numbers that are each less than 1), less than or equal to (1 minus their product)? (r-s) less than or equal to (1-rs)

Q: 3: Using Laplace Transforms, find the solution of the initial value problem: d²y dx² +9y 9. sin(t).…

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Q: A graph has 25 edges. The sum of the degrees of all the vertices of this graph is Select one: a. 25.…

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Q: Given U = 2xy, Px = 3, Py = 4, and I = 90 Use the Lagrange multiplier method to find the optimal…

A: Given :          U=2xy, Px=3, Py=4, and I=90 We have to use the Lagrange multiplier method to find…

Q: 1 (b) Find Fourier cosine transform of f(x)=< -1 <x< 0<x</

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Q: An Suppose an >0 and a diverges. Prove that - n = 1 n=11+ an ∞ an an contrary suppose Σ converges,…

A: This is a problem of sequence and series.

Q: Determine the values of r for which the differential equation y" + 7y +12y = 0 has solutions of the…

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Q: 2. Determine the values of ʼn and h required to approximate fx²sin (-x) dx to within 10% using the…

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Q: = —y (2 — y). Draw a direction field for the differential equation y' : Based on the direction…

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Q: 11. A tank contains 100 gallons (gal) of water and 50 ounces (oz) of salt. Water containing a salt…

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Q: The cost, in thousands of dollars, of airing X 30-second television C(x)=40+ 3,000x + 0.064x² Your…

A: Introduction: The second derivative test is a method for determining the absolute maximum and lowest…

Q: = ²/²/²(e² + e^²³) 3. Obtain the Maclaurin series for cosh x using the fact that cosh x = -

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Q: In what directions is the derivative of f(x,y) = xy + y2 at P(6,7) equal to zero? Select the correct…

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Q: tandard form

A: Introduction: The center, vertices, and asymptotes of a hyperbola totally determine its graph. When…

Q: sin(2x³) x² 11. Approximate justify your result. within 0.0001 if x = 1/3 using its Mac expansion…

A: Solution: Given function is, f(x)=sin2x3x2 sin(x)=∑n=0∞-1nx2n+12n+1! f(x)=∑n=0∞-1n2x32n+12n+1! x2…

Q: L-1{6(s+1)} 54 a. 3t² +t3 b. 3t³+ t² c. 6t² + ³ C. d. 6t³ + t² لاح

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Q: L{5cosh2t-3sinht} 5s 3 a. s²-4 5s s²-1 3 b. s²+4 5s s²-1 3 C. s²-4 s²+1 5s 3 d. s²-4 s²-1 - +

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Q: Find a closed form for the generating function of the sequence an n3" (n ≥ 0). Clearly show all…

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Q: e moves along line segments from the origin to th F(x, y, z)=z²1+ 3xyj + 2y²k. work done.

A: In this question, the concept of line integral is applied. Line Integral The function to be…

Q: Use the chain rule to find where First the pieces: End result (in terms of just t): d = 江 西 血麵| 2 =…

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Q: dy Write down a differential equation of the form dt solutions all approach y = as t- →8. y' = = 78…

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Q: es. If the individual course and the  order in which the courses are selected does not matter, then…

A: Given as,  5 trails and each has 12 courses.

Q: 6. Please Solve the Dirichlet problem for a disc of radius R centered at the origin. The boundary of…

A: As per the question we have to first define the Dirichlet problem for a disc of radius R in polar…

Q: 0 shares of

A: Given as, Dividend declared = 18,000,000 Number of preferred shares = 40,000 Dividend per preference…

Q: 1. Solve the following Linear Systems of Equati 1.) 6x + 2y4z = 15 -3x - 4y + 2z = -6 4x - 6y + 3z =…

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Q: 12. Z z²+1

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Q: Show that the substitution x=e, y=e converts the equation Hu дzu ди ди +2 +x дх2 дуг Әх ду into the…

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Q: rgence. If result is converg

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: 3. Use the definition of Taylor series to find the Mclaurin series expansion of f(x) = ln(1 + x²).

A: Given function is  fx=ln1+x2

Q: 3. Find f'(x) and f"(x) if f(x) = ln x+2 cos³ z.

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Q: 4. A spherical balloon is to be deflated so that its radius decreases at a constant rate of 15…

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Q: There is a country with six states. There are 300 states in the legislature, and the populations of…

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Q: For the following differential equations, - Classify whether the equation is ordinary or partial…

A: The differential equation involving one dependent variable and more than one independent variable is…

Q: 3. Use the definition of Taylor series to find the Mclaurin series expansion of f(x) = n(1+x²).

A: Taylor series for a function f(x) defined at a is given by f(x)=∑k=0∞f(k)(a)k!x-ak…

Q: Identify the graph of the |f(x) = 2, over the interval 0 < x < 27 and has period 2 f(x) -2π & # 70…

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Q: 3. dy/dt = e e- -∞ <yo <

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Q: Find a closed form for the generating function of n3" (n ≥ 0). the sequence an Clearly show all…

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Q: Phase Line Diagrams. Problems 1 through 7 involve equations of the form dy/dt = f(y). In each…

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Q: b.) Evaluate the following integral: !!! * xyz dv if S is the region bounded by the cylinders x² +…

A: Use the following formulae, to obtain the solution. a-b2=a2-2ab+b2∫Cfxdx=C∫fxdx∫xndx=xn+1n+1+C Where…

Q: Find a differential equation that corresponds to the given direction field. Consider differential…

A: To find the differential equation that corresponds to the given direction field :-

Q: 13. Pharmacokinetics. A simple model for the concentration C'(t) of a drug administered to a patient…

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Q: QUESTION 3 Let V be a vector space and let u, ve V. IfW= (au+Bela, ß e R), prove that W is a…

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Q: Newton's law of cooling states that the temperature of an object changes at a rate proportional to…

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Q: If r is real and w complex, what is (w-r)(conjugate of w-r) equal to?

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Q: 4. The boundary of a field is a right triangle with a straight stream along its hypotenuse and with…

A: Solution:- It is used to relate the three sides of the right-angle triangle, and the theorem can be…

Q: 4x - 10 Let f(x)= 1-(2x-5)** a. Find the Taylor series representation for f about x = 2.5 that is…

A: As per the question we are given a function f(x) and we have to : Find the Taylor's series…

Q: Note: The formula for logistic growth is given by PN+1 = r PN(1-PN). A population grows according to…

A: Solution : Given, Formula of logistic growth, pN+1=rpN1-pN r=0.5 p0=0.9 By putting the given value…

Q: Denote by ×7 the operation “multiplication modulo 7” where ? ×7 ? is the remainder when ? × ? is…

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Q: ∞ 00 Suppose an>0 and a diverges. Prove that n=1 n =. an contrary suppose Σ an p=g¹ + a₂ converges,…

A: We have given that , an  &gt; 0 Also , ∑n=1∞ an diverges. We need to show that , ∑n=1∞ an1 + an…

Q: Consider the system of equations x+2y+32 = 0 2−g=0 x + kz = 0. a) Calculate the determinant of the…

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Q: 1. Find the Inverse Laplace Transforms of the following. 4) 48-60√/s s4

A: We know that, 1) if n is an integer then, L-1{1sn+1}=tnn! 2) if n is not an integer then,…