Find the general solution of the following linear second order homogeneous O.D.E.: ý + 2ý – 15y = 0

Q: . Find the equation of the plane through (-3, 8, -8) that is perpendicular to the plane 7x - y + z =…

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Q: The hourly cost function (in dollars) of 3 generators, each as follows: where x₁ is the output power…

A: Given problem:- The hourly cost function (in dollars) of 3 generators, each as follows: where x₁ is…

Q: 1. In the differential equation (x+2y-1)dx+(2x+4y-3\dy=0, we let the substitution %3= 2. In the…

A: 1) Here, the differential equation is: (x+2y-1)dx+(2x+4y-3)dy=0⇒dydx=-x+2y-12(x+2y)-3

Q: Question 3 Find the domain of the folowing function 4xy fix.y)= O (kyly*x?} O {kylly2x) O (kylly>x)

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Q: (-2 if XS-1 S(x) = {x² -3x+8 if if -1<x<2 x22

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Q: In the differential equation 4(3x+ y– 2)dx– (3x+ y)dy = 0, we let the substitution dw=

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Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

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

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Q: Determine whether the geometric (– 1)"3" series * is convergent or divergent, n=1 8" and if it is…

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Q: Find the gradient of the function at the given point. W = x tan(y + z), (3, 7, -3) Vw(3, 7, -3) =…

A: Given;  w=x tan(y+z), (3,7,-3).

Q: A bacteria culture initially contains 3000 bacteria and doubles every half hour. Find the size of…

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Q: Solve the following. Show the step-by-step solution. 1. Find the equation of the tangent line and…

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Q: solve the following differential equations using the substitution suggested by the equation.

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Q: ||r'(t) × r"(t)|| Use the formula k(t) = to find k(t). 13 r(t) = el2"i +e-j 12ts K(t)

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Q: Item # 6. 15 pts Suppose that a population of bacteria for an experiment increases according to the…

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Q: Compute f'(x) a.) f(x) = (x2+1)e-x^2 b.) f(x) = (4e-x-

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Q: Rojana is 8 years older than AJ, and the sum of their ages is less than 24. Find their possible…

A: Let Age of Rojana is x , and age of AJ is y. Given, Rojana is 8 year older than AJ. Therefore, x=y+8…

Q: (a) Find lim 0 arctan(3r)

A: Since you have posted multiple questions which are not interlinked i can do first question as per…

Q: 5. x3 + 2x – 6 dx x4 + 2x2

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Q: f(x)=x+ 1. Donain 2. Intercepts (y-only) 3.Any Symmetry 4. Cvitical Paints 5. Intervals ok…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: Find a polynomial of degree 3 such that f(0) = 5, f'(0) = 10, f''(0) = 15, and f'(0) = 20. P3(x) =O

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Q: Evaluate the integral. m/4 cos ti+9 snt d

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Q: Find the gradient of the function at the given point. w = x tan(y + z), (3,9,-5) Vw(3, 9, –5) =

A: For a given vector fx, y, z the gradient vector denoted by ∇f is ∂ ∂ xf∂ ∂ yf∂ ∂ zf So, ∇w=∂ ∂…

Q: dy 2 Solve (x2 - 1)+ 2xy x2-1

A: (x2-1)dydx+2xy = 2x2-1dydx+2xx2-1y=2(x2-1)2this Diff eq is Linear Diff Eq.dydx+P(x) y =…

Q: A product is introduced to the market. The weekly profit (in dollars) of that product decays…

A: A product is introduced to the market. The weekly profit in dollars of that product decays…

Q: Consider the sequence defined by a, = In(2n³ + 2) – In(5n³+2n² + 4). Find the limit of an as n → ∞.…

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Q: Consider the following function. f(x) = (x + 4)2/3 (a) Find the critical numbers of f. (Enter your…

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Q: Use the accompanying tables of Laplace transforms and properties of Laplace transforms to find the…

A: L{cosnt cosnt} =? (n=/m) We know that  Cosnt cosnt =[cos(n-m)t+cos(n+m)t]/2 Taking Laplace…

Q: 3. y = Væ – 1, æ = 5 , y = 0 , revolved at y axis

A: To solve the following problem

Q: Find the gradient of the function at the given point. w = x tan(y + z), (3, 9, –5) Vw(3, 9, -5) =

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Q: Find the solutions of the system of inequalities by graphing: x + y > –1; 2x + y < -3

A: x+y=-1y=-x-1(line with negative slope and intercept -1)2x+y=-3y=-2x-3line also with negative slope,…

Q: The total cost of producing x instruction manuals is given by the function C(x) = 800 + 27x – 0.6x?…

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Q: Write each symbolic statement as an English sentence. p: Taylor Swift is a singer. q: Taylor Swift…

A: Following are some common logical connectives: ∨   -   Disjunction (or) ∧   -   Conjunction (and) →…

Q: 2. x3 - y3 = c³, find y" %3D HOOAT d²x 3. x* = at?, find dt2 1983

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Q: 4y" – 0 +12y' + 9y - 0 e. f. y" – 6y' + 9y – 0

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Q: Find u · v, u· u, ||v||2, (u · v)v, and u · (3v). u = (4, -3, 5), v = (0, 6, 4) (a) u: V (b) u.u (c)…

A: I am attaching image so that you understand each and every step.

Q: Find the area of the shaded region. r = Vcos 20 r = 10 cos e NOTE: Enter the ezact answer. A =

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Q: 2. In the differential equation 4(3x+ y-2)dx-(3x + ydy -0, we let the substitution dw=

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Q: Use the shell method to set up and evaluate the integral that gives the volume of the solid…

A: Let gy be continuous and nonnegative, then, the volume of the solid of revolution formed by…

Q: Find the solutions of the system of inequalities by graphing: x + y 1

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Q: 5. In the differential equation (1+3xsin ykdx-x cos ydy = 0, we let the substitution %3D

A: Follow the procedure given below.

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 2y2 + 6, Vf(4, 2) = eBook

A: A detailed solution is given below

Q: Express the function below using window and step functions and compute its Laplace transfo 0, 0<t<4…

A: The given function is: g(t)=0, 0&lt;t&lt;45,4&lt;t&lt;53,5&lt;t&lt;82,8&lt;t

Q: If f (x) = Vx + 7 and g(x) find f(x) g(x). %3D Keypa Answer Keyboard Shorte f(x) · g(x) =

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Q: Find positive numbers x And y satisfying the equation xy=14 such that the sum 2x+y is as small as…

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Q: r = - 10i + (1 – 1² )j + t k O It is a parabola in the plane z = – 10, with vertex at (1, 0, – 10),…

A: Find your answer below

Q: Express the given equation in polar coordinates. 144xy = 121 121 p² sin? 0 = 144 121 ? cos 0 sin 0 =…

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Q: Write and evaluate the definite integral that represents the volume of the solid formed by revolving…

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Q: Find the area of the region enclosed by the rose r = 10 cos 30. NOTE: Enter the ezact answer. A =

A: Here, the polar curve is r=10 cos 3θ which is as shown:

Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) 2…

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