Design a differential equation whose fundamental solutions are y₁ (t) = e-t/2 and y2(t) = e-2t.

Q: xy' - ( 1 + x ) y = xy2

A: xy' -1+xy=xy2

Q: Find for the function y = 29*. dy dx

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Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

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Q: d the maximum of the objective function C = 7x + 8y subject to the feasibility region below. 2 H-…

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Q: t v = au + bw, where u = (1,

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Q: Solve 2 sin² (x) + 3 sin(x) + 1 = 0 for all solutions 0 < x < 2π x = Give your answers as a list…

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Q: Find sets of parametric equations and symmetric equations of the line that passes through the two…

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Q: Evaluate the following indefinite integral. 8 dt t10 J ← +C

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Q: Evaluate the following indefinite integral f11 sin(x) - 2 cos(x) dx = +C

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Q: x²y² lim (x,y)-(0,0) x++y*

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Q: -4 y 8 5 (0, 3) a. x ≤ 5, y ≤ 6 b. x ≥ 5, y ≤ 6 c. x ≤ 5, y ≥ 6 d. x ≥ 5, y ≥ 6 -1 (0, 6) (5, 6)…

A: The answer is in step 2

Q: Find the total area of the shaded region boundeed by the following curves: x = 12y^2 - 12y^3 x =…

A: The given curves are: x=4y2-4y           and            x=12y2-12y3

Q: At an Oregon fiber-manufacturing facility, an analyst estimates that the weekly number of pounds of…

A: As per our company guidelines, we are supposed to answer only the first 3 sub-parts. Kindly repost…

Q: 4. In what direction(s) is the directional derivative of f(x, y) = xy + x² at P(2, 3) equal to 0?

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Q: An inferior product with a large advertising budget sells well when it is introduced, but sales fall…

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Q: Simplify completely. Assume the variables represent positive values. 9√175x³ 4x√28x

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Q: Find the average value of f(x) = Provide your answer below: -x+3 x3 Submit an exact answer using…

A: Use the formula for average value

Q: Approximate the critical numbers of the function shown in the graph. Determine whether the function…

A: The given graph is:

Q: The city of Raleigh has 6900 registered voters. There are two candidates for city council in an…

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Q: Given f(x, y, z) = √√−4x − 5y – 2z, find fx (x, y, z) = fy(x, y, z) = fz(x, y, z) = = -1 - 4x - 5y -…

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Q: Given f(x, y, z) = fz(x, y, z) = fy(x, y, z) = fz(x, y, z) = x² + 5y² + 3z², find 2

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Q: Suppose f is a one-to-one differentiable function and its inverse f^-1 is also differentiable.  a).…

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Q: Make a sign diagram for the derivative of the rational function. 2x + 8 --Select-- O ( ) = -Select-…

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Q: Consider the points below. P(1, 0, 1),  Q(−2, 1, 3),  R(6, 2, 5) (a) Find a nonzero vector…

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Q: The mass at time t of a radioactive substance is m(t) = m(0)ekt, where m(0) is the initial mass and…

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Q: If xy + 3x = -3 then find at the d²y dx² point (1,-6) in simplest form.

A: Given query is to find indicated derivative.

Q: 2 The curve y = ax + bx+c passes through the point (1,8) and is tangent to the line y = 5x at the…

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Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = 5-x², 0≤x≤…

A: Topic:- application of integration

Q: The cartesian coordinates of the point P is: ← A 0 2 1 32 R P (1, 0, 3) AC (1, 2, 3) BC (1, 2, 0) Co

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Q: X

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Q: Simplify completely: -5√45x + 10√125x

A: We have to simplify the given expression.

Q: Simplify completely. Assume the variables represent positive values. √6x²y-√√/36xy²

A: Simplify the expression completely

Q: Derivative of 7x^2/3

A: We have given to find derivative of  7x23 Let,  y=7x23 Derivative is given as  dydx=ddx7x23 dydx=7…

Q: Evaluate the integral by interpreting it in terms of areas. (1-x) dx -5

A: Given Integral:- ∫-561-xdx

Q: The monthly demand function for x units of a product sold by a monopoly is p = 5,200² dollars, and…

A: Note:- According to the company policy we can solve only three subparts so please upload the next…

Q: dy If −5x² + y² = 5 then find at the point (2,-5) in simplest form. dx²

A: Given the equation: -5x^2+y^2=5

Q: Please solve value problem. dy alx cos²x sinx your answer function of z. ourswers. the following…

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Q: Consider the following. u = (3,9), v = (6, 2) (a) Find the projection of u onto v. 54 18 10' 10 (b)…

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Q: Suppose that a patient receives an injection 9 mg of a certain drug and that 60% of the drug is…

A: It is given that The initial amount of drug intake=9 mg60% of the drug metabolize each day

Q: aluate the definite integral given below. ter an exact answer. л/4 1.24 (3 sin (x) - 2 cos (x)) dx

A: Given query is to find the value of the integral.

Q: 10. Find a function f such that f'(x) = 3x³ and the line 24x + y = 0 is tangent to the graph of f.…

A: As we know that: The slope of the tangent line to the curve is equal to the derivative of the given…

Q: For what values of p does √x-Pax 1 -Pdx converge?

A: We need to find values of p.

Q: Solve the following differential equations. y' = y - xy3e-2x

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Q: Use implicit differentiation to find the derivative of 5x^2y+2xy^2=-3 y'=

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Q: Use logarithmic differentiation to find (dy)/(dx) y = ((e ^ x)/(sin x)) ^ 3

A: We will find the required derivative.

Q: The direction angle y of the vector (1,1,1) is 45° Cos-¹) 60° 30° BO .CO .D O

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Q: If a population is now 7.6 billion people and it continues to grow at an annual rate of 1.4%…

A: Topic- Exponential function Current population=7.6 billion=7.6×109annual rate of growth compounded…

Q: Find the derivative of the function. 6x fox u g(x) = u² - 1 3x u² + 1 du 6x 0 6x • LC² (u) du = [,…

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Q: Suppose that the percent p (as a decimal) of people who could correctly identify two of eight…

A: We need to find out the number of days that will madimize the percent.

Q: Find f'(x). f(x) = 3x - In x² f'(x) =

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