A differential equation (DE) is a mathematical equation for an unknown function that relates the values of the function itself to its derivatives of various orders.True or False?

Q: dz Calculate for z = 4x² + 3y², x = sin(t), y = cos(t) dt

A: Topic- derivative of a function we are given, z=4x2+3y2x=sin(t),y=cos(t)we know…

Q: Suppose the density of a wire is given by p(z) = 0.6 +0.09 sin(27) kg/m, where is the distance from…

A: NOTE: Refresh your page if you can't see any equations. . the given density function is the length…

Q: Given f(x, y, z) = x²y³z − 3xy²z³ + 5x²z − y³z, find fxyz

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Q: Solve the following differential equation: 4y'' +12y' + 9 = 0

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Q: What volume of refrigerant should be recovered for disposal from an oldrefrigerator? The length of…

A: Consider a cylindrical pipe with diameter 14 inch and 15 feet of long. To calculate its volume.

Q: The unit tangent vector for the parametrized curver (t) = (8, cos 2t, 2 sin 2t) at 0 < t < 2n is

A: To find the unit tangent vector

Q: Use the substitution x indefinite integral 97dx x²√x² + 16 4 tan (0) to evaluate the

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) √er (5 + 6e 6e)7/2 dr

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Q: don't understand how I can graph this function, can someone please help as well as explain

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Q: Precalculus   Find an equation of the circle with center (2, 5) that passes through (−3, 1).

A: Given query is to find the equation of the circle.

Q: f'(x) = || √4 + X 1 2√4+x (4+x) State the domain of the function. (Enter your answer using interval…

A: Given query is to find the domain of the function and is derivative.

Q: 10) A semicircle of radius 2r is inscribed in a rectangle so that the diameter of the semicircle is…

A: The length of the rectangle is l = 22r = 4r The width of the rectangle is w = 2r Formula Used: The…

Q: Use the tabular method and the properties of limit to find the limit lim ex-4 X-4

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Q: Laplace transform ((d^2/dt^2)(y(t))) + 4y(t) = 6y(t). What is y(t) if y(0)=6 and y’(0)=0

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Q: 8. 4p pt| Pt1 4p

A: 4pp+1 - p+14p

Q: 2. Find the derivative of each of the following functions: y = x¹2 (i) (ii) (iii) (iv) y = 3x ¹ y =…

A: 1) y=x12Differentiate w.r.t.'x'dydx=ddx(x12)We know thatddx(xn)=nxn-1Thereforedydx=12x11

Q: 2-y If x = 32, find 2y 4. y+2 2y√ √2y B. dx B. Find y' if y = 4x-1 y-2 2y√ √2y (2x²-3)(3x+2)…

A: We can answer both the question in the below steps.

Q: Using the appropriate theorems, explain why the function is continuous at every number in its…

A: Given function, f(x)=2x2-x-2x2+4 Function is undefine if x2+4=0x2=-4x2=4i2x=±2i∉R

Q: lim x118 x³ + 8x 2x³ + 5x² - 2x - 2

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Q: 1. Pirkko wants to invest 9 000 euros so that after 8 years she will have 14 000 euros. What is the…

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Q: Find y' if y= 48x³+34x2-8x+15 (4x-1)² 48x³+34x²-8x+33 (4x-1)² If y = 3u² - 2u + 4 and u = x² + 3x -…

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Q: EXAMPLE 3 Suppose that a ball is dropped from the upper observation deck of a building, 350 m above…

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Q: QUESTION 3 Derive a Differential Equation that is free from arbitrary const

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Q: If a ball is thrown into the air with a velocity of 42 ft/s, its height (in feet) after t seconds is…

A: We have to find the velocity when t = 1 second.

Q: The demand equation for the Roland portable hair dryer is given as follows where x (measured in…

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Q: Construct the truth tables for the given compound statements. 1. ~p ^ ~q р T T F F q T F T F ~P ~q…

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Q: The range of y = tan-¹ x is A. R Evaluate lim h-0 A. undefined B. [-1,1] (x-h)³-x³ h B. 3x² C. x +…

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Q: 14. Find a y=r³ parametrization for the path that travels along the graph of z from (-1,0) to (1,0).

A: To find the parametrization of the path that travels along the graph of y=x3-x from (-1,0) to (1,0).

Q: A ladder 15 ft long leans against a vertical wall. If the lower end is being moved away from the…

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Q: Given U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15), A = {1, 4, 7, 10, 13), B = {1, 2, 3,…

A: topic - sets  we are given  U ={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15} A={1,4,7,10,13}…

Q: Solve for y' if y = sec55x - tan²5x A. 0 B. 1 If y = x[sin-¹ (sin x)], find y' A. 2x B. -2x C. 5…

A: (1) Given that , y=sec55x-tan25x y'=?

Q: Thank you! I am a bit lost because the equations are a bit messy with the computer. Would it be 3e^x…

A: GIven function :- y=3ex+8x3

Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x)…

A: Concept: The limit derivative of the function f(x) at x=x0 f'(x0)=limh→0f(x0+h)-f(x0)h

Q: Solve the following differential equation:    4y'' + 12y' + 9y = 0

A: we have to find the solution of given differential equation.

Q: Consider f(x)=5x-3-41/x^2 Find the average rate of change of f(x) with respect to x over the…

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Q: 1. Find y' of tan(x²y) = 3x + y²

A: Given:      tanx2y4=3x+y2 differentiating on both sides   ddxtanx2y4=ddx3x+y2  Applying…

Q: Find an equation of the tangent line to the graph of y = B(x) at x = 6 if B(6) = 0 and B'(6) = -1/2

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Q: Determine the solution of the 1st Ordered Differential Equation: y(x² + y²)dx + x(3x² - 5y²)dy = 0

A: y(x2+y2)dx+x(3x2-5y2)dy=0x(3x2-5y2)dy=-y(x2+y2)dxdydx=-y(x2+y2)x(3x2-5y2) Substituting  y=vxy'=v'x+v…

Q: 2. If x = t + cost, y = sint, find d²y dx²*

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Q: cm 10 cm

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Q: What is the average velocity of the curve y= square root of ( x2-2x) over the interval of [ 2,7]

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Q: . If the money is invested at a rate of 5% compounded continuously, when ill the amount triple?

A: Given: Interest = 5%

Q: A rectangular piece of land has dimensions 1050 ft by 550 ft. Find the area of the land to be…

A: The length of the rectangular land, l = 1050 ft Width of the land, w = 550 ft To evaluate: The area…

Q: Q4¹ Find function's domain, function's range, and determine if the domain is an open or closed…

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Q: Drum Tight Containers is designing an open-top, square-based, rectangular box that will have a…

A: we need to find out thr dimensions that will minimize the surface area

Q: An object moves with the acceleration vector ä(t) = with initial ity vector Po= and initial position…

A: Given acceleration of an object after time t is a→t=-2.i⏜+j^+3k^ Let the position vector of the…

Q: The graph of f is given. State the numbers at which f is not differentiable. (Enter your answers as…

A: Note:  1. A function is not differentiable at discontinuity. 2.A function is not differentiable at…

Q: show complete solution

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Q: If y = sin(x - y) find y'. A. cos(x-y) 1+cos(x-y) B. cos(x-y) 1-cos(x-y) C. cos(x - y) D. -cos(x -…

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Q: Consider f(x)=5x-3-41/x^2 c) Find the equatino of the tangent line at x = 2 to the graph of y =…

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