Use the Laplace transform to solve the given initial-value problem. dy -y = 1, y(0) = 0 dt y(t) = %3D

Q: 5-Vx 4) lim x-25 x-25 5) lim 7-x ל-x ( x² – x3 if x <2 6) Given the function g(x) 15x – 14 if x 2 2 ...

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Q: Determine whether the given series is convergent or divergent. Justify your answers. +0 +00 (2n)! (c...

A: ACCORDING TO BARTLEBY GUIDELINES, WE ANSWERED ONLY ONE QUESTION.  

Q: A cuboid has a square base of side (2 + 3)cm and a volume of (16 + 9 3)cm³. Without using a calculat...

A: It is given that, A cuboid has a square base of the side 2+3 cm and Volume of 16+93 cm3. Without usi...

Q: Find (f-1)'(a) for f(x) = ーX-3 when a = 3x +2 (Enter an exact answer.) Provide your answer below: ((...

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Q: A particle moves along the x-axis so that at time t >0 its position is given by x (t) =t² – 10t + 10...

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Q: x3dx 3. S (x4+4 )4

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Q: dx sin? - cos 2

A: Here, the given integral is: I=∫0πsin2x2cos7x2dx Substitute x2=t⇒x=2t⇒dx=2dt as x→0⇒t→0 &amp; as x→π...

Q: The arc length along the parabola y = x² from (1,1) to (2,4) is given by which of the following inte...

A: Let's find. 

Q: (a) (6) Decide if the following improper integrals are convergent or divergent using Basic Compariso...

A: To decide the convergence of the improper integrals.

Q: 1. Sand is being poured into a conical pile in such a way that the height is always one-third of the...

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Q: he directional de -) = 3x?y -4xy 3x², 2. %3D ne giu divection gie

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Q: Show detailed solution for all. a) Provide the Maclaurin series expansion of f (x) In(3 - 2.x) b) Fi...

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Q: A particle moves along the x-axis so that at time t 0 its velocity is given by v(t) = 3t2 – 60t. Det...

A: v(t)=3t2-60t,    t≥0the particle is moving to the right whenv(t)&gt;03t2-60t&gt;03t(t-20)&gt;0

Q: Find the remainder if F(x)=6x^3+49x^2+90x+56 is divided by 3x-3

A: F(x)=6x3+49x2+90x+56 Since 3x-3 is linearwhere 3x-3=0⇒3x=3⇒x=1 Remainder of F(x) when divided by 3x-...

Q: 4. Find the volume of the wedge cut from the first octant by the cylinder z = 12 – 3y², and the plan...

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Q: Q1. Fill in the blank with a suitable mathematical expression. 1. The function f(x) is symmetric abo...

A: As per bartleby guidelines we only give first question answers. 

Q: (a) Graph the given function, (b) find all values of x where the function is discontinuous, and (c) ...

A: A function f(x) is said to be continuous at a point x=a iff limx→a-f(x)=limx→a+f(x)

Q: Find the area under the given Cunves: D= 9-X From X = - 2 to X = 8

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Q: Give some examples of limits in real life situation (preferably in a persons life)

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Q: 3. s varies directly as r and inversely as square of difference of q to t. If s=12 when r=10, q=5 an...

A: Question: S varies directly as r and inversely as square of difference of q to t .If s=12 when r=10 ...

Q: Question 6 P Consider a room in the shape of a 4 m cube, 4 meters on each side. A bug at point P wan...

A: Given problem:-

Q: Letting I répresent the grams of salt in Tank A, and y represent the grams of salt in Tank B, set up...

A: Rate of change of salt concentration = difference of inflow salt concentration and outflow salt conc...

Q: x (xyx)dx = y(xy2)dy wheen x-2,

A: As per Bartley guidelines we are supposed to answer only one question per post.  This post contains ...

Q: List the eigenvalues of A. The transformation x-Ax is the composition of a rotation and a scaling Gi...

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Q: ーズ 10. S- ex

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Q: A rectangular box with a volume of 64 ft is to be constructed with a square base and top. The cost p...

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Q: A pine tree growing on a hillside makes a 76°angle with the hill. From a point 83 feet up the​ hill,...

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Q: ) Find | sin can) cas (ga)da cos (gx) dx

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Q: Using the integration bay parts formula with u = x², dv = cos x dx, the integral x* cos x dx becomes...

A: Given u=x2   &amp; dv=cosx dx∫x2 cosx dx  

Q: sin? - cos' 2 2 zdx 2.

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Q: differential equation .2x 2

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Q: If x + y = 0 and x # 0, then what is the value of x 2007 y 2007 O -1 O 2 O 1

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Q: Question Select your answer. Find the equation of the tangent line of f(x) = x2 + 5x at x = 2. y = 1...

A: A detailed solution is given below

Q: CoS 2X sin x,co

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Q: Determine the derivative of the ff. functions 1. y = 100 cos 3x 7. y = 8x³ sin (1 - 5x)

A: topic - derivative of a function note : As per bartleby guidelines we are supposed to answer only fi...

Q: - graph and fined Demain and Range For ye sinx-3

A: Note: According to our expert guidelines only first individual question is to be answered kindly rep...

Q: 1 1.1 18 6 2. Find the sum of the first 5 terms of the geometric series +

A: topic - sum of geometric progression

Q: I Find the second derivative(y") of the following functions and simplify the final results. 1. y = x...

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Q: The point P has coordinates (-1, 4, 11) and the line / has equation r = (i) Find the perpendicular d...

A: The perpendicular distance, ?,between a point ?(?,?,?) and a line with direction vector d→ is given ...

Q: С. 1 Evaluate the following limits x2 +6x+5 1) lim x-5 x²+2x-15 x(х-5)-24 2) lim x→8 x2-8x (2+x)3-8 ...

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Q: find the second derivative of y = x In x A 1/x в) 1/2х D) 2x

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Q: By the fests. 2. a³y = x²(2a² – x²)

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Q: Using the integration bay parts formula with u = x- dv = cos x dx, the integral x cos x dx becomes

A: The given integral can be solved as follows:

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. 1 x = -(y2 + 2)3...

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Q: O Find a general salution answ r リーx- C-X

A: The given differential equation is: xy'=12y2+y which can be written as: y'=12xy2+yx⇒y'-yx=12xy2 whic...

Q: Find the maximum profit and the number of units that must be produced and sold in order to yield the...

A: It can be solved using differentiation and quadratic formula.

Q: Consider

A: Please refer to the image below

Q: Consider the following. 18/1 + e−x = 2 (a) Find the exact solution of the exponential equation in ...

A: The given equation,   181+e-x=2

Q: A cancer tissue is in the shape of a sphere whose radius is increasing at the rate of 2 mm per day. ...

A: "Since you have asked multiple question, we will solve the first question for you. If you want any s...

Q: SHOW YOUR SOLUTIONS. I. Eliminate the arbitrary constants. 3. x = c, cos wt + c2 sin wt ,w is a para...

A: topic - differential equations