L{t}(s) = / t dt te -at %3D

Q: Зx + log dy find dx If y = 4 — Зх -

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Q: Integrate (x)(e^-x)dx within the limits of (1, infinity)

A: Givne that  Integrate (x)(e^-x)dx   limits of (1, infinity)

Q: |The projected rate of increase in enrollment at Newhampton College is estimated |by dE 5000(t +…

A: Isolate the variables E and t in the given differential equation. dEdt=5000t+1-32dE=5000t+1-32dt

Q: In some chemical reactions, the rate at which the amount of a substance changes with time is…

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Q: Find dx * for y = (x² + 2)°(1 – x³)* using logarithmic differentiation.

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Q: A culture initially has P number of bacteria. At t = 3hour the number of bacteria is measured to be…

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Q: Find the present value P of a continuous income flow of c(t) dollars per year using c(t)e-rt dt, J-…

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Q: Find the rate of change of the distance between the origin and a moving point on the graph of the…

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Q: A particle is traveling upward and to the right along the curve y = ln x. Its x-coordinate is…

A: Given a particle is travelling upward and to the right long the curve y=lnx. It is given that dxdt=x…

Q: Can you help me with this problem step by step?

A: To determine the derivative of given function.

Q: For any logistic equation, show that the point of inflection occurs at y = L/2 when the solution…

A: Given: The logistic equation

Q: 3. Water is being poured into a 10 liter leaky container so that the volume of the water, V,…

A: A differential equation is an equation that contains functions and their derivatives.  A…

Q: In the equation, x² +y² = 45, what is the value of the rate of change in y with respect to time t…

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Q: Consider and solve the initial value problem of a new form of life discovered on a distant planet.…

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Q: A point moves along the parabola y = x² in such a way that the rate of change of x : kx, || dx dt…

A: Since dx/dt = 10 at x = 5, therefore 10 = 5k k = 2 Now, calculate dx/dt at x = 7. dx/dt|x=7 = 2*7 =…

Q: 5. A termite population begins with 150 termites and increases at a rate of m'(t) termites per week.…

A: Termite population starts with 150 termites and increases with the rate of m'(t) termites per week

Q: 1. (a) If V is the volume of a cube with edge length x and the cube expands as time passes, find…

A: Topic = Derivative

Q: Find the present value P of a continuous income flow of c(t) dollars per year using where t1 is the…

A: Given, c(t)=100,000+4000, r=5%, t1=10 p=∫0t1c(t)e-rtdt Now plug the values of t1  and r…

Q: | Suppose that electricity is draining from a capacitor at a rate proportional to the voltage V…

A: The given differential equation is dVdt=-140V, where V is the voltage and t is the time in seconds.…

Q: An environmental study of a certain community suggests that t years from now the level L(t) of…

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Q: |The projected rate of increase in enrollment at Newhampton College is estimated by dE 5000(t +…

A: Given, The projected rate of increase the enrollment student at Newhampton college is estimated by…

Q: dy Q1) Find dx for : 1) y = log3(3x3 + x2)2 x In(sec- x)

A: I supposed to do only first question as our company guideline. Please repost other question as next…

Q: b) Find the equation of the line tangent to the graph of y=log; (5x +1) at x = 2

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Q: /4 Find the derivative of y with respect to t. (a) y = In(3te-1) (b) y = esin t (In t² + 1) (c) y =…

A: Given functions,  (a)  y=ln3te-1 (b)  y=esintlnt2+1 (c)  y=tlog3e(sint)(ln3) The objective is to…

Q: 2. Find the instantaneous rate of change for y= arctan- at x = 3. 2 12 A. 85 2 В. 13 3n D. 4 С. О

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Q: Consider and solve the initial value problem of a new form of life discovered on a distant planet.…

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Q: Find dy dx I-Ln(x+3)=tかが(x:)

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Q: A honeybee population starts with 100 bees and increases at a rate of n' (t) bees per week. What…

A: Integral formula is ∫abf(x)dx=F(b)-F(a) ∫04n'(t)dt=n(4)-n(0) From the given integral…

Q: Determine the instantaneous rate of change of the function f(x) = [x² si sin (2¹) 1+√t x3 At x=1 dt

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Q: 1 What is the instantaneous rate of change of Y at x = 2? O -1 none of these -1 1 3 4

A: Given : y = 1/x

Q: Find dy/dx using logarithmic differentiation. y = (8 + x)3/x, x>0 dy dx II

A: y=8+x3xTake natural log both side ,ln y= ln 8+x3xln y = 3xln 8+x ∴ ln ab= b ln a

Q: 7. Find dy and hence determine the rate of change of y with respect to x for the following…

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Q: Find dy/dx using logarithmic differentiation. 1 y = r(x+1)(x+2)

A: Solution

Q: y=ln(θ+4) dy/dθ=

A: Given function :

Q: What does r'(t)dt represent if r'(t) is the rate of growth of a dog in pounds for the t year?

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Q: (b) If n'(t) is the growth rate of a bee population in bees per week, what does n'(t)dt represent?

A: Given,n'(t)=growth rate of bee populationt=time in weeks

Q: Solve Y for csc(3Y) + e2%cot(y²) = log2/xy dx

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Q: What is the result of integrating a population growth rate betweentimes t = a and t = b, where b…

A: Integrating a population growth rate between a to b that is ∫abRatedt

Q: Find dy/dx using implicit differentiation: xe^y − y^2 − x^2 = 2 and Find dy/dx using logarithmic…

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Q: Calculate the instantaneous rate of change of g at the point (4, 1, 2) in the direction of the vec…

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Q: The rate at which a solid substance dissolves [dQ/dt] varies directly as the product of undissolved…

A: Given that 20 lb of substance is initially thrown in tank therefore A=20. Also, saturation…

Q: If oil leaks from a tank at a rate of  r(t) gallons per minute attime t , what does ∫0120 r(t) dt…

A: Oil leaks from a tank at a rate of  r(t) gallons per minute at time t.

Q: dy Find dx by logarithmic differentiation. e2x – 1 y = In e2x + 1

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Q: A new fast-food firm predicts that the number of franchises for its products will grow at the rate…

A: Given

Q: Show that an investment that pays out R dollars per year continuously for T years has a PV of R(1…

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Q: Suppose x and y are functions of third variable t. In the equation x2+y2=45, what are the values of…

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Q: Because of job outsourcing, a town predicts that its public school population will decrease at the…

A: .

Q: Calculate the exact value of the intergral ∫ln(x)dx where b = 3 and a = 1

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Q: 1 - Find a formula for the rate of change dv/dt of the volume of a balloon being inflated such that…

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

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.