In the 2000 U.S. Census, a small city had a population of 50,000. By 2010, the population had reached 72,387. If the city grows continuously by the same percent each year, when will the population be growing at a rate of 4,000 people per year?

Q: xy' + y = x³y³ Inx

A: This question is related to differential equations, we will solve it using given information. 

Q: 2xy + x² + x*)dx –(1+ x²)dy = 0

A: See the details solution in below

Q: Find the derivative of y with respect to x. y= (x° Inx)° 9. %3D dy dx

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Q: (x – a)² + y? = a²

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Q: Test the series below for convergence using the Ratio Test. 97 n! n=1 The limit of the ratio test si...

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Q: 3. Given a = (--6,6, 3) and b= (1,-1, -2) (a) Give the exact value of the angle between vectors a an...

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. x = 5 + 4y2,   ...

A: We use the formula S=2π integration of y √(1+x'2)dy from 1 to 2

Q: eX(1+ sin e^) dx 2. sin? ex

A: We can solve question no 2 as below.

Q: 4. (a) Solve the initial value problems, dy = sin t + 1; yE)=; dt (b) Evaluate V1 – x² dx. |

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Q: 7. || v dA, D= {(x, y) | -1< y< 1, -y - 2 <x<y} D.

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Q: 11. What is the y-intercept of the line that is tangent to the graph of y =-x +4x at (1, 3)? a. -2 C...

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Q: Direction: Read then solve the question carefully. Click the letter of the correct answer. Find the ...

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Q: Homogeneous Diffe rential Equation: (x² + 2xy – 4y² kdx (x² –8&.xy – 4y° kty = 0 %3D Use the substit...

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Q: Families of Curves: Parabolas with vertex ( h, -3) and it opens to the left

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Q: (y-cos²x)dx + cosx dy = 0 %3D

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Q: Find the area of the surface generated when the curve y = x2 from x = 0 to x = 3 is revolved about t...

A: Let's find. 

Q: 8x Use the alternative formula for the derivative to find the derivative of f(x) = x-9 ...

A: We have to find derivative by using alternative formula.

Q: In the Wizard World, currency exchange is inconsistent. One Galleon from the Wizarding World is equi...

A:

Q: ind the first and second derivatives of the function. 1+ 12z W = (8-z) 4z dw dz dz? 2.

A: Topic:- derivatives

Q: Vx2 – 16 if x 0 . Find the following: Note: If the g(a) or lim g(x) does not exist write DNE. 1. li...

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Q: The graph of the derivative f'(t) of f(t) is shown. Compute the total change of f(t) over the given ...

A: Function change and slope     Answer is  192

Q: D^(3+1) (D-2)^(7+1) y = 48e^2x

A: Put D=m then solve it. 

Q: The indicated function y, (x) is a solution of the associated homogeneous equation. Use the method o...

A:

Q: The equation of the family of straight lines with y-intercept and slope equal is

A: Equation of family of lines

Q: x?y? dy (xdy+ydx)%3D8y%

A: Let's find. 

Q: cos (6x4) – 1 Let f(x) Evaluate the 9th derivative of ƒ at x = 0. %| x7 f(9)(0) = Hint: Build a Macl...

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Q: xdy- (4x²-2y)dx = 0

A: This question is based on solution of linear differential equation.

Q: x +1 xp- x3 + x2 – 6x d.x

A: As per our guidelines we are supposed to answer only one question. Kindly re-post other question as ...

Q: 2 Separation of Variables: x(y+1)dx + dy = 0 %3D

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Q: In Asahikawa, Japan, the temperature in the morning was recorded at -15 degrees Fahrenheit. At night...

A: Given data Temperature in morning = -150F Temperature drop till night = 100F

Q: f(x) = -x + 1lx? – 28 %3D

A: We have the function                                   f(x)=-x4+11x2-28 then  Solution (a): Use the ...

Q: At noon, ship A is 130 km west of ship B. Ship A is sailing east at 30 km/h and ship B is sailing no...

A:

Q: 1. Engineers have observed that when transferring a message I (an input signal) through a physical m...

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Q: Direction: Read and understand the statement before answer. Click "TRUE" if the statement is correct...

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Q: (NAS1) Find the local linear approximation L (x)of the function f (x) = 5 – xåt x = 2 -

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Q: Solve the initial value problem: (y² – y³)dx + (1 + 4xy – 4xy²)dy = 0, y(÷) = 2.

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Q: Solve for the indefinite integrals of the following functions. Show a COMPLETE set of solution then ...

A: Since you have posted multiple questions i can do first question as per our company guidelines pleas...

Q: 4. Homogeneous Diffe rential Equation: (r+2y-4y kx-(x' -8ry-4y kdy= 0 Use the substitution x = y = w...

A:   Differential equation  are mathematical tool to define rate of change for whole equation. 

Q: Test the series below for convergence using the Ratio Test. 00 n5 0.8" n=1 The limit of the ratio te...

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Q: lim f(x) if f (x) = - ² – 2 if x 1) X f(x)

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Q: D Evaluate without using calculator. Use the pythagorean identities rather thae reference txiangles....

A: a To find sin θ and cos θ if tan θ=34 and sin θ&gt;0.b To find tan θ and cot θ if sec θ=4 and sin θ&...

Q: Solve the following problems a. Which of the following are the coordinates of a point where the tang...

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Q: Find the derivative of the function y = (cot x- csc x) 1 %3D dy %3D dx

A: ddxcotx-cscx-1

Q: Cy+2)(3y-1)

A:

Q: Test the series below for convergence using the Root Test. 8n 4n + 1 n=1 The limit of the root test ...

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Q: Determine whether the series converges, and if so find its sum. 4k+2 Σ 7k-1 k=1 1) This series can b...

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Q: Consider the equation æ27 + 36 æ – 1 = 0 Which of the following statement is true? O The equation ha...

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Q: Find fla) for f) = x? +6 Aind fre) for fY) = x-5_ Frnd flay for f(x) = × ² -4x+} Find fr x) for floc...

A:

Q: u = 3 + x² V3+ x²

A: We can find the integral as below using substitution method

Q: Find an equation of the tangent line to the graph of the equation at the given point : y = 16 – x² ;...

A: The given equation of the graph is y=16-x2 and the point is (3, 7) . We have to find the tangent lin...