Solve the given differential equation by separation of variables. ds dr = KS

Q: 4. Give the general equation of the plane containing the point (3,-1,4) and I 2-2 perpendicular to…

A: To find the general equation of plane :-

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Q: Find the volume and the dimensions of the largest rectangular box in the first octant with three…

A: The following figure represent the box,

Q: 7. Determine the dimensions of a rectangular box, open at the top, volume of 32 ft3, and requiring…

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Q: − 2y)i − 4yz№ + → ne integral ƒF. di

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Q: What concept is most essential in calculus because other core concepts such as continuity, the…

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Q: 15. A palindrome is a word that can be read the same way in either direction (such as RACECAR). How…

A: Here We can use basic counting and making the boxes in whch we try to fill the letters and then try…

Q: Find the distance from the point S(0,0,12) to the line L: x = 4t , y = -2t z = 2t 3

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Q: What is the limit of 3x4 as x approaches 1 2 ? 12 2 evaluated 3 16 0 1 16

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Q: QUESTION 6 Let V = WW+ where V is a finite-dimensional inner product space over C and W is a…

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Q: dy dx e5x+4y = e

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Q: f(x) = 4x - 1.8x2+1.2x3-0.3x4 find the maximum using Newton's method (X0 = 3 with a percentage error…

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Q: Mr. Espinoza's debt of P160,000 is amortized by making equal payments at the end of every three…

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Q: Use the Jacobi method and Gauss-Seidel method to solve the following system until the L¹-norm of Ax…

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Q: Find the residues

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Q: 9. Convert ₁42(4-4x²-y²)dydr into a triple integral with dV = dydzdx.

A: To Convert: The integral ∫-11∫-4-4x24-4x2(4-4x2-y2)dydx into a triple integral.

Q: G <-2 1+X 1-X 2 dx 2-X 2+x dx

A: Follow the steps.

Q: A small store sells spearmint tea at $2.79 an ounce and peppermint tea at $4.77 per ounce. The store…

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Q: A Korean corn dog is a cylindrical piece of hotdog, rice cake, or mozzarella cheese, evenly coated…

A: Given: Calculate how much larger (in cm2) the cross-sectional area of the XXL item C is compared to…

Q: Let n E w. Suppose that f:n → A is onto A. Prove that A is finite.

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Q: Find the equation of the parabola with directrix x + 2 = 0, axis y = 4, and latus rectum 4.

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Q: A firm wants to determine how many units of each of two products: Wall clock and Alarm clock, they…

A: This is optimization problem.

Q: Find slope of the tangent and tangent line of the given functions.w.r.t  x  and y i) f(x,y)= sin x…

A: The given problem is to find the tangent line of the given function at given point (0,0). Given…

Q: Please write clearly and understandable way. Write all the corresponding Given with their…

A: Introduction: The formula for the moment of inertia of a region about the y-axis is given by,…

Q: <=<0 If f is the Fourier series of g(z)= 9z, 0≤z<1, then 11, 1≤z <5 f(2)= What does f(-5) equal?…

A: Fourier series of a function f(x) in the interval -L≤x≤L Fx=a0+∑n=1∞ancosnπxL+∑n=1∞bnsinnπxLWhere…

Q: Using the Laplace transform, solve the IVP. y₁ = 5y₁ - 4y2 - 9t² + 2t, y2 = 10y₁ - 7y2 - 17t² - 2t,…

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Q: A Ferris wheel is 57.85 m tall and has a diameter of 54.4 m. What are the dimensions of a scale…

A: Given information Height h=57.85 m=5785 cm Diameter d=54.4 m=5440 cm Scaling factor k=195 We have to…

Q: A furniture company produces school tables and chairs. The production of each product requires a…

A: We have to formulate the maximization problem and then we can proceed further.

Q: Please clarify the answr for behavior as x approaches negative infinity, sign of y if x is between…

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Q: Using the Laplace transform, solve the IVP. y = 5y₁ - 4y2 - 9t² + 2t, y2 = 10y₁ - 7y2 - 17t² - 2t,…

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Q: Consider the implicit relation between x and y defined by ƒ(x) − fƒ(y) + f(xy) = 0 for some…

A: We can solve as follows

Q: 3. Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i - 2j+ 2k. Find the unit vector…

A: Solution :- Given : X = - i + 3j and Y = 4i - 2j + 2k  Than 3X - (1/2)Y = 3( - i + 3j ) - (1/2)(4i -…

Q: A. Find the inverse Laplace transform of the following transfer functions. 3 9. s² + 6s +13

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Q: The table below shows the height, h, in meters, of an object that is thrown off the top of a…

A: Given,The table which is showing the height of the object(h) in meters as a function of time(t) in…

Q: Calculus Chain rule diagram and equations with 3 intermediate variables and 4 final variables Chain…

A: Note : Your answer starts from the next step according to Bartleby guidelines.

Q: Economics 5. Based on sales data over the past year, the owner of a DVD store devises the demand…

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Q: verify that the given vectors are solutions of the given system. Then use the Wronskian to show that…

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Q: a) Determine whether S = {(1,0,-1), (2,1,0), (3,1, -1), (1,1,1)} spans. R³. b) Find all c E R for…

A: (a) To check: The given set S={(1,0,-1),(2,1,0),(3,1,-1),(1,1,1)} is linearly independent or not.…

Q: Convert ¹4-42(4-4x²-y²) dydr into a triple integral with dV = dydzdx.

A: Given integral is ∫-11∫-4-4x24-4x24-4x2-y2dydx Which is the integral of volume. So z=4-4x2-y2…

Q: Find the flow of the field F = V(x² ze) once around the ellipse C in which the plane x + y + z = 1…

A: The given field is F=∇x2zey We have to find the flow around the ellipse in which the plane x+y+z =…

Q: Express integral I y + x (-4x-2y) -0,x= 1 and y=0,y-1-xto T. of u- dydx in terms of (u)and (v) given…

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Q: B. The dimensions of a rectangular solid at a given instant (t.) are (a = 13 cm). (b=9 cm) and (c =…

A: Given  Dimensions of rectangular solid  a=13cm, b=9cm, c=5cm .Rate of change of a and c increase…

Q: d² y dt² + 3 dy dt +2y(t) = 2e²¹ ; y(0)=0_

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Q: Find the area of ​​the region that lies inside r = 1 - sin (θ) and outside r = 2 + sin (θ).

A: We have to use the integration method to find the area between two polar curves. First we have to…

Q: 9. i Convert S²₁ 4²(4-4x² - y²) dydr into a triple integral with dV = dydzdz.

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Q: find the centroid of area region bounded by y=x^3, y=4x

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Q: Find a Fourier series expansion of the periodic function f(t)=-2t, πstsa f(t) = f(t+2π)

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Q: Let a E A and f: A→A be a function such that a ran (f). Suppose that h: w → A satisfies (a) h (0) =…

A: here we can use contradiction to prove this stetements.

Q: Find the distance from the point S(0,0,12) to the line L: x= 4t , y = -2t z = 2t 3

A: Follow the steps.

Q: First verify that the given vectors are solutions of the given system. Then use the Wronskian to…

A: