Exercise: Show that the following differential equations are homogenous and solve. 1. (x+y³)dx+xy dy=D0 ans: x'(x²+2y)=c

Q: A farmer wants to fence an area of 37.5 million square feet in a rectangular field and then divide…

A: Given that a farmer wants to fence an area of 37.5 million square feet in a rectangular field and…

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Q: (a) Suppose f(x) = cos (15x) b* and f'(0) = 2. Find b. 2 The value of b is e (b) Suppose f(x) = sin…

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Q: The absolute minimum value of the function f(x) = –3 sinx on the interval [2, 8] is

A: To find the absolute minimum value of f(x), first we have to find the derivative of f(x) i.e. f'(x).…

Q: Find the centroid of the region cut from the first quadrant by the circle x +y =

A: Given x2 + y2 = 81 y=81-x2 Area of Quadrant(A) = πr24                              A  = 81π4

Q: Sketch the graph of a function that is continuous on (– 0,00) and satisfies the following sets of…

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Q: D(x) is the price, in dollars per unit, that consumers are willing to pay for x units of an item,…

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Q: Under certain​ conditions, the number of bacteria present in a colony is approximated by…

A: Given, f(t) is the number of bacteria present at time t in minutes. f(t)=(A0)e0.022t A0= 2100000…

Q: Consider the differential equation x² y" – 3xy' + 3y = 0. (a) Verify that y = cjx + c2x is the…

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Q: A concert promoter sells tickets and has a marginal-profit function given below, where P'(x) is in…

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Q: 3. A 1 000-metre track is to be built with two straight lines and semicircles at the ends as shown…

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Q: dy = 12y – 3y?. Consider the differential equation dt Use a phase-line analysis to find the…

A: Here, the given DE is: dydx=12y-3y2 The fixed points are given by  dydx=0⇒12y-3y2=0⇒3y(4-y)=0⇒y=0,4

Q: 1. (20) Solve IVP of the harmonic oscillator: dy dy dt2 + 4- + 6y = e-2", y (0) = 0, y' (0) = 1. dt

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Q: Find an equation for the ellipse that satisfies the given conditions. Foci: F(0, ±/10), vertices:…

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Q: 1. Let f be an odd function and g be an even function with f(2) da = 2 3 f(x) dæ = 7 3 9(x) dx = -3…

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Q: Select the correct equations in the image. Based on the the equations of the parabolas, identify…

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Q: n²+n+1 En=1 n4+n² 00

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Q: Determine the open intervals on which the graph is concave upward or concave downward. (Enter your…

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Q: Test differentiability at x = 0 and x 1 for the function x3 + 2x; х — 2; 1 0 <x<1 f(x) = x 2 1 x +…

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Q: Consider the following. u = -6i - 2j - 4k, v = 2j + 2k (a) Find the projection of u onto v. 0, - 3,…

A: As we know that; The expression for the the vector projection u onto v is: projvu=u·vv2v And The…

Q: geometric series n=1 b) Find the value of r such that the serie 00 Σ 5 E(-1)"- is equal to . If it…

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Maximize…

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Q: Assume that lines which appear to be diameters are actual diameters. 66° H Find the measure of GHF

A: Clearly FH is the diameter of the circle

Q: 2.2 7. Using the table of values for the function g shown below to estimate f, g(x)dx using L3, R3…

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Q: Sin 5

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Q: Find the limit of the V4n +9 sequence lim Show your work. n- 00 9 n+4 Determine whether the (- 1)…

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Q: The region {(*+y)|x2-7, 0syse} is is represented below. Find the area of this region to two decimal…

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Q: Use cylindrical shells to find the volume of the solid generated when the region enclosed by the…

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Q: Determine whether the integral is convergent or divergent. 4 dz z2 + 6z + 5 convergent O divergent…

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Q: Activity 1.3.2. Consider the functionf whose formula is f(x) = 3 – 2x. d. Without doing any…

A: Consider the function  y=3-2x

Q: Antiderivatives resulting ir x2 dx x4 + 3

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Q: Find the open intervals where the function is concave upward or concave downward. Find any…

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Q: Given that lim f(x) = 0 X→a lim g(x) = 0 lim h(x) = 1 lim p(x) = 00 Xa lim q(x) = ∞, Xa evaluate if…

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Q: Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral. a…

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Q: Consider a nonhomogeneous differential equation y" + 4y = -12x + 10e. (a) Verify that yp = -3x + 2e*…

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Q: Find f. f '(t) = 4/(1+t^2)     f(1) = 0

A: Topic = Integration

Q: f (x,y) = 2x^3 + y^2 - 9x^2 - 4y + 12x +1028. Find all critical points of f. For each critical…

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Q: sin 8 What is the exact value of Show your work for partial credit.

A: Find the value of sin(7pi/8).

Q: Let F(x) = f(f(xæ)) and G(x) = (F(x))² . You also know that f(9) = 3, f(3) = 2, f'(3) = 5, f'(9) =…

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Q: Find the area under the graph of the function over the interval given. y=x; [1, 5] 2. The area under…

A: Explanation of the answer is as follows

Q: f (x,y) = x^2y - 2x^2 -4y^2 +66. Find all critical points of f. For each critical point, determine…

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Q: Let f(x) = V3x . Consider the portion of the curve where 0< y <2. Find the exact value of the…

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Q: 4. Consider the function f(x) = (2x - 3)5. Discuss the continuity and %3D differentiability at x =…

A: 4.f(x) = (2x-3)15 from the graph, f(x) is not differentiable at x=32 , since slope changes at x=32…

Q: A culture of the bacterium Salmonella enteritidis initially contains 50 cells. When introduced into…

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Q: Find u - v, 2(u + 3v), and 2v - u. u = (4, 0, -8, 6), v= (0, 2, 6, 4) (a) u - v - (b) 2(u + 3v) (c)…

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Q: Determine the open intervals on which the graph is concave upward or concave downward. (Enter your…

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Q: Find the coordinates of the point(s) on the curve y = Va + 3 that are closest to the point (8, 0).…

A: Given problem:- Find the coordinates of the point(s) on the curve y = √(x + 3) that are closest to…

Q: Write the given system without the use of matrices. 1 -1 9. 1 3 d 3 -7 1 y + 2 -1 t dt -2 dx dt dy…

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Q: USE THE LIMIT DEFINITION OF DERIVATIVE:  A wire 10 cm long is cut into two pieces, one of length ?…

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