Radium decomposed at a rate proportional to the quality of radium present. Suppose that it is found that in 25 years approximately 1.10% of a certain quantity of radium has decomposed. Determine approximately how long it will take for ½ the original amount of radium to decompose.

Q: x+2 Determine the case of the following proper rational function after simplification: (x2 -…

A: Here, the rational function is: x+2(x2-4)(x3-8)=x+2(x2-22)(x3-23)=x+2(x-2)(x+2)(x-2)(x2+2x+4)

Q: Evaluate: dx (x+1) log(x+1)

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Q: To reduce the DE (x+2y-4)dx-(2x+y-5)dy=0 to a DE with homogeneous coefficients, use the…

A: solution:-x+2y-4dx-2x+y-5dy=0dydx=x+2y-42x+y-5the system of linear equation…

Q: Which of the following is the antiderivative of the integral function: * f(xex) dx - ex + C none of…

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Q: Find the average value of the function f(x, y) = xy over the triangle with vertices (0, 0), (1,0)…

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Q: How many antiderivatives does a function of the form f(x)=x" have when n*0? A) none B) 1 infinitely…

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Q: Evaluate the given definite integral [ 2x³ – 6x² dx, from x = 1 to x = 2 X²

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Q: Find the dimensions of the rectangle of maximum area that can be inscribed in a right triangle with…

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Q: A tank contains 50-liters of brine in which 20 grams of salt is dissolved. Pure water is being…

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Q: We can apply General Power Formula of Integration on which of the following integrals? A / fes…

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Q: The Critical Point of y = xe*

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Q: 5. Find the volume of the tetrahedron bounded by the coordinate planes and the plane 3x + 6y + 4z -…

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Q: Find the area bounded by : f (x)=e*, g(x)=ex and x=3. (e²+ 1)² A sq. units e2 B (e³ + 1)² e3 sq.…

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Q: Stretching spring: Eighteen pounds of force is required to stretch a spring 3 ft. from its natural…

A: Given that, Stretching spring: Eighteen pounds of force is required to stretch a spring 3 ft. from…

Q: (D³ - 5D + 4)y = 0, when x = 0, y = -2, y' = 8, y" = 0

A: The given differential equation is: D3-5D+4y=0 when x=0, y=-2, y'=8, y''=0.

Q: y = x²sin (3x)

A:

Q: Solve the integral: Seln(2x² + 3x −4)³ (4x + 3)dx eln(2x² + 3x-4)³ (4x+3) 3(2x²+3x-4) A + C…

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Q: y = x²sin (3x)

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Q: Find the length of the curve of 8x = y² + 2y-² from y = 1 to y = 2.

A: Length

Q: Stretching spring: Eighteen pounds of force is required to stretch a spring 3 ft. from its natural…

A: To find the work done.  Option D is correct.

Q: 1. ²₂(x² − 2xy² + y²³) dx dy

A: Solve the following integration .

Q: Evaluate the following indefinite integral using Trigonometric Integrals f sinª x cos³x da where a…

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Q: Compute the Fourier cosine series for the given function f. a) f(x) = π - x, 0<x<T

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Q: لله √ √³ √ √² zysin(2² + y²) dz dy −

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Q: 1 -4 The reverse order of SO SAY ex² dxdy is equal to e-1 8e None of them O

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Q: HOMOGENOUS LINEAR DIFFERENTIAL EQUATIONS. (D3 + 2D2 – 5D – 6)y =

A: Topic:- differential equations

Q: Determine the area bounded by f(x)=x²-x and x-axis. Ⓒ / unit² A ® B / unit² © unit² D -unit²

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Q: Show if the following limits produce an indeterminate form. Then, evaluate the following limits. lim…

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Q: Integrate the equation using the method in trigonometric substition

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Q: The general solution of (D³+4D)y=0 is Ay=ex(c₁cos2x+c₂sin2x) B y=c₁+c₂cos2x+c3sin2x Ⓒy=c₁ex+c₂e²x +…

A:

Q: xdx (x+122

A: The objective of the question is evaluate the indefinite integral.

Q: d If g(x) == _S^*[e' − In(2t+1)]dt, find g ''(x) . - dx -2 2 A (2x + 1)² 4 B (2x + 1)² 4 (2x+1)2…

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Q: Two small planes approach an airport, one flying due west at 100 mi/hr and the other flying due…

A: Solution is here

Q: 19. Find the volume of the solid that results when the region enclosed by = 2y, y = 2, y = 3 and x =…

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Q: when the first nine terms of an arithmetic sequence is added. its sum is 72. what is the value of…

A: The fifth term will be ,a5=a+4d=8

Q: HOMOGENOUS LINEAR DIFFERENTIAL EQUATIONS. (D3 – 6D2 + 12D – 8)y = 0

A:

Q: Let f(x)=√3x-2 the y-axis and find the volume of the resulting solid. 83 (A) -unit ³ 135 83 (B)…

A: We will draw the curve f(x) and y=1. Points of intersectionf(x)=3x-2   and y=11=3x-2 1=3x-2x=1Point…

Q: The function is X 2 = y² What is 8²% მ2 Y x²

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Q: Determine the integral: [x²cosxdx A x²sinx + 2xcosx+2sinx + C B x²sinx + 2xcosx-2sinx + C (C)…

A: Given,∫ x2cosxdx

Q: In the indefinite Integral in(cosh x + e*)- A In(cosh x + e*) B) sinh x + ex D In(cosh x + e*) sinh…

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Q: y'+xy=xy^3 Solve for the solution What is the integrating factor? What is the dependent variable?

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Q: D sec²u=1+tan²u

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Q: 3. The auxiliary equation of the differential equation (D² - 6D+9)y = 0 falls under Prove your…

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Q: The given function v = ln (xy) + ex+y Determine Ov/ox

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Q: The hyperbolic paraboloid (saddle) f(x, y) = x² - y² + 4 is shown in the 3D model below. Find the…

A: Here, to find the volume f(x,y)=x2-y2+4 between the rectangle R=[-2,4]×[-1,2]

Q: cot3x Lim X-o cotx 0

A: Given limx→0cot3xcotxTo evaluate the limit:

Q: Question 3 Iff is continuous on [a,b], then T True F False b then f(x)dx = f(x)dx T a

A: Here it is given that f is continuous on [a,b] From the integration we can take the constant value…

Q: The reverse order of 4 So Say ex² dxdy is equal to e-1 8e None of them

A:

Q: Given A B C D f(x) dx = 0 and 11 6 0 ¹² f(x) dx = 11 6 I 11 5 55 6 evaluate S²3f(x) dx - ₁2f(x)dx.…

A: we have to find the integral

Q: Which of the following represents the volume of the solid generated by revolving the region bounded…

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