A stone dropped in a pond sends out a circular ripple whose radius increases at a constant rate of 2 ft./sec. After 12 seconds, how rapidly is the area enclosed by the ripple increasing?

Q: The length of a rectangle is given by 4t - 3 and its height is √2t, where t is time in seconds and…

A: The area of a rectangle with length L and height H is given by A=L×H. We use chain rule , power rule…

Q: Evaluate the following indefinite integral using Partial Fractions S x² +4 (x²+4x+3)(x-2) dx

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Q: The given function v = ln (xy) + ex+y Determine 02v дхду

A: Given  v = lnxy + ex+y We have to determine  ∂2v∂x∂y.

Q: 28. After 500 years, a sample of radium-226 has decayed to 80% of its original mass. Find the half-…

A: Let A is original amount, A=100% Given t =500 year, At= 80%A At=20% half life h=?

Q: 7.Find of z = x3 + 5x2 y + 6 02z дхду

A: find ∂2z∂x∂y of z=x3+5x2y+6 formula: ∂xn∂x=nxn-1

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

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Q: The general solution of (D³-4D2)y=0 is A y=c₁+ ₂²x+c₂e-²x By=c₁+ c₂x + c3e4x - 4x Ⓒy=C₁ + c₂x + c3е¯…

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Q: Refer to the definite integral to answer the following questions 3 1² (2²) (x²) dx

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Q: 3. Look at the figure below. Find the value of x and the measure of each angle. n 1.x = 2.42 = 3.26…

A: We know that alternative interior angles are same Therefore 5x-14=3x+18 Subtract 3x+18 from both…

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

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Q: Using the method of undetermined coefficients, the modified form of a particular solution for the…

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Q: * The evaluation of So So x y ex² dxdy is 0.25 e - 0.5 0.25 e - 0.25 None of them

A: The objective is to evaluate the double integral.

Q: Let f(x)=√√3x-2 on the interval [ 13.1] axis about the y-axis and find the volume of the resulting…

A: We need to find volume.

Q: fx(2x + 5)³ dx

A: Integral

Q: In(x+2) 1. S dx 2x+4 2 2. fx² ex dx 3. f tan³x dx 12

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Q: Find the volume of solid generated by revolving the region bounded by f(x) = x² + 1and g(x) =…

A: Given that , fx=x2+1 and gx=-x2+2x+5 find the volume of solid generated by revolving the region…

Q: x³√/x² + 1dx

A:

Q: 5. The auxiliary equation of the differential equation (4D³ - 13D + 6)y = 0 falls under Prove your…

A: Given; ( 4D^3-13D+6)y=0

Q: 9. Find the area between y = √x and y = √x+1, over the interval 0≤x ≤4

A:

Q: A car is travelling at the rate of 88 ft/sec when the brakes are applied. The car begins to…

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Q: 2. Use polar coordinates to find the volume of the solid under the paraboloid z = x² + y² and above…

A: Let's find volume of solid by using polar coordinates.

Q: 6. Determine the area of the region bounded by x = −y²+ 10 and x = (y 2)²

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Q: 3. Use Use the disk method to determine the volume of the solid obtained by the revolving the region…

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Q: 5. Use the cylindrical shell method to determine the volume of the solid obtained by the revolving…

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Q: Compute the Fourier sine series for the given function f. a) f(x) = x², 0<x< π

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Q: y" - 3y' + 2y = 2x² + ex + 2xe* +4e³x

A: As per the company's guidelines we are supposed to solve first question for you, kindly repost other…

Q: lim (lnx) = . x →+∞

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Q: Question 1 A body cools from 60°C to 50°C in 5 minutes. How much more time (in minutes) will it take…

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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: What is the annihilator for y=x e*cos 2x ?

A: Our Aim is to compute the annihilator for y=x ex cos 2x -(i)

Q: The improper integral A 0 B 1 с e D 8 +∞ St 0 ex dx is

A:

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

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Q: S x² - 2x² + 3x² -x +3 "x²³ - 2x² + 3 +3

A:

Q: Find the critical points of the function f(x) = x³ + ¹/5x² + 50x + 7. Use the First Derivative Test…

A: We have to find the maximum and minimum.

Q: Given [ f(x) dx = 0 and 11 0 11 6 55 6 rwax = 11 6 " evaluate S злах-п -1 2f(x)dx

A: Given,∫-11f(x)dx=0,∫01f(x)dx=116,To find ∫013f(x)dx-∫-102f(x)dx

Q: me general solution of (D²-2D+1)y=2sin > A y=c1eX +C,xe* + sinx+cos x y=C1eX +C,Xe* + sinx ©…

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Q: What is the value of C if r(π/3)=2? * O 2 0 TT/2 none of the choices

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Q: dx using miscellaneous substitution will yield to secx + 1 Transforming A B © ² с -dz 1+z² © S²+ /…

A: Please see the answer below.

Q: 2. Find the general solution of xdy + (3xy + y - e-3x) dx = 0

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

A: In the given problem we have to find out area of region bounded by given curve with the help of…

Q: Given x4 (x + y) = y2 (3x - y), use implicit differentiation to find dy/dx

A: Given: x4 (x + y) = y2(3x - y)

Q: Given f(x)=4x+1 and g(x)= x²+x-3: Use the washer method to determine the volume of solid obtained by…

A: Let's find volume of solid by using washer method when given two curves rotated about x axis.

Q: y = Arctan ( 2+x 1-2x

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Q: 4. Find the general solution to each of the following differential equations. (a) 2xy² - 1 +…

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Q: Question 5 Which of the following is not true? A None of the given choices ℗ √ ² in(x²) dx = I'm √…

A: The objective is to find which option is not true.

Q: Evaluate: L{cos(3+2t)} s cos32sin3 A s²+4

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Q: 5. The auxiliary equation of the differential equation (4D³ - 13D + 6)y = 0 falls under_ Prove your…

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Q: 1. Evaluate the following limits (a) (b) x sin r lim 2-0 1- cos x lim (1+a/x), a, b>0 x →+∞

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Q: Solve x² = 4y + 4 and x = y = 2 128 A sq. units 5 B none of the choices 2 21 sq. units 3 for the…

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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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