Find the area bounded by the curve y (x- 2)(x + 1)(2x – 1) and x-axis.

Q: The Laplace transform of th is valid for O s>n O s>0

A: The Laplace transform of tn is        Ltn=n!sn+1, for s>0

Q: Given the differential equation: y"+3y'- 4y = e42 Propose an appropriate particular solution Yp = (A...

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Q: Find f'(a). 2t + 12 (t) t + 9 f'(a):

A: Given that: f(t)=2t+12t+9

Q: x² – 3y + 3 = 0 2y + x + 2 = 0

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Q: solve the differential equation and express final answer with the value of C (3x^2 +y^2) dx + 2xydy...

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Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by ...

A: Topic. = Volume

Q: A solution containing at 2 lb of salt per gal is poured at 3 gal per min into a 300-gal tank that in...

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Q: If the Laplace Transform of F (t) = vi what is the Laplace Transform of is 4s 2 F (t) = e' vt3?

A: Laplace transform of F(t) = et root t3

Q: Find the exact length of the curve. X = Vу (у — 3), 16 <y S 25

A: First differentiate wrt y

Q: 9.

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Q: Find the most general antiderivative of the function f(x) = 2(5 – 2)?. Answer: F(x) =| %3D

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Q: d'y Given the differential equation + y = e-6" sin(x) dx? Propose an appropriate particular solution...

A: follow the procedure given below.

Q: Applying variation of parameters to the DE: y"- y = e + e-", | we get the following system of equati...

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Q: Given the differential equation, d'y dy = e" sin() cos (), the proposed particular da? dx solution i...

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Q: 2. If P(0) is a point on the unit circle and 0 (0)? , what is the coordinate of P

A: Given query is to find the coordinates of p.

Q: For the following differential equation, (3D - 3D2 - 3D+ 6) y= 0. how many arbitrary constants are e...

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Q: What is the result when you square a binomial?

A: When square a binomial

Q: A 300-gallon capacity tank is originally filled halfway with a brine solution that contains 2 Ibs of...

A: Given:   Data is given

Q: A 2-lb object, that stretches a spring by 1.5 inches, is released with a downward velocity of 32 ft/...

A: We have to find the differential equation that models the system.

Q: 3 4/3 3,213 +7 for 1sx<8. - -X Find the length of the curve y = 7x ... The length of the curve is (T...

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Q: The half-life of a radioactive material whose rate of disintegration is proportional to the amount o...

A: Let X0 be the initial amount of material when t =0            After time t the amount which is left ...

Q: The Laplace transform of a constant, k, is valid for O s>k O s>k O s>0 O s<0

A: Laplace transformation of a constant k is  L{k} = k/s It is valid for s &gt;0

Q: Solve [y (In x – In y) + x] dx +a (In y – In a) dy = 0 xlny + yln x = Cx None of the choices ylnx + ...

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Q: Find the exact value of each trigonometric function 2. COS 135 degrees 4. TAN 930 degrees 6. COT ...

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Q: Suppose that 4 J of work is needed to stretch a spring from its natural length of 34 cm to a length ...

A:  4 J of work is needed to stretch a spring from its natural length of 34 cm to a length of 48 cm. (a...

Q: Given the differential equation (D + 9D² + 27D + 27) y = ln(2x - 3). Propose %3D an appropriate part...

A: We will find the particular solution for the given differential equation.Below find the solution in ...

Q: Show that the function f(x) = |x - 3| is not differentiable at 3. We have x- 3 if x 2 3 f(x) = |x - ...

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Q: If f)=6X+12, hind the slopeof the secaut line between the values of X,= -5 and Xa = - 6- %3D

A: The given function is: fx=6x+12 To find the slope of the secant line between the values of x1=-5, an...

Q: Find L{{t"+3)*} O none of the choices given n! sn+1 n! 2. +6 S2n+1 n! 6. sh+1 (2n)! n! s2n+1 +6 sn+1...

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Q: 5) Find the average value of f(x) = x on the interval [1, 8].

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Q: The dimensions of a box are b, b+1, b+4. Find how fast the total surface area A increases as b incre...

A: Topic:- geometry

Q: Find the Laplace Transform of the piecewise function. (2 ,0<t<4; w(t) = { í 1? ,t 4. O 252+e-48 (2+8...

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Q: 3) The magnitude of a velocity vector is speed. Suppose that a wind is blowing from the direction N4...

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Q: Given a differential equation of the form y (x) + p (x) y = q (æ). where it follows that Su(x)g(x)dx...

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Q: Find the L{y(t)}, given the initial value problem y" - 3y' + 2y = t - 2; | y(0) = 0, y'(0) = 1 %3D %...

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Q: BASIC PROPERTTES OF INTEGRATION IHTEGRATE THE FOllowING: 8. 2 t 22 tz I 32 +3z*+x° 9) + " () वg 3. 3...

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Q: e2x +2e* -dx e* +1 2.

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Q: dy dy Given the differential equation 2. da3 +2. dx2 dr Propose an appropriate particular solution. ...

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Q: Find the exact values of the six trigonometric functions of the angle e shown in the figure. sin(0) ...

A: The given triangle has lengths 8 and 6

Q: A 2-lb-per-gallon salt solution is pumped in a 400-gallon tank at a rate of 2 gallons per minute. At...

A: We will find that how much salt is in the tank as soon as it starts to overflow.Below find the solut...

Q: siny+ tan y = siny %3D 12. 1+ secy

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Q: xdy ydx = 0; y (1) = 2 %3D Which of the following is a solution to Oy3D+ 1 + In(2) O In(y) = x +2 Oy...

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Q: Solve the given differential equation by using an appropriate substitution. The DE is a Bernoulli eq...

A: We need to solve DE.

Q: The definition of the error function also defines an "error term" E(x, y). Find E(x, y) for the func...

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Q: solve the differential equation: y' + (4/x)y = x^4

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Q: After applying variation of parameters to y " +y = sec(x), the following equations are obtained c{ (...

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Q: (5an 20 elan 20 sec²2 Bd ß 1. e?x +2e* dx e* +1 2.

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Q: 9) If a cup of coffee has temperature 95° C in a room where the temperature is 20° C, then, accordin...

A: topic - definite integral

Q: Find the Laplace transform of: F (t) (2+t) e*. ( 3n.)! f(s) = + (s+4)* s+4 (s+4)3n+1 (3n)! f (s) = 2...

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