Solve the differential equation by variation of parameters. y" + y = sin(x) y(x) =

Q: A particular computing company finds that its weekly profit, in dollars, from the production and sal...

A: P(x)=-0.005x3-0.1x2+600x-800a)P(10)=-0.005(103)-0.1(102)+600(10)-800P(10)=-5-10+6000-800P(10)=5185Cu...

Q: 2. A triangle has a height that is increasing at a rate of 2 cm/s, and its area is increasing at a r...

A: Area of the triangle , A =12(Base)(Height) Product Rule of Differentiation : du.vdt=u.dvdt+dudt.v

Q: Let f(x) = Vx. Which of the following is the Taylor polynomial of degree 1 for f(x) centred at a = 1...

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Q: Calculate the integral of f(x, y, z) = e over the tetrahedron W in the figure (the region in the fir...

A: To solve the given triple integral. 

Q: 2020, the population of Ethiopia was 1.65 times as large as the population of Thailand. We can also ...

A: Given query is to find the population of Ethiopia in terms of percentage of population of Thailand.

Q: Write an equation for a rational function with: Vertical asymptotes at x = 1 and x = 3 x-intercept...

A: Question- Write an equation for a rational function with:   Vertical asymptotes at x = 1 and x = 3  ...

Q: Find the absolute extrema of the function f(2) = 6a? – a³ on the interval – 1 < e < 7 This function ...

A: Here we have to find the absolute extrema of the function f(x)=6x2-x3.

Q: Given z1 = 2 - i sqrt 5 and z2 = 2 + i sqrt 5 find z1/z2

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Q: Transformation by Trigonometric Identities Evaluate: integral of sin^12 2x cos^7 2x dx. Use the guid...

A: Let I is the value of Integration.

Q: For each of the following functions, find all local maximum and mini- mum points. х, х# 3, 5, 7, 9 5...

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Q: 2. For the line through P(3, 2, – 1 ) and Q( – 2, 1, – 4 ), determine each of the following : a) vec...

A: For the line through P3, 2, -1 and Q-2, 1, -4, to determine each of the following: a vector equation...

Q: Convergent Sequence If a1=√5, a2=fourth of √5 raise to 3, a3=eighth of √5 raise to 7, a4=sixteenth ...

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Q: An equation of the plane passing through A(2,1, –1), B(0,–2,0), and С (1,-1,2) is: 7х — 5у — z %3 10...

A: We have to find an equation of the plane passing through A(2,1,-1), B(0,-2,0), and C(1,-1,2).

Q: 1.5 (0,7, 0.2y f0.7,0.2) O5 ー15 - O.5 0.5 1.5 -0.57 (-1,2,-1) -15 -2

A: The f' is undefined where the graph of f has shard edges that is at x=-0.7,0,0.7,1 f(x) has sharp ed...

Q: The range of the function f(x, y) =16-4x² -9y is equal to: [0, 4] [0, 16[ O This option O This optio...

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Q: A sample of radioactive material starts with 0 grams . After 3 half -lives have passed , how much ra...

A: Let's find. 

Q: dx Vx

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Q: Using Integral or comparison test, determine if the series is converging or diverging. +00 nyn n² + ...

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Q: 6. A vertical tank shaped like a truncated square pyramid is filled with water. Find the work requir...

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Q: Use an appropriate test to determine if the series ) 2n converges or diverges. n+ en

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Q: (D² – 1) y = e-2* sin (e-*)

A: I am attaching image so that you understand each and every step.

Q: 3. Use the Comparison Test to determine if the series 5n Cos 2n n3 + n2 +1 n=1 converges or diverges...

A: Using P and comparison test. 

Q: demand for an electric fan is related to its selling price P (in dollars) by the equation n=3420-90...

A: QUESTION- demand for an electric fan is related to its selling price P (in dollars) by the equation...

Q: The slope of the tangent line to the parabola y = 2a2 + 2a + 6 at the point ( – 2, 10) is: The equat...

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Q: The concentration of a drug in the bloodstream C(t) at any time t, and hours, is described by the eq...

A: The concentration of drug reaches its maximum when                         C'(t) = 0find the values ...

Q: The domain of the function f(x,y)=3x+e 1s: D ={cx;y)eR?/(x +Dn² + y² 23} D ={x;y) eR?/(x –1)² +y² <3...

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Q: cos x dx 1 - cos? x d)

A: We have to find the antiderivative if the given part d.

Q: Solve the following triangle. B= 70°, C= 30°, b=7 (Simplify your answer) (Type an integer or decimal...

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Q: Evaluate the integral if it converges and enter the exact value. If the integral diverges, indicate ...

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Q: . We are given r'y-5x+24y 6/ỹ, where x and y are both functions of t. If dx = 2, x= 1, and y=9, what...

A: Given query is to find indicated derivative.

Q: -5 -4 -3 -2 3 4 3 -4+ 18x For the above rational function f( x) = identify its three inflection poin...

A: It can be solved using differentiation.

Q: Compute the double integral p x'ydA over the domain D indicated as 0 < x < 3, x < y< 5x + 5. Use sym...

A: Given problem:-

Q: 5. The management of Porter Airlines finds that its monthly marginal revenue can be approximated by ...

A: Find your answer below 

Q: 7. Let C be the curve y = 3x for 0 <x S 1. 0.5 Find the surface area of revolution of C about the x-...

A: Given: y=3x3 for 0≤x≤1

Q: 3. A piece of sheet metal, 100cm by 50cm, is to be used to make a rectangular box with an open top b...

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Q: Express the limit of Riemann sums as a definite integral. Do not evaluate! 7i 4+ 7i – 3 ( 4+ 7 lim l...

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Q: For what numbers​ x, −2π≤x≤2π​, does secx=​1? For what numbers x does secx=−​1?

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Q: Evaluate the integrals of the functions graphed by using the formulas for areas of triangles and cir...

A: Given query is to find the value of the integral.

Q: Suppose f(x) is continuous and increasing on [a, b], and concave up on (a, b). Is S6 (the Simpson's ...

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Q: 21n|sinh (1/2 »)|+C

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Q: Consider the series > and n=1 Vn3 + 3n – 1 n312 n=1 Write an inequality comparing 1 1 to for n > 1. ...

A: Please see the below picture for detailed solution. 

Q: Evaluate the integral if it converges and enter the exact value. If the integral diverges, indicate ...

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Q: 1 n > 3. Let an n Vln n Use the Integral Test to determine if the series > an converges or diverges....

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Q: Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the so...

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Q: dx I [; (1-2x) I= [sin (4x) cos(4x)dx (In(x))3 dx I

A: Given

Q: 1. Consider the curve of the function f (x) = 2x² a. Find an expression for the slope of the curve a...

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Q: Evaluate the integrals of the functions graphed by using the formulas for areas of triangles and cir...

A: Area of triangle =( base *height )/2 Area of semicircle = (π(r^2))/2

Q: For the demand function x=D(p)=/100-2p : (a) The elasticity is E(p)= (b) When p=25 , the elasticity ...

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Q: Let {an}=1 be a convergent sequence such that a1 = V5 and an+1 V5 an. Compute lim an.

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Q: Express the definite integral as a limit of Riemann sums. Do not evaluate! Csc da 3

A: a=3, b=6For each  n (number of sub-intervals) , we get∆x=b-an=6-3n∆x=3nAnd for  i = 1 , 2 , 3 , . . ...