5 -4 4 6 e 5t A = -4 5 4 f(t) = %3D 12 e 5t 45 -6e 5t x(t) = ...... %3D 4.

Q: 2 3 = e* x*0,(2x - y) +,(x-y) i=0

A:

Q: 3. What is L (s+3)* S-5 4t. A. B. e2 +2e* e"t +2e 4 4t e°t +2e" C. e 37? +2e10r 3t 2 С. е e + 2e10t…

A:

Q: 2. A population of honeybees begins with 100 bees and increases at a rate of b(t) bees per week.…

A:

Q: S(3x2 — х + 2) е -* dx | A - (3x2 – x + 2)e* (бх 1)e * + 6 e¬* + C (-3x² – 5x – 7)e¯* + C (3x? —х+…

A:

Q: 2. 2 PER SON GAME PLAYER A's PAYOFF FUNCTION f(x,9)= x(48 - 4x+g) PAYER B's PAYOFT FUvNCTION…

A: Given- Player A's payoff function fx, y = x48 - 4x + yand Player B's payoff function gx, y = y96 -…

Q: (b) Given the data 5 10 15 20 f(x) 0.08716 0.17365 0.25882 0.34202 find f(6) using appropriate…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 3ר2 d²y' |1+ () = c2 dx2 second order second degree first order third degree second order third…

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Q: (10x)" 1. E n=1 (x - 5)" 2. (5)" n=1 (x-5)" 3. (n!)5" n!(10x - 5)" 4. 5" A. 10 В. О C. 00 D. 5

A: We use the Ratio test to solve the given question.

Q: dx S- xV x2 +4 Evaluate: 그yx2+4-4 + C A) x +4 +4 x² + 4 - 4 + C x2 + 4 +4 1 B 2 x² +4 – 2 + C x² + 4…

A:

Q: 1 F(s) F(s) s2-6s+34 s2 +4s+4 s2-4s+53 s2-6s+9 This option This option

A: Laplace transform

Q: 3. From 1970 to 1990, Sri Lanka's population grew by approximately 2.2 million persons every five…

A: Solution is given below

Q: 5s + 7 (s + 2)2 A. f(t) = e-2t (5+ 7t) C. f (t) = e-2* (5 – 7t) B. f(t) = e-2t (5 + 3t) D. f(t) =…

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Q: 2 L₁ (2x - e²x)² dx A. B. C. D. 31e¹+36e²+3 12e4 31e¹+36e²-3 12e4 31e4-36e²+3 12e4 31e¹-36e²-3 12e4

A:

Q: 2.x S(1 + e2) e d O e^x + e^ -x + c O e^-1- e^x + c O (c^2x 1) / e^x + c O (c^-2x -1) e^x+ c

A: Integral is in some sense the inverse of the derivative. This is seen from the fundamental theorem…

Q: S(3x + 5)e3*+5 dx D 1 e3x+5 3 (3x +4) + C 3x+5(3x + 6) + C B)e C) e3*-5 (3x + 6) + C D) e3*+5(3x –…

A: Using substitution method of integration & By parts rule

Q: A certain community consists of 2000 people, and one individual has a particularly contagious strain…

A: Given

Q: s- 5 s2 +s - 6 3 A. f(t) = -3t 8 C. f(t) =e D. f(t) = -e-3t 3t 8 B. f(t) = e-3t 3 e2t %3D 3 e2t

A: Introduction: The Laplace transform is an integral transform in mathematics that turns a function of…

Q: x² + 3 x < -4 Зх — 5 —4<I<-1 -1< x < 2 5x +1 4<x <7 2х + 8 7<х 3. Find the following where M(x) = 7…

A: For every x check the interval where it belong and see the corresponding function value

Q: a. b. INGIN IN C. + S (S-1)² e35 + 5-1 e-3s S 5+1 d. None of the above L{2+ (t-3)et-3 U(t-3)] = +

A: Consider:  L2+t-3et-3 Ut-3=L2+Lt-3et-3 Ut-3 Now, L2=2L1=2×1s                      since L1=2s So,…

Q: e (2e – 1) dx (ear – 2)*(e³< + 1)+ ,3x A 2e3x – 1 В 2e 6x – e 3x © (e3 – 2)4 +(1 +x?) @ E ,6x – e 3x…

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Q: 14. An investment account with P invested for T years at compounded rate, r grows to a value of V.…

A: It is given that, Principal =  P  Time =  T years  Annually compounded rate = r

Q: ху+ 3x — у—3 ху— 2х + 4у—8 dy dx e* (y + 3)$ C = e (x + 4)5 e' (x – 3) C = e-×(y+4)$ Option C Option…

A: The given differential equation is, dydx=xy+3x-y-3xy-2x+4y-8=xy+3-1y+3xy-2+4y-2=x-1y+3x+4y-2 Now…

Q: E -17 Sx-8 F. x-1<2 . x-10s-16 H. x+23 J. 4.4 <x-7.2 13 L. 4. 12 12 r+04 -08 시

A:

Q: Two models, R1 and R2, are given for revenue (in billions of dollars per year) for a large…

A: The value of t=11 corresponding to the year 2011 . Evaluate the integral below to calculate the…

Q: s2 + 9s + 2 (s – 1)2(s + 3) A. f(t) = et +3tet – 2e-3t C.f(t) = 2e + 3te – e-3t B. f(t) = et + 2tet…

A:

Q: In the given question  two models R1 and R2 are given for revenue (in millions of dollars) for a…

A: Solution Given  two models R1 and R2 are given for revenue (in millions of dollars) for a…

Q: [5 1 2] 5. Find e4 for A = |0 3 0 L2 1 5]

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Q: 1 d) 2r- dz - r e² – e-z e) J ez +e-z° rp- In 3 f) 1 ez +e-z Ip-

A:

Q: 5s + 7 (s + 2)2 A. f(t) = e-2" (5 + 7t) C. f(t) = e-2" (5 – 7t) B. f(t) = e-2"(5 + 3t) D. f(t) =…

A: Use partial fractions and Laplace table.

Q: 6-9 d x.dy 2.

A: A double integral is given. We need to evaluate the double integral.

Q: 1. 1 0 1 0 0 1 1 0 |A → 0 4 0 E A → 1 EE, A → 0 E3 E2 E A = 2 -1 1. 0 0 1. -1 1 E1 E2 E3 Е

A:

Q: 1 2 3. 4 0.7 0.3 0.1 0.05 0.01 Give the exponential model. y = 1.55 x 0.50* O y = 1.99 x 0.22 O y =…

A: Explanation and solutions is given below.....

Q: III. Exponential 1. S(1 – 2etanx) sec² xdx e2t dt 2. S 1+6е2t+9e4t

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Q: s2 + 9s + 2 (s – 1)2(s + 3) A. f(t) = et + 3tet – 2e-3t C. f(t) = 2et + 3tet – e-3t 3. f(t) = et +…

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Q: 2. S(e" + e-3)² dt

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Q: 7. y = 2*32x5x V36x y = 8. 6x5 V144x3 9. у — 10. у %3 (2x3)? 2x2 1. If y x x² and y increases from…

A:

Q: S e3(2e * – 1 ) dx (ear – 2) (e3* + 1) 4 (A) 2e3x – 1 B) 2e 6r – e 3x © (e3r – 2)+ D (e*+1)+ (E ,6x…

A:

Q: es L-1 (s- 1)(s +2)/ %3D O (1/3) e^t-(1/3)e^(-2t) O (1/3) e^2t-(1/3)e^(-2t) O [(1/3) e^(t-1)-(1/3)…

A: Note: Our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: (47 s - 2)e* + 4 s+ 2 s'(e* –1) 2) f(1)=4x -t, (0<t<27) Ans. F(s) = ,27s

A:

Q: 4. e+1) xp- 2x a. x-2e*-e2 1 + C 1 b. 2e*-ex + C 2x + e" +ze* +C -X 2° d. None of the above

A: To evaluate: The integral ∫ex+12e2xdx. Concept used: Algebraic formula: a+b2=a2+b2+2ab Integration…

Q: y 3.0아 (1, e) 2.5 2.0아 y-e* 1.5 1.0 y = xe*2 0.5 -1.0 -0.5 0.5 1.0 1.5 2.0

A:

Q: sʻ + 3s+10)(s+5) a. G(s) = %3D (s + 3)(s+ 4)(s² + 2s+100) s³ + 4s² + 2s+6 (s+8)(s² + 8s+ 3)(s² + 5s…

A: To find the inverse Laplace transform of the function, first convert the function into partial…

Q: s+3 Find L-1 L(s+5)(s2 -1). A)글et-3e-t +est 12 B)e* - -5t +=e 4 C) e* -e-t -e-5t 12 4 D)e* 5t +-e 1.

A: Some Laplace transform Formulas: L-11s+a=e-atL-11s-a=eat To find Laplace inverse of s+3(s+5)(s2-1)…

Q: 1.4. E e-2k k=0 1.5. (-1)* k=0 k+1 1.6. k=53 k-1 M8

A: To analyse the given series.

Q: e 3* (2e 3x – 1) dx (e6x – 2)4(e3* + 1) + A 2e 3* – 1 | бх B 2e Ox – e 3x © (e3r_2)4 D D (e3+1)+ E…

A: Please see the below picture for detailed solution.

Q: A patient receives an injection of 1.4 milligrams of a drug and the amount remaining in the…

A:

Q: S. (e3* + 1) / (e3* + 1)²– 4 Evaluate: e™dx e sec -1 6. 3x +1 -+C 2 A e +1 e 3r B sec -1 +C 2 C None…

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Q: Business Calc 2 please show detailed steps! Thanks!

A:

Q: 1.) Bacteria multiplies in a rate in which a bacteria splits into two new cells, thus doubling its…

A: how many bacteria will we have at 6:00 am the following day?

Q: 1.a. Age of Students (x) 10 9 10 12 12 11 11 9 9 Solution: P78 =. D6 = Q1 =

A: Given data: x = 10,9,10,12,12,11,11,9,9 To find: 1.Q1 2.D6 3.P78

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.