(i) Show that the solution of the logistic equation dr az – br dt (3) is given by 1(t) a – br(t) r(0) a – br(0) (4) (ii) Solve Equation (4) for r(t).

Q: Find two roots for the following equation using Newton-Raphson method: tan x +x-1=0

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Q: What is the particular solution to the differential equation (1-xy)? + (y² + (1-xy)- )dy = 0 and y =...

A: Givendx1-xy2 + y2 + x21-xy2dy = 0withy(4) = 1

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A: The word Combination is used when there is  any importance of order in selection. The word Permutati...

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Q: Different sets of 5 cards formed from a standard deck of 52 cards.

A: Problem of combinatorial.

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Q: Q1) Evaluate the following integral: y = | tanx dx

A: We have to evaluate the integral:y=∫tan3xdxy=∫tan2xtanxdxy=∫sec2x-1tanxdx                Using tan2x...

Q: sin³ydy The is equal to 1+ cosy 1 A. cosy +, cos²y + C 1 B.-cosy + cos²y+C 2 1 C.-cosy -- cos?y + C

A: Note:- As per our guidelines, we can answer the first part of this problem. For the remaining part p...

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Q: 3. -1 -1 -2 -3-2-1 0 12 01 2 34 -2-1 4 -3 -2 -1 FIGURE 6.1.12. and saddle point (2, -1). Spiral poin...

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Q: c) Explain why there cannot exist a simple graph of order 11, where the vertices have degrees 1, 1, ...

A: Q5. (c) Simple graph : A simple graph G is a graph that does not have more than one edge between any...

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Q: QI) Evaluate the following integral: y = tanx dx

A: Given  To evaluate ∫tan3x dx

Q: U = {(a,−a,b,c) | a,b,c ∈ ? } and W = {(p,q,-p,r) | p,q,r ∈ ? }. Is U ∩ W = {0}? If it isn't, then ...

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Q: Xe^x-cosx =0 (0.5 ,0.6) Solve using These methods: a) upto 3 decimal places for Bisection method. b)...

A: Thank you for the question.  According to our guidelines we can answer only first question and kindl...

Q: Q5) Evaluate the following integral by using Partial fractions Method: x- x = t + 1). (x – 1)² dx (x...

A: Given the integral is y=∫x3-xx2+1x-12dx

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Q: Solve the following system of four equations using Jacobi Method. Assume initial value of unknowns t...

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Q: The values of C, and C2 so that y(x) = C, sin x + C, cos x satisfies the following conditions: y(0) ...

A: The constants C1, C2 can be calculated using the initial conditions. It is known that ddxsin x=cos x...

Q: p' = rP a where 0 < a< K and r is a positive constant. Identify all equilibrium populations and dete...

A: We will find equilibrium points by equating P'=0 then depending on sign of P' draw phase diagram and...

Q: 1- Solve the following systems linear differential equations (by elimination) dx = -9y, (a) dt dy = ...

A: (a)Given that, dxdt=-9ydydt=-4x Now we solve this system.  

Q: d. |A ∪ B̅ ∪ C̅| e. |A̅∩ B ∪ C| f . |A̅∩ B̅ ∩ C|

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Q: 10. Solve the initial value problem dy dy dt dt2 +8 -9y =0 y(1) = 1, y'(1) = 0.

A: 10 Given differential equation is d2ydx2+8dydx−9y=0 and y1=1, y'1=0. We have to find the solution of...

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Q: The product of two numbers is 24. Find the numbers if (a) the sum of the two numbers is minimum, (b)...

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Q: Use induction to prove Vn > 1: 3| (n³ + 2n).

A: Proof :-

Q: Find the round-off error of the following using 5 significant digits: 1 1. 3 2. tan 150 3. 1 — п 4. ...

A: Question number 4:   11531153  ≃  4.86294Round off error = 115 3 - 4.86294                          ...

Q: Which of the following is the general solution to the differential equation 2ydy – xcos(xy)dy – ycos...

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Q: Construct the dual problem associated with the primal problem. Solve the primal problem. Minimize C=...

A: Given problem is Minimize     C =58x +48y +11zsubject to,                      2x+y+z  ≥ 8          ...

Q: Find the derivative of the vector function below r(x) = sin²(secx 2)i +csc°(vx² +1)j +8tan(x -) k

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Q: Choosing 3 household chores to do for a day. Combination Permutation

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Q: Solve the truth value of the well-formed formula (WFF) below. If the answer is 0 chose FALSE, is the...

A:  The logical symbol "∨" is used to denote "OR" . The logical symbol "⊃" is used to denote "IF..THEN"...

Q: Let A and B be sets. The union of A and B is A U B = {x|x E A V x € B}. The intersection of A and 3 ...

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Q: Q1) Find Eigen values of matrix ( 2.

A: Given matrix is 1254 Take,   A =1254 For Eigen values, first we'll calculate the characteristic equa...

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Q: for series. 8. Suppose that > an and bn are convergent series with an, bn > 0 for all natural number...

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Q: Q4 Let f : R →R be the function defined by 1 f(r) = = a) Is f is one-to-one? If yes, then explain wh...

A: An one- one  function is a function that maps distinct elements of its domain to distinct elements o...

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Q: Use sigma notation to write the Taylor series about x = xo for the function. e*; xo = 4 00 4 (x) k! ...

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Q: Exer. 1-14: Find the vertices and foci of the ellipse. Sketch its graph, showing the foci. 9. 2. 25 ...

A: The vertex of ellipse x2a2+y2b2=1 is a point at which it makes its maximum turn.  Let a&gt;b. Then a...

Q: Q3) Find the limit for the following function by using L'Hopital's rule: x- sin x lim x3

A: We have to find the limx→0x−sinxx3 by using L'Hospital's rule. L'Hospital's rule is defined an follo...

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Q: 2) From the figu (a) Pouring temp (b) Cooling rate (c) Liquidus tem (d) Solidus tempe (e) Super heat...

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Q: Determine the length of the altitude from vertex B to side b of triangle ABC if c = 14 cm, a = cm, a...

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