where p(t) is the proportion of the population that knows the rumor at time t and a and k are positive constants. (a) When would half the population have heard the rumor? (b) When is the rate of spread of the rumor greatest?

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A: Topic:- limits

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Q: C. Evaluads the Sum 20 [ (₁²+3) ² (

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Q: c) L-1, 4s² - 21s+ 30 (s² - 6s+13) (s – 4) -

A: Above question is solved.

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A: Concept: Determinants: For a square matrix, a determinant can be defined in several ways. The first…

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A: 14)    Given differential equation y''+y'=0 ......................(1)    We can substitute…

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Q: Let F(x) = f(f(x)) and G(x) = (F(x))². You also know that f(9) = 7, f(7) = 3, f'(7) = 8, f'(9) =…

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Q: Solve the following Differential Equations with Laplace Transforms y" - by' + 15y = 2 sin (3t), y…

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Q: 9) Ур H Asin(2t) + Bcos (2t) Q13) The general solution for y' a) = 3x² + c b) = y Q14) The solution…

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Q: Given f(x) = x² sec x, find f'(x). Ox² cos x + 2x sec x O x² secx tan x + sec(2x²) O 2x sec x tan x…

A: f'(x)=x2secx'         =x2'secx+secx' x2        =2xsecx+secxtanxx2

Q: ƒ(5x² + 4x³ − 2x + 1)dx 이름 +2 -를 +a + C 5 2 O x5 x5 + x²-x²+x+C O 20x5 + A O 20x³ + 12x² −2+ C…

A: Given, ∫(5x4+4x3-2x+1)dx

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Q: Find the area common to the circle r = 3 and the cardioid r = = 3(1 - cos 0)

A: Figure of area enclosed by both curve÷

Q: Find f'(x) where f(x) = x. 2? O f'(x) = 2 (1+x. ln2) O f'(x) = -2 (1+x. ln2) ○ f'(x) = 2 (1-x. In2)…

A: Given :f(x)=x.2x

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Q: Consider the following. y = = In(x²) Find y'. y' = Find the slope m of the tangent line to the graph…

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Q: The Laplace transform of signal xi(t) is shown below. Determine the initial value x(0)

A: Above question is solved.

Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

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Q: Determine the critical point/s of f(x) = ln(x² + 4x + 14) on [-4,2]. 0x= -3 Ox=1 0 x = 0. 0x = -2

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Q: 31. The function fƒ: R→ R is defined by f(x) = (a) Show that f is a bijection. (b) Determine f¹(x) x…

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Q: Use the shell method to find the volume of the solid formed when a hole of radius 1 is drilled…

A: We have to solve above problem.

Q: 6 Find the area enclosed by the given curves. * y = x³ and y = 4x

A: As per our guideline we are allowed to answer only one question. Kindly repost the other question as…

Q: Q14) The solution of y" + y = 0 by using power series method, is: - a) y(x) = ao + a1 ( 1 - 12/11 c)…

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Q: Given the complex numbers z = 2 + j3,zz = -1 - j2,andzg=4+j4 find; Im (高)x+x@zs)+Im(zz+z) (元)

A: solution

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Q: Evaluate improper integrals if they converge, or 1/7 a) S. 72 de dx shab diverge

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: Find the orthogonal trajectories of x = C exp (-y²). Oy=C*exp(-x) Oy=C*exp(2x) Oy=C*exp(-x^2) O…

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Q: 2x² + y² +3z² = 1 y² = 4x x² -z² = y 2z = x² +4y² 2x + y − z =1 z = 4y²-x² E

A: We have to match the graph with equation and write name of these shapes.

Q: ? Question Draw the gradient f( − 1, 1), starting at ( − 1, 1), on the contour map of f(x, y) = xy.…

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Q: 3. A 72 N force acting in the direction of vector (2, -1, -2) moves an object from P(3, 4, 2) to…

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Q: The distance between the points (-8, m) and (m, 9) is 13. What are the possible values of m? a) 3 or…

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Q: 3x + 1 Evaluate (x-1) (x+2) dx using Partial fractions.

A: This question can b solved using the concept of partial fractions.

Q: Q19) The general solution of 2x2y" + 3xy' - 15y = 0, is: a) y(x) = ₂x² + ₂x³ b) y(x) = C₁x + c₂x-3…

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Q: Q3) Given, u (x, y) = xy is harmonic, find a harmonic conjugate v(x, y), write u+iv as a function of…

A: As we know that for complex analysis z=u+iv   then u and v are conjugate to each other.Then by…

Q: t b) tz 16) L-¹ (5-3)²+25) = c) tz estsinst a) 5 d) t est sin3t 5 b) c) e-at sin3t 5 eatsinst d)

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Q: f(x) = 3x² - 5x+21

A: SOLUTION-

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Q: 1) Find the equation of the tangent line and normal line to the graph of the function y=x√√x-1 at…

A: As we know that; The expression for the equation of the tangent line is: y-y0=mx-x0 Where m is the…

Q: Q2) Determine using Cauchy Riemann equations the function below is analytic or not? f(2)=x² +…

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Q: Solve step by step in digital fe 6x - 1 a) lím x→ 1/ 2x - 6 b) lím X-00 x² - 9

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Q: 1)y=(8+7x³) Find the derivative of the following functions 2)y = (x +5)*(2x + 3) 3)y=√(x²+3)²

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Q: 12. Setan 2x sec² 2x dx

A: As per guidelines we can solve only one questions at a time, so if you need more answers kindly…

Q: Given the points A: (2,3,6) and B: (-3,-4,1), find the vector u = AB ū = < U

A: NOTE: Refresh your page if you can't see any equations. . here we have