One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction y of the population who have heard the rumor and the fraction who have not heard the rumor. (a) Write a differential equation that incorporates this assumption and is satisfied by y. (Use k for the constant of proportionality.) dy dt (b) Solve the differential equation. (Let y(0) = Yo:) (c) A small town has 2000 inhabitants. At 8 a.m., 160 people have heard a rumor. By noon, half the town has heard it. At what time (in hours after 8 a.m.) will 90% of the population have heard the rumor? (Do not round k in your calculation. Round your final answer to one decimal place.) hours after 8 a.m.

Q: Consider the Initial Value Problem: y = y + 3x – 5, y(1) = -2. An approximation of y(1.2) with step…

A:

Q: 4 Find the limit lim 3 Enter I for oo, -I for -o, and DNE if the limit does not exist. Answer:

A:

Q: Consider the following problem: a box with an open top is to be constructed from a square piece of…

A:

Q: xp ( 14

A:

Q: 3.x1 + 2x2 6.x1 + 2x2

A: Solution: The equation can be written in matrix form

Q: The following is the graph of: 十- 2元 2元 3 2 3 2. R一6 R一3

A:

Q: II. Given the function g defined by g(x) = -* if x*-2 4. if x=-2 Find the value of the indicated…

A: at x=-2, function is defined as:g(x)=-4;       if x=-2ANSWER 14:g(-2)=4

Q: 1 (f) log16 VI+1 = 4.

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Compute the surface area of revolution about the x-axis over the interval [3, 6] for y = 4x + 5.…

A: The equation of the curve is given by y = 4x+5 Formula Used: S = 2π∫36y1+dydx2dx To evaluate: The…

Q: Find by implicit differentation; Dthat the tangent to the eclipse x =1 at %3D Point (TorYo) is LoX…

A:

Q: Find the intervals on which the function is increasing or decreasing. f(x) = 2x° - 3x2 - 72x + 4…

A: We need to determine increasing and decreasing interval.

Q: Evaluate the first derivative of the following functions: g(x) : = cosx – sinx f (x) = 4x²cosx g(y)…

A:

Q: (2x³+9)dx (x²+3)(x²-2x+3)

A: This is a problem related to partial fraction of decomposition and integration. Based on the general…

Q: 1. Bob, Glen, and Paul (the authors of our text) are sitting around enjoying their nice, cold…

A:

Q: and fyx are equal. fxY ух Find the second-order partial derivatives of the function. Show that the…

A:

Q: a. What is a convergent sequence? Give two examples. b. What is a divergent sequence? Give two…

A:

Q: The percentage of men 65 years and older in the workforce from 1970 through 2000 is approximated by…

A: We need to find increasing and decreasing interval and interpret the result.

Q: Find the dy/dx by implicit differentiation. 1. 4x2 – 9y2 = 1 2. x³ + y3 = 8xy 3. x? – 7xy + y2 = 0 |

A: As we know that; The sum/difference rule: f±g'=f'±g' The Power law; ddxxn=nxn-1 The Product rule:…

Q: 4 Find lim х — 4 Væ – 2 x→4

A:

Q: dy у — х dx Y + x

A:

Q: 1-3x (ii) Find the values of A, so that the function f(x) = Ax +2x-3 24 continuous for all values of…

A: answer is in next step

Q: X 21. The height, s, of a ball thrown straight down with initial speed 32 ft/sec from a cliff 48…

A:

Q: 3. Find the area of the region between the curves y = Vx and y =x2.

A:

Q: |tan 3x sec 3xdx 3.

A:

Q: Assume that x and y are both differentiable functions of t and are related by the equation…

A: topic - derivative of a function

Q: For a certain automobile, M(x) = - .015x + 1.49x - 7.9, 30 sx s 60, represents the miles per gallon…

A:

Q: Maximum and minimum Function Values 1. Find the absolute maximum and minimum values f(x) = 4 – x2 on…

A: We can solve the given problem as follows:

Q: A. Evaluate the following integrals. dx 1. 5+x²

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

Q: Let f''(x) = 36 sin(6x) and suppose f'(0) 6 and f(0) = 4. Find f(5) a(;) =

A:

Q: Find the first partial derivatives of the function. 4exy f(x, y) = x + y

A:

Q: The function f whose gradient vector is vf(x,y) = (xIn(v + 7), 7x + y + 7> has two critical points…

A:

Q: Find the absolute maximum and minimum of the function f(x,y) = 8y - 72x- 4 over the closed region…

A:

Q: Suppose H (x) = V4x-8. Find two functions fand g such that (fog)(x) = H (x). Neither function can be…

A:

Q: Find the area under the curve f (t) = 3 − x2 + 5x from x = −2 to x = 4 .

A: Find the area under the curve f (t) = 3 − x2 + 5x from x = −2 to x = 4 .

Q: (20,400) on the function y = x². Find the ratio Ay/Ax for Suppose that we choose the point P = each…

A:

Q: state the arder, degree, and linearity of the filowing differe ntial squtions ) ax* 9 + asx) : 3x-4…

A:

Q: Apply the Direct Comparison Test to determine whether converg Vn3 + 1 n=2 erges.

A:

Q: Let f(x 1 What is the range of f(x)? x-y O [0, ∞) O (0, 0) O All reals O There is no range

A:

Q: For the function f(x) = find f'"(x). Then find f"(0) and f"(4). 3+ x f"(x) =| Select the correct…

A:

Q: dx V4-9x2 2.

A: topic - indefinite integral

Q: = 0.3(1- 2) (-)P. dt 200 at time t. he population in equilibrium? he population increasing?

A:

Q: Find the first partial derivatives of the function. f(x, y) = (e* + e)3 f, = fy =

A:

Q: First find f' and then find f. f"(x) = 10x³ + 2x? – 5x – 7, - f'(1) = –6, f(1) = -3. f'(x) = f(x) =

A:

Q: 5. Find the length and width of a rectangle that has an area of 32 square feet and a minimum…

A: Given, area A=32 sq.ft Let, x be the length and y be the width. The formula for the area of a…

Q: 3. Let f(x) = 1+x + x² + x° +x* + x°. %3D Find T3(x), the Taylor polynomial of f at r = 0 with…

A:

Q: Evaluate: -ld. dx 1 2 5.027 2 5.205 2 5.025 2 6.025

A:

Q: A thermometer is taken from an inside room to the outside, where the air temperature is -12" C.…

A: Explanation of the answer is as follows

Q: 4x 20. Write log2 assthe sum and/or difference of ² - 3x - 18 logarithms. Express powers as factors.

A: The given logarthim expression,       log24x3x2-3x-18

Q: If V (t) is the amount of oil in a barrel being filled at time t, what physical quantity is…

A: Let's find.

Q: Find the first partial derivatives of the function. x9 - y5 f(x, y) = x + y fy =

A: The objective is to find the partial derivatives of the function.