Consider a beehive of 100,000 bees. Suppose that an outbreak of a virus occurs in the beehive. Once a bee becomes infected, the bee remains infected and does not recover. The virus does not kill the bees. Let I(t) be the number (in thousands) of bees that are infected at time t days after the start of the outbreak. The rate of increase of I at time t is proportional to the product of the number of bees which are infected at time t, and the number of bees which are not infected at time t. (a) I(t) satisfies the ODE dI dt. = BI(100-I)

Q: 40. YA 3 2. 0 y = f(x) 2 +3

A:

Q: A semicircular gate on a dam has a diameter of 6m and is positioned with the straight portion…

A: We know that  force F=ρgAd ρ is the density of water g acceleration due to gravity A area d is the…

Q: Convert the point (x, y, z) = ( − 2, – 1, 1) to cylindrical coordinates. Give answers as positive…

A:

Q: PROBLEM : Find the root of the function f(x) = cos x cosh x +1 using the following methods.…

A: The given function is, f(x)=cosxcoshx+1. To Find: (i) Approximated root using 3 iterations of…

Q: Given the system of equations 4a 2b + 11c + 3d = 20 6a + 3b - 2c + 15d = 25 10a + b 2c + 5d = 30 12a…

A:

Q: Set up a triple integral in spherical coordinates for the volume inside the cone z = x² + y² + z² =…

A:

Q: Part a: Set up an expression for the profit from producing and selling x items. We assume that the…

A:

Q: TRANSCRIBE THE FOLLOWING TEXT IN DIGITAL FORMAT

A: Cauchy integral formula states that, if fz is analytic function within and on a simple closed curve…

Q: Broadly speaking, what is a mathematical closure? O A. Only relations have closures. They are…

A:

Q: Consider the statement: For all integers a and b, if a is even and b is a multiple of 3, then ab is…

A:

Q: What are free columns?

A: A matrix is a rectangular array containing the set of numbers arranged in rows and columns. A matrix…

Q: 15. Let a be a real number. We will explore the derivatives of the function f(x) = eax. By using the…

A:

Q: Suppose that f(x, y) = x² − xy + y² − 3x + 3y with D = {(x, y) | 0 ≤ y ≤ x ≤ 3}. 1. The critical…

A:

Q: Consider the relation below on the set {s, t, u, v}. {(s, t), (t, t), (u, v), (v, v)} What pairs…

A:

Q: The following table shows the number of new (single-unit) houses started, in thousands, in the…

A: North East (N) Middle west(M) South (S) West (W) Total 2012(A) 50 90 280 110 530 2013(B) 60…

Q: For each vector field F(x, y, z), compute the curl of F and, if possible, find a function f(x, y, z)…

A:

Q: X 0 2000 A television camera at ground level is 2000 feet away from the launching pad of a space…

A:

Q: Let c0, c1, c2.... be defined be the formula cn = 3n − 2n for every integer n ≥ 0. Show that this…

A: Given, c0, c1, c2, . . . be defined be the formula cn=3n-2nfor every integer n≥0. To prove that this…

Q: Determine which of the following pairs of functions are linearly independent. ✓ 1. f(0) = cos(30)…

A:

Q: (3) Give an example of a series 1 Cn that diverges even though cn < 0.0000001 for all n and limn→∞…

A: To Find: A series∑n=1∞cn for which (i)  cn&lt;10-7 for all n. (ii) limn→∞cn=0. But the series…

Q: Find the centroid of the lamina bounded by the x- and y-axes, the line x = 2, and the graph of y =…

A: What is Centroid: The centroid of a three-dimensional solid or a two-dimensional planar lamina…

Q: List the critical numbers of the following function in increasing order. Enter N in any blank that…

A:

Q: Consider the following where the principal P is invested at an interest rate of r per year for t…

A: To find the accumulated amount of the given investments.

Q: 3. 395 X 76

A:

Q: Let W be the set of all vectors of the form shown on the right, where a, b, and c represent…

A: I have given the answer in the next step. Hope you understand that

Q: M2x2 → P2 by g ( a b c d (a + 2b)x² - cx + 3d.

A:

Q: The position of a planet that a closest to and farthest from the sun are called its  perihelion and…

A: Given AB=1.47×108 km, AC=1.52×108 km ∴BC=3×108 kmOB=2.99×1082=1.495×108 kmOA=1.495×108-1.47×108…

Q: 4. Show the IVT root on the function fix)=2x²2x²-3x+1 on [1,2] 5. Find i limx-√x+2-X -4x²-3x+10 16.…

A: Disclaimer:  Since you have asked multiple question, we will solve the first question for you. If…

Q: = eat. Use 4. Consider the equation x" - 2ax' + a²x = 0, which has solution x = reduction of order…

A:

Q: A 9.7 100.3 B 8.3 109.5 C X 93.5 D 11.7 125.7 E 8.0 117.5

A: The given points are A(9.7,100.3),B(8.3,109.5),D(11.7,125.7),E(8,117.5).   We have use Lagrange…

Q: A = = 4 0 1 4 1 -2 -2 -1 1

A:

Q: Solve the differential equation y" +aty' -2ay=1, t>0. Where a is a real parameter and initial…

A:

Q: √√9-x²-y² L.LV aff √x² + y² + 2² dz dy dr. √6-x² Consider the integral (a) Convert the given…

A:

Q: 1. Write the following matrix as a system of equations. Then use the matrix to solve the system. X…

A: Convert given agumented matrix into system of equations. Solve given augmented matrix by Gaussian…

Q: T‐Talk cell phone company charges a flat rate of $15 per month plus $0.10 per minute in calls.…

A:

Q: Calculate L6 for f(x) = √√/7x + 1 over [1,3].

A:

Q: Set up a triple integral in cylindrical coordinates for the volume of the solid region E, where E is…

A:

Q: Find the centroid of the region W lying above the sphere x² + y² + z² = 30 and below the paraboloid…

A: Given the sphere x2+y2+z2=30,and below the paraboloid z=18-x2-y2 . And the density of δ(x, y, z)=1.

Q: Find the surface area of the part of the plane 2x + y + z = 4 that lies inside the cylinder x² + y²…

A:

Q: Consider the system described by 0 -=[-2₁2 x(t) = -2 -3 x(t) where x(t)=(x₁ (1)x₂ (t))". (a) Compute…

A:

Q: 2. Let T: R³ R³3 be the linear transformation defined by T((x, y, z)) = (x+z, -y-z, 2x+y+3z). a.…

A: Linear transformation and ker of T

Q: b) A radioactive substance with decay constant k is produced at a constant rate of a units of mass…

A: The initial value problem is provided as: Q'+kQ=a, Q(0)=Q0.  For a differential equation of the…

Q: Margo borrows $1900, agreeing to pay it back with 8% annual interest after 17 months. How much…

A:

Q: Problem 4. Let A= 9 0 0 4 0 3 3 1 Find a matrix B such that B2 = A.

A:

Q: 4). For the sequence, determine if the divergence test applies and either state that lim n→∞ an does…

A: Concept: Divergence test: The nth term for Divergence states that if   then the series  is…

Q: The matrix C= -52 -2 -987 40 28 = has multiplicity −1 79 has two distinct eigenvalues, X₁ < A₂: 1 53…

A:

Q: What is 30% of 255?

A:

Q: Find the Laplace Transform of the following functions: 1. f(t) = (2e-4t + sin t)²

A: We have to find the Laplace Transform of the following function. 1)  f(t) = (2e-4t+sint)2

Q: Determine the values of "z" that satisfy the equation e²z+e² + 1 = 0 ("z" is a complex number)

A:

Q: Verify that (¹)² = i²i but that (i²)i ‡ į²i ("i" imaginary unit)

A: What is Complex Number: A real number and an imaginary number are effectively combined to create a…