Activity 4: Let's do this Logistic Growth dy Let y = f(t) be the size of a certain population at time t. We say that the type of growth y has is called logistic growth if y satisfies the differential equation = ky (K-y), where y is the size of the population. (Balmaceda J.M.P, et al.) dt Problem: Ten Philippine eagles were introduced to a national park 10 years ago. There are now 23 eagles in the park. The park can support a maximum of 100 eagles. Assuming a logistic growth model, when will the eagle population reach 50?

Q: Show that the quadrilateral having vertices at (1, −2, 3), (4, 3, −1), (2, 2, 1) and (5, 7, −3) is a…

A:

Q: 2. If f(x, y) = log (x² + y²), then ƒ + fyy is equal to 1 (a) x² + 2 (b) 0 + y 2 x² - y² y²-x² (c)…

A: We need to find the partial derivatives fxx , fyy  of the function f(x, y)=log(x2+y2) to find fxx +…

Q: Solve the following system using the Newton-Raphson method for one iteration, given that…

A:

Q: Show if x, is convergent or divergent T.3 'n sin(x) dx 1+x S'

A: Introduction: The convergence or divergence of an infinite series depends upon the sum of the…

Q: Find the total possible number of 5 letter words such that they are alphabetically first in the…

A:

Q: Check the operation Division over Numbers. Associativity of binady Subtraction and the of Complex…

A: We have to check the associativity of binary operation that is subtraction and Division over the set…

Q: 1) Solve by using Laplace transform the partial differential equation 2² 8² dt2 =9. y(0,t) = 0,…

A: Solution

Q: The values of mass m, spring constant k, dashpot resistance c, and force f(t) are given for a…

A:

Q: In Exercises 15 to 22, (a) determine whether the graph is Eulerian. If it is, find an Euler circuit.…

A: (a) Consider the given graph, Eulerian Graph theorem: it states that an Eulerian trail exists in a…

Q: →Step 1 Given- 5 9 -3 4 1 -1 -7 -7 4 -3 65 -21x1 X2 X3 X4 ช 2 -7 2 3 | -107 9 -2

A: Solution

Q: Prove the following using the Principle of Mathematical Induction: n(n+1)(2n+1) for n EN. a. P(n):…

A:

Q: Using separation of variables find a one parameter family of s dy 8x² + 3 -2x e dx xy tions of the…

A: Solution

Q: Find the total area of the region satisfying the E

A:

Q: Can the graph G be orientable? G:

A: Yes the graph is orientable.

Q: an= (-5)n an an = COS 4n+n3 3n+4" os(T) 8

A: The detailed solution with explanation is presented as the next step.

Q: Determine whether a triangle with the given vertices is a scalene, isosceles, or equilateral…

A:

Q: Use Laplace transform to solve the partial differential equation: o'y dy ox² at +xl where y(x,0) =…

A:

Q: If u = f(y + ax) + (y-ax), then to №² u №² u (a) a² (b) dy² 2 Əy² 2 (c) - a². (d) a №²u น 2 Əy² №² u…

A:

Q: prove that every subset of negligible. set is negligible.

A: I have used definition of negligible set.

Q: In Exercises 29 and 30, a floor plan of a museum is shown. Draw a graph that represents the floor…

A: Let the rooms be a,b,c,d,e,f,g The floor plan can be made as follows.

Q: Use Laplace transform to solve the partial differential equation: 8² y dy = +xt where y(x,0) = 0,…

A: Solution

Q: (1) Using Legendre polynomials, find linear least-squares approximation to f(x) = In|xl.

A:

Q: Consider sets A and B with |A| = 7 and |B| = 4. How many functions f: A → B are surjective?

A:

Q: Determine whether each set is a vector space. If not, explain why. a) The set of all quadratic…

A:

Q: In Exercises 9 to 12, determine whether the two graph are equivalent. 9. B C C A D B

A: given two graphs

Q: Solve for the value of x. Points A and B are both centers of the given circles. 9 H 8 B

A: Solution

Q: If the slope of the line connecting the origin and a point P is 3/4 and the ordinate of P is 6, what…

A:

Q: 12 4 () (23) () (73) 1 1 1 24 24 5

A:

Q: 2) 2x2 csc(x) dy dx

A: The solution is given as

Q: Can the graph G be orientable ? G:

A: We say that a connected graph is orientable if and only if every edge belongs to a cycle. We see…

Q: Please explain Compute the GCD (The Euclidean Algorithm for finding) of the following 1.…

A:

Q: If A = 3ai +4j-k and B=4i+j-3k, find the value of a if A normal to B.

A:

Q: In Exercises 15 to 22, (a) determine whether the graph is Eulerian. If it is, find an Euler circuit.…

A: First find the degree of all the vertex.  The degree of vertex  V of a graph is the number of edges…

Q: Set up, but do not evaluate, the integral for the surface area of the solid obtained by rotating the…

A:

Q: x(n)= a"u(k − n) for k>0

A: Introduction: The Z-transform translates a discrete-time signal, which is a sequence of real or…

Q: Find a root greater than zero of f(x) = ex − 2x – 5 - using the Fixed-Point Iteration Method with an…

A:

Q: Find the sum of the divisors of 120. Generalise the result for an arbitrary natural number M

A:

Q: Use Laplace transform to solve the partial differential equation: o'y dy = +xt where y(x,0) = 0,…

A: Solution

Q: A and B are two events such that P(A) = 0.4 and P(An B) = 0.2 Then P(An B) is equal to O 0.8 O 0.6…

A:

Q: In Exercises 15 to 22, (a) determine whether the graph is Eulerian. If it is, find an Euler circuit.…

A: a) In the given graph the four vertices A, B, E and F are of odd degree,hence by the Eulerian Graph…

Q: Test each of the following series for convergence by the Integral Test. If the Integral Test can be…

A: This question from series and convergence.

Q: If ƒ (0) = 1, ƒ (1) = 2, ƒ(2) = 33, f(3) = 244. Find a cubic spline approximation, assuming S" (0) =…

A:

Q: In Exercises 15 to 22, (a) determine whether the graph is Eulerian. If it is, find an Euler circuit.…

A:

Q: Solve the following PDE (Paryial Differential Equation) for t > 0. Express the final answer in terms…

A:

Q: If a, b are complex constants and a real parameter, what does the equation z = a cost+bsint…

A:

Q: Given P(A^c-complement)=0.40, P(B) =0.40, P(AUB)=0.75, P(A)= 0.60, P(B^c)=0.75 Find P((AnB)^c)

A: Additional Law of Probability gives P( A ∪ B ) =P(A) + P(B) - P(A∩B)

Q: Assignment (ABET) A mass weighing 5 lbs. stretches a spring 6 in. If the mass is pushed downward,…

A: Solution :-

Q: How many functions f: {1,2,3,4} {1,2,3,4} are there satisfying: a. f(1) = 1 or f(2)= 2 (or both)? b.…

A: Solution :-

Q: calculate the volume of G where G is bounded by 2= x² + y²₁ ²²+ y² = 4, 200 SS f d v

A:

Q: Question 3: The function f(x)= max x, searches for the maximum value between a number. Prove…

A: