4. If P(x) represents the population of rabbit in a forest. If the population grows exponentially and given as: p(x) = 2000 x 20.01t. Where t is in months. a) Find the initial population. b) Find the population of rabbit after 6 months. c) If the population of rabbit grows to 8000. Find the number of months.

Q: P= Let A = -38 70 105 7 15 20 27 -5 -10 Find an invertible matrix P and a diagonal matrix D such…

A: The objective of the question is to find an invertible matrix P and a diagonal matrix D such that D…

Q: Find the derivative. d dx 3x²+1 A ex-3x² +1. (3x³ - 6x) B. ex³-3x² +1. (3x² - 6x + 1) cex³-3x²+1.…

A:

Q: The trace of a square n x n matrix A = (aij) is the sum a₁1 + a₂2 + ... + ann of the entries on its…

A: Given that V is the vector space of all 2×2 real matrices and H is the set of all 2×2 real matrices…

Q: Find the particular solution of the differential equation that satisfies the initial condition.…

A:

Q: For the vector fields defined in part (b), evaluate separately each term in the iden- tity given in…

A:

Q: Follow the steps to solve the below differential equation using series methods. Assuming the…

A:

Q: A small computer manufacturing company forecasts the demand over the next n months to be di i = 1…

A: We need to determine the number of units produced using regular production and overtime production…

Q: Rental costs for office space have been going up at 7.4% per year compounded annually for the past 5…

A:

Q: Find the final amount in the following retirement account, in which the rate of return on the…

A:

Q: The matrix A = The larger eigenvalue 2₂ is -1 7 4 1 3 -1 5 -3 -1 2 -3 1 1 6 -4 has two distinct real…

A: According to the given matrix, find the eigenvalues and eigenspaces:

Q: A transformed logarithmic function has a domain of {xe R | x>-3}. What is the range of the…

A: Given that a transformed logarithmic function has a domain of . To find the range of the transformed…

Q: 2. Calculate the product of each pair of the following determinants, using Property 12, and check…

A:

Q: Runge-Kutta method

A:

Q: At what value(s) of a does f (x) = 5x¹ - 45 x² have a relative minimum? -3 and 3 only 0 and 3 only 0…

A:

Q: Consider the following. (Round your answers to four decimal pla f(x, y) = x cos(y) (a) Find f(8, 3)…

A: Consider .To compute  and .Also to compute .

Q: Max Z = 5X1 + 3X2 Subject to: 6X1 + 2X2 ≤18 15X1 + 20X2 ≤ 60 X1, X2 ≥ 0 Determine the Sensitivity…

A: We have given: VariablesX10X20Objective…

Q: Solve 3 So 5² √ In ( ² ) a dx E

A:

Q: - Let 3 -1 1 -3 3 3. Find a non-zero vector x that maximizes the ratio. What is this maximum value?…

A:

Q: 1. Find the value of the integral 2/³ 3x²√√sin (x) dx for n=4 and n=8 intervals Using high-accuracy…

A:

Q: = A tank initially contains 40 pounds of salt dissolved in 600 gallons of water. Starting at t 0,…

A:

Q: Consider the parabola p(x) = -1.3x² + 6.2x + 7.1. For which interval [A, B] is B [PC as large as…

A: We will find the interval for which the integral has large value.

Q: 19. A botanist finds that the number of fruit, F, a certain plant produces depends on the total…

A: 19.  Given that a botanist finds that the number of fruit, F, a certain plant produces       depends…

Q: Show that the differential form in the integral is exact. Then evaluate the integral (1,2,3) Compute…

A:

Q: Find the least-squares solution of the system fe || II 1 3 2 4 x 6 E 16

A:

Q: 2721 Q3. Assuming that e = = 2.71828182845... is correct to 11 decimal places, show that 1001 is a…

A: To check the convergent each fraction must be satisfied                          where  e =…

Q: Describe the behavior of f(x) when x approaches from the left of the vertical asymptote -3 of…

A: Given function isWe have to describe the behaviour of  when x approaches from the left of the…

Q: Find all abelian groups of order 2700 b rohant sodhur

A:

Q: Jenny makes two investments as described below. Jenny evaluates the investments at the end of each…

A:

Q: Explain why (sinx-2)(cosx + 2) = 0 has no solutions.

A:

Q: 5 A tin of soup has the following information on the label. 4g 200 grams of soup contains…

A: The objective of this question is to determine the fraction of the soup that is protein and the…

Q: Find a parameterization of the cap cut from the sphere x² + y² + z² = 16 by the cone z= Choose the…

A:

Q: 2. (a) Trace the curve y²=(x-2) (x - 5)².

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Evaluate the integral // (vxF) dS, where S is the portion of the surface of a sphere defined by x² +…

A: Where S is the portion of the surface of a sphere defined by  and .We have to find .

Q: consider a game of 4×4 Tic-tac-toe in which a player must get four in a row to win. Determine the…

A: To determine the number of 4x4 Tic-tac-toe games that end on turn 7, we need to consider the…

Q: consider the relation R on R, where R = {(a, b) | a ≤ b+1}. (a) Is the relation R reflexive,…

A: i.Let  then So the relation  holds for all .So  is reflexive.ii.Since the relation is reflexive so…

Q: (31/1/2 03 A= 1 1 - 1 3 3 3 1 0 0 0 0 0 0 0 -130 0 0 10 3/

A: According to the given matrix A, find an invertible matrix P such that .

Q: Graph of f Based on the graphs of function f and function g, determine the value of lim x→0 0-1333 O…

A:

Q: $(= 2² + +x), where 0<x<3. Let f(x) be defined such that f(1) =2 and f'(x) = cos( Part A: Find the…

A:

Q: Snow being produced by a snow machine is blown onto a ski mountain at a rate modeled by S(t)…

A: Given that S(t) represents the rate at which snow is being produced by a snow machine on the ski…

Q: Sketch the domain D in the (x, y)-plane satisfying ≤ y ≤ 2e- and e ≤ y ≤ 3e. In your sketch, label D…

A:

Q: . Let n be a positive integer. Find the continued fraction expansion for √n(n+1).

A:

Q: Find all solutions of the following system of linear equations: dx dt = = 4x + 8y, Xg dy dt = Hi, I…

A:

Q: Solve √√(7-x)(x-3) dx

A: Let the given integral is                                           use the substitution…

Q: Use upper and lower sums to approximate the area of the region using the given number of…

A: The given graph is:The given equation is .Find the upper and lower sums.

Q: Let p and q be distinct odd primes such that gcd(p−1, q−1) = 2. Does there exist an integer M such…

A: The objective of the question is to determine if there exists an integer M that satisfies the given…

Q: The body metabolizes an antibiotic over time (this is why we take it for several days at specified…

A: Let  represents the concentration of the antibiotic that remains in the body at time , where  is…

Q: d) Solve the following game for optimum strategies and the value of the game given the following…

A:

Q: Ron has made deposits of $179.00 into his savings account at the end of every month for 18 years. If…

A:

Q: Question 3 Maximum revenue. Suppose the price-demand equation for x units of a commodity is…

A:

Q: Given 7: -9 -10 0 find the closest point to in the subspace W spanned by -5 -6 -4 and 64

A: We have to find out the closest point of  in the subspace W spanned by Here noted that ,let,So…