Unrestricted. Bacterial Growth A cenain colony of bacteria grows at a rate proportional to the number of bacteria present. Suppose that the number of bacteria doubles every 12 hours. How long will it take this colony to grow to five times its original size?

Q: 2. Use Fundamental Theorem of Calculus (a) Jedz where C:z=et,0 ≤ t ≤T;

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Q: [3] 37 Let A = Write 2A. Is det(2A) equal to 2det(A)?

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Q: Math Review: Light travels at a constant speed of 3.0 x 105 km/s. The distance between the Sun and…

A: We know that Distance = Speed * Time  So, Time = Distance/Speed. d=vt gives t=d/v.

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Q: Consider a lake that is stocked with walleye pike and that the population of pike is governed by the…

A: Given: The logistic equation of the population is given by                      P'=0.1P1-P10 where…

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Q: Find the rate of change of the distance D from the origin of a point moving on the graph of f(x) =…

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Q: 1. Recall that the image of the elementary vectors e; determines column i. Find the matrix th…

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Q: Mark the correct statements. i. Every plane curve has a tangent vector different from the zero…

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Q: Let f(x) = cos(x²). Approximate the integral I = = f(x) da in three different ways, each with n= 4:…

A: As you post multiple questions according to guidelines I only solve the first problem, please post…

Q: 1. (x3 + y3) dx + 3xy2dy = 0

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Q: Let V be a vector space of dimension n and a scalar product. Recall that for U≤ V a subspace, U¹ ≤ V…

A: Sol:- To prove that dim(U) + dim(U⊥) = n, we first choose a basis for U, say {u1, u2, ..., um}.…

Q: Which relation below is a total order? O A = {2,3,4} ordered by the relation R on A defined as…

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Q: A balloon is rising vertically above a level, straight road at a constant rate of 1 ft/sec. Just…

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Q: Consider a damped undriven oscillator whose equation of motion is given by *=-w²x-yż Assume that the…

A: Given the equation of the damped undriven oscillator x¨+γx˙+ω02x=0. The general solution is given as…

Q: If $8000 is invested at 8% compounded continuously, what is the amount after 9 years?

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Q: Use Taylor's formula for f(x,y) at the origin to find quadratic and cubic approximations of 3…

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Q: The differential equation - 25y = 0 has auxiliary d'y dx² equation with roots = 0 Note Use m as the…

A: The given differential equation is d2ydx2-25y=0 We have to find the auxiliary equation of the given…

Q: Use the cylindrical coordinate system to find the area of the curved surface of a right…

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Q: A particle is moving in the plane, so its coordinates and y are functions of t, and its polar…

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Q: A married couple had a combined annual income of $67,000. The wife made $3000 more than her husband.…

A: Let's use variables to represent the incomes of the husband and wife. Let x be the husband's income…

Q: The three prisms shown in the following image have the same height and volume. If s=5 cm, then the…

A: The three prisms are in the shape of Cylindrical prism Cuboidal prism Rectangular prism s= 5cm They…

Q: Find an approximation of y(1) using Euler's Method and h=.2 for dy/dx =4x-3y , y(0)=1

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Q: In a 4L jug and 7L jug, can we measure out 6L? Why or why not?

A: Yes, it is possible to measure out exactly 6L of liquid using a 4L jug and a 7L jug.

Q: 19. Iff is a function such that f'(x) = sin(x²), then the coefficient of x' in the Taylor series for…

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Q: dy 9. Without solving for y(t), find the steady states of the logistic equation = 4y - y², and dt…

A: 9. Given that the logistic equation is                          dydt=4y-y2.

Q: - Evaluate z = 0 and 2 = a. A. B. C. III. dV where G is the solid enclosed by the sphere x2 + y² + ²…

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Q: Given the subset of the vector space R²x² of real 2x2 matrices. v={[a b]la, b, c ER} V= subset of V…

A: Given that the subspace of vector space of real 2×2 matrices. V=abc-a|a,b,c∈ℝ. Let W be the subset…

Q: Suppose f(n) = 9n² 16n + 42(log(n))² and g(n) = 4n². Using the formal definition of Big- O, prove…

A: First of all, let        h(n) = log(n) - n + 1    => h'(n) = 1/n - 1 < 0 for all n > 1…

Q: The length of a rectangle is increasing at a rate of 8 in./s, while its width is decreasing at 3…

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Q: 2 A (left) stochastic matrix is one which has only non-negative (0) entries, and such that the…

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Q: 1. Find the equation of the tangent plane for the implicitly defined surface xy + xz+yz = 1

A: First we arrange the equation of the surface into the form  f(x,y,z)=0 xy+xz+yz-1=0

Q: 32x² 50y² - 128x + 300y = 1122 a. Standard Equation b. Center c. Location of the vertices d.…

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Q: System of congruences (smallest +integer for answer): x = 3(mod 7) x = 4(mod 9) x = (1 mod 6)

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Q: 1. Find the inverse of the matrix M using the Matrix Inversion Algorithm. Show your work. (The…

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Q: −2 4 6   −2 1 1 1 −1 1. (a) Find the expected payoff to the row player if the row player R uses the…

A: Hnnn Bbb Bb

Q: Inference  Given the premises: 1. If the steak is well done, it’s overcooked. 2. If the steak is…

A: Given:  Premises:1. If the steak is well done, it’s overcooked.2. If the steak is overcooked, the…

Q: Find the multiplicative inverse of a mod n, using 2 different methods. Show your steps in each case…

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Q: Let f be a function that has s'(0) = S(0) -- derivatives of all orders on the interval (-1,1).…

A: Given the function f, that has derivatives of all order on the interval -1,1. f(0)=1,f'(0)=12,…

Q: Given this graph: h What are the vertex connectivity and edge connectivity, in that order, of the…

A: We see we can not make the given graph disconnected by removing only one vertex.  If we remove the…

Q: Solve y"-10y'+29y = 0, y(0) = 1, y'(0) = −3 y(t) = The behavior of the solutions are: O Oscillating…

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Q: 2 A (left) stochastic matrix is one which has only non-negative (> 0) entries, and such that the…

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Q: Consider the function f(x) = − 8x - 5 on the interval [-7, 7]. Find the absolute extrema for the…

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Q: Find the Riemann sum approximation of the double integral -150 •16 (3x (3x - 9y) dA where D is the…

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Q: In each case, find elements a and b from a group such that lal |b| = 2. %3D a. Jab| = 3 b. lab| = 4…

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Q: 3. What is the 1st term in an arithmetic sequence whose 26th term 165 and common difference 6?

A: What is the 1st term in an arithmetic sequence whose 26th term 165 andcommon difference

Q: except -2. Use the definition to justify the example. *5. Suppose f: DR with xo an accumulation…

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Q: The principal P is borrowed at a simple interest rate r for a period P = $5000, r = 5.5%, t = 6…

A: The principal P is borrowed at a simple interest rate r for a period of time t. We need to find the…

Q: Find the rate of change Answer at y = 9, if y = √x + 1 and dx = 5. Write the exact answer. Do not…

A: Given ,             y=x+1  Rate of change  dydt at  y=9 and  dxdt= 5 .

Q: Compute the indicated product.       −1 3     4 2     0 1     3 1 3 5 3 4

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.