Let the rate of growth dN/dt of a colony of bacteria be proportional to the square root of the number present at any time. If there are no bacteria present at t = 0, how many are there at a later time? Observe here that the routine separation of variables solution gives an unreasonable answer, and the correct answer, N ≡ 0, is not obtainable from the routine solution. (You have to think, not just follow rules!)

Q: The population of mosquitoes in a certain area increases at a rate proportional to the current…

A:

Q: x=t(e²¹

A: We have x=te2t+4

Q: Apply Newton’s method to estimate the solution of x3 − x − 1 = 0 by taking x1 = 1 and finding the…

A: Let us take f(x)=x3 − x − 1 So, f'(x)= 3x2 - 1 Given x1 = 1

Q: (x+xy²)dxte*, ydy=D0

A: Given: x+xy2dx+ex2ydy=0 ⇒x1+y2dx+ex2ydy=0 ⇒ex2ydy=-x1+y2dx ⇒y1+y2dy=-xex2dx

Q: The population of mosquitoes in a certain area increases at a rate proportional to the current…

A:

Q: 9) d = 1/2(at²) Solve for t in terms of a and d

A:

Q: 3 j = [8] T(0) = 6 -2

A:

Q: Solve S P + + (P)(r)(t) for i. for t. =

A: Given,          S=P+Prt

Q: If the Equation Hx = c is inconsistent for some c in Rn, what can you say about the equation Hx = 0?…

A:

Q: Solve for F(s) L[(1+ e2t)²] a. 1 2 1 s's-2's- 4 Ob. 1 2 s - 2 s's+2 1 + s's+2' s + 2 d. 1 + s's-2' s…

A:

Q: Solve the given initia-value problem. x' Need Help? Read Submit Answer

A: In this question , we will find the solution of the initial value problem .

Q: If m= 1/2 and n= −4, then 3mn=?

A: Given  m=12 and n=-4. We have to find 3mn.

Q: 6. Given f (x) = 6x – 4, solve for x for which f (x) = 7 -

A: For the given f(x), equate f(x)=7.

Q: If we know that Pr(A U B) = 0.6 and Pr( A n B )= 0.2, can we find Pr( A) and Pr (B)?

A: We have to find wheather we can find probabiities or not.

Q: solve the following equation In(t) = 3

A: The given equation is ln (t)=3

Q: Consider the following problem; max f(x₁, x₂) = -x²-x² subject to (₁-1)³ ≥ x² Check whether the…

A: As per the question we are given an optimization problem with objective function : f(x1 , x2) = -x1²…

Q: An efficiency study of the morning shift at a certain factory indicates that an average worker who…

A: Given, Qt=-t3+6t2+24t a. Compute the worker's rate of production at 11:00 A.M. Here t=3 ( Difference…

Q: The population of mosquitoes in a certain area increases at a rate proportional to the current…

A:

Q: Use Fixed Point Iteration Method to find the roots of the following. Iterate until the root is…

A: Ans- The Fixed Point Iteration Method is given by the formula: x_{i+1} = g(x_{i}) where g(x) is a…

Q: 1. Solve for the variable x. F = kx – kxo A. x=F-kxg А. х- O B. x=F-kx, k F- Kxo О с.х3 C. x= D.…

A: The given equation is F=kx-kx0

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.