We are given this situation to model using a differential equation: Snow is falling at a constant rate of 3/5 in per hour and is being removed at a constant rate of 45% of the amount of snow on the ground per hour. Removal of snow began at 4 in. If we let h(t) be the height of the snow at time t, then the rate of change of the height of snow would be equal to 3/5 - 0.45h. My question is, why doesn't time appear in the differential equation? Our equation, dh/dt = 3/5 - 0.45h is autonomous, but why?

Q: hive reason роr your апним : ő (s,t) Parameterized the upper hemisphere - 220 then Ѓ= -2 (s,t) 8 r…

A: Given Information: parameterized the upper hemisphere , .To check: parameterized the lower…

Q: dy (5) Find the general solution of the linear differential equation : - dr + (8x + 1)y= e 82.

A:

Q: 6. Consider the system x' = 2r y=-y. I (a) Sketch the vector field. (b) Show that for every solution…

A:

Q: A correctional facility firm has hired a total of 116 new prison guards to send to its four…

A: Given that:A correctional facility firm has hired a total of 116 new prison guards to send to its…

Q: A sequence {u} is defined by the recursion formula Un+1 1. (a) Prove that limn→∞ un exists. (b) Find…

A:

Q: A major coffee supplier has warehouses in Seattle and San Jose. The coffee supplier receives orders…

A: SeattleSan JoseDemandSalt Lake cityRenoSupply

Q: 2. Consider the matrix A = 40-1 03 0 10 2 . (a) Find the eigenvalues of A. (b) Find a basis for the…

A: Let us find the eigenvalues and eigenvectors.

Q: y X Answer ऐ रे ५= २० X Determine the volume of the solid obtained by rotating the area shown about…

A:

Q: $95905.41 loan with a 30 year term at a rate of 7.695%, calculate the monthly payment, the total…

A:

Q: 3 -9 a = 2 b=-6 2 -6 For each of the following vectors, determine whether it can be written as a…

A: In this question, we will write the vector as a linear combination of the given vectors.

Q: Andrea has 6 hours to spend training for an upcoming race. She completes her training by running…

A: Let d be the distance for an upcoming race.According to the given data, she runs at a speed of 9 mph…

Q: From the figure:

A: The solution given by the expert is correct.

Q: (a) A student derived the following: f"(x) ≈ = f'(x + h) — f'(x - h) 2h 1 [f(x+h)-f(x) 2h h f(x) -…

A: We have to derive the formula for

Q: 2 Prove that it a) = (a+b) = (- 1/(-a)= -( - عاها - (a+b) = (- (-a7²b) + (a+b))

A: To prove these properties, you can use the properties of real numbers and basic algebraic…

Q: ind the solution of the following initial value problem. 4y" - y=0 y(-2) = 1, y/(-2) = -1

A: Given that the differential equation is                                 To find the solution of the…

Q: An enterprise is planning to achieve a competitive advantage in a local market. Total number of…

A: An enterprise is planning to achieve a competitive advantage in a local market. Total number of…

Q: 4 I I 1 1 I A 140 I 1 1 1 1 I

A:

Q: Selected values of the function f, which is continuous on the open interval 1 < x < 8, are shown in…

A: if a function f(x) is continuous on a closed interval [a,b], then the function is also bounded on…

Q: Prove that if a is an odd integer, then a² = 1 (mod 8).

A:

Q: 1. For each of the following sets, decide whether they are closed, bounded, compact (both) or…

A:

Q: Prove that if x is rational, then x² is rational.

A: We know thatA rational number is any number that can be written as a fraction, where both the…

Q: 1.- Determine the equation of the line that passes through the point (20, 10) and is perpendicular…

A: Since you have posted a multiple question according to guidelines I will solve first(Q1) question…

Q: [Periodic functions] Which of the following functions are periodic? For those that are, find the…

A:

Q: Let {an}_1 be a bounded sequence in R and ƒ : R → R be a continuous and increasing function. Prove…

A:

Q: se the following graph off to sketch a graph of f. K 20 16 42 CO

A: From the given graph of  it is clear that its a quadratic function as its parabolic.Which means the…

Q: Sample --A- Q: Test the series converges, diverges, absolutely converges or conditionally converges:…

A:

Q: 3.-The equation of a line is 8x - 15y - 60 = 0. a) Represent it graphically b) obtain the value of m…

A: The given st line is8x -15y-60=0ie, 8x-15y=60

Q: 4.- Given the equations of the lines: Line 1: -3x + 11y +15= 0, Line 2: 3x + 11y+88 = 0, Line 3:…

A: Here we have to find whether lines are parallel or perpendicular to each other.

Q: Pictured are the contours (z=0 to z=4.5 contour interval 0.5) of f(x, y) = x² + 2xy + y² together…

A:

Q: if $A$ and $B$ are events, then $\Pr[A\cap B]\geq \Pr[A]+\Pr[B]-1$

A:

Q: 1. for the case of repeated real roots what would the general solution be? 2. if i was to let y1(t)…

A:

Q: Consider the following equation of a quadric surface. x=9-y²-9z² a. Find the intercepts with the…

A:

Q: Let C be the helix in R³ defined by r(t)= (cost, siht, t), 0≤t≤2π [ (x²y+z)ds کے

A:

Q: Select all of the following graphs which are one-to-one functi

A: We have to identify the one one function graph.

Q: How do i approach the following question?  Let A and B be sets. Prove that A ∪ B = A ∩ B if and…

A:

Q: 6. Let m be an odd positive integer. Prove that every integer is congru- ent modulo m to one of the…

A:

Q: Consider the Squirrel-Coyote system given by S'=2S-4SC C'= SC-C (1) Sketch the nullclines of the…

A: Given Information:To find:(1) Sketch the null clines and phase plotter.(2) Reason to the solutions…

Q: Let ū= 2 + 2Ĵ - 2k and J = 2î - 2Ĵ + k. + Verify that the vectors i and I are perpendicular and have…

A:

Q: Exercise 2.3.9: Are x, x², and x4 linearly independent? If so, show it, if not, find a linear…

A: LetThe wronskian of the function

Q: Consider the following cube, whose edges have length 1: P 1 1 1 R Which point on the line segment PR…

A:

Q: Find and classify the critical points of (x² – 3x) (y² – 7y). - Z= For each classification, enter a…

A: We have to classify the critical point

Q: 2.12x₁2.12x₂ +51.3x3 + 100x4 = π, 0.333x₁ -0.333x₂ - 12.2x3 + 19.7x4 = √√2, 6.19x₁ + 8.20x2…

A: We shall perform Gaussian elimination using partial pivoting. And then use BACK SUBSTITUTION to find…

Q: Candidates A, B, C, and D are competing to win an award. There are 5 voters in this election. The…

A: We have to identify the voting scheme in order to have  win the award.

Q: Given a parabola with equation y = ax^2 where a is a constant, determine the value of a for which…

A:

Q: D. Prove or disprove: Let A, B, and C be sets. If A = B - C, then B = = AUC.

A:

Q: der the pair of simultaneous inequalities: 2x − 3 < 3x − 2 and 4x − 1 < 2x + 3.

A: To solve it lets solve idividually and then take the union

Q: Let A = {Romeo, Juliet, Anthony, Cleopatra, Gandhi, Mandela}, B = {Juliet, Mandela, Cleopatra}, and…

A: {Romeo, Juliet, Anthony, Cleopatra, Gandhi, Mandela}, {Juliet, Mandela, Cleopatra}  {Isabella,…

Q: Show that if a, b, cER then: (p) if b0, c# 0, then (a) when it happens that a-ba-b = = 21120 d a…

A: =set of real numbers form a field with respect to usual addition '+' and usual multiplication '.'…

Q: A Consider the following DAG: L B G D C LL F E Give an example of a topological sort, a maximal…

A: Let us define the definitions one by one......................Topological Sort:The topological sort…

Q: Section 12 1) Prove that = · 2 + 1 1/²2.3 1J ~/t 1 0 in (n+1) (n+1) for all nen ·3+~+=

A: