7. What is wrong with the following description of ordinary differential equations? ''The order of a differential equation is the highest derivative in the equation.'' What should a good definition of ODEs include to overcome this problem?.
The differential equation d^2y/dx^2 + y dy/dx + 3y = 0 has order________ The differential equation partial differential y/partial differential x - partial differential y/partial differential t = 3xy + t is an ODE is a PDE is linear is nonlinear The differential equation partial differential y/partial differential x -.
The function -16t^2 + 64t + 192 give the height S, in ft, of a model water rocket launched with a velocity of 64 ft/second from a hill that is 192 ft high. a) determine how long it will take the rocket to reach the ground, b) find the interval.
the demensions x and y of an object are related to its volume V by the formula V = 4x^2y.
a. How is dV/dt related to dy/dt if x is constant? dV/dt = (?)dy/dt
b. How is dV/dt related to dx/dt if y is.
The following results were obtained from a liquid limit test on a clay using the Casagrande Cup device. Determine the liquid limit of this clay; If the natural water content is 38% and the plastic limit is 23%, calculate the liquidity index of the natural clay..
6) In words, explain a method by which we can solve homogeneous linear differential equations with constant co-efficients.
7) In words, explain methods by which we could solve non-homogeneous linear differential equations with constant coefficients..
Thank you!
The altitude of a triangle is increasing at a rate of 3.000 centimeters/minute while the area of the triangle is increasing at a rate of 1.000 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 9.000 centimeters and.
the gasoline gauge on a van initially read 1/4 full. when 11 gallos were added to the tank, the gauge read 3/4 full. how many more gallos are needed to fill the tank?.
(6r2 5) (c) y' if y ln( (d) dt if f (t) vi t2 ln 1 -te) (e) f (r) if f(T) cos2(3r) 5 sec (VT2) (4t2 5) tan(t) dy if y dt t3 2t f y COS r (h) if y 5 da (22+4+1).
The function/given the height of a ball .h. above the ground (measured in feet) in terms of the number of seconds elapsed since the ball was thrown inward from a bridge that is some distance above the ground t. Let h f(t) and /(t) Approximately how lush is the bridge.
The following data represent the number of people in a particular state aged 18 to less than 68 with a high school education.
Age
Number (thousands)
18 to less than 28
28 to less than 38
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The figure below show direction fields with solution curves for initial condition to the equations below. Determine which direction field of Figure 1, (I),(II),(III) or (IV), corresponds to which of equations Explain your answer..
The GCD Lemma can be extended to more than two numbers at a time. The case of three is as follows: Suppose that n, m, r elementof N such that no natural number greater than 1 divides all three. Then there are integers A, B, C such that An +.
The following one-parameter family of differetial equations has one bifurcation value. Find the bifurcation value and sketch phase lines for values of the parameter slightly smaller than, equal to, and slightly larger than the bifurcation value. Hint: this kind of bifurcation is referred to as a "pitch fork"
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The graph illustrates the prevalence of migraine headaches in males and females in selected income groups.(Source: Adapted from Sue/Sue/Sue, Understanding Abnormal Behavior, Seventh Edition) Write a short paragraph describing your general observations about the prevalence of migraines in females and males with respect to age group and income bracket. Describe.
The base of a 13-ft ladder that is leaning against a wall begins to slide away from the wall. When the base is 12 ft from the wall and moving at the rate of 6 ft/sec, how fast is the top of the ladder sliding down the wall?
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6. Two ships are sailing toward a very small island. One ship, the Pinta is east of the island and is sailing due west at 15 mi/h. The other ship, the Nina is north of the island and is sailing due south at 20 mi/h. At a certain time the.
The following formulas, called the Frenet-Serret formulas, are of fundamental importance in differential geometry;
1. dT/ds=kN
2. dN/ds=-kT+tB
3. dB/ds=-tN
use the fact N=B x T to deduce Formula 2 from formaulas 1 and 2.
The formula
D= 5 e -0.4h
can be used to fid the number of milligrams D of a certain drug that is in a patient's bloodstream h hours after the drig was administered. when the number of milligrams reaches 4, the drug is to.
The function f(x) = x + 3 is one-to-one. Find an equation for f^-1(x), the inverse function. f^-1(x) = (Type an expression for the inverse. Use integers or fractions for any numbers in the expression.).
the acceleration due to gravity g on a spacecraft is inversely proportional to its distance from the center of the earth. At the surface of the earth g=32.2 ft/s^2. Given that the radius of the Earth is 3960 mi how fast is g changing on a spacecraft approaching the Earth.
The function
(a) Find and classify all the singular points of f(s) in the extended complex plane.
(c) Hence, using the complex integral formula, evalute F(t) (by applying the following theorem: https://s3.amazonaws.com/iedu-attachments-message/6453f0d06d72a085d9e6ab1f49ba06f7_4cf99b8bb20ec087d965d19296662c9e.jpg)
f(s) =In s/squarootS Find and classify all the singular.
The graph of a function f is given. Use the graph to answer the question. Find the number, if any, at which f has a local maximum. What are the local maxima? f has a local maximum at x f has a local maximum at x 0, the local maximum.
The Fibonacci sequence is a recursive sequence defined as follows: a_1 = 1 a_2 = 1 a_n = a_n-1 + a_n-2 (for n > 3) The sequence starts as 1, 1, 2, 3, 5, 8, 13, 21, ... where each term is the sum of the previous two. Clearly this.
The answer is y(t)= c1+e^(x)((x^2)/2)-x+c2) but I am not sure how they got there. Thanks in advance!
Write the general solution to the given ODE. y''-y'=xe^x The answer is y(t)= c1+e^(x)((x^2)/2)-x+c2) but I am not sure how they got there.
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Consider f(t)= > 0? alpha alpha for some > alpha ? 3) Does the Laplace transform of f(t) exist for s infinity for some alpha as t < infinity c)neither 2) Is f(t) of exponential order < = t < infinity b)discontinuous but piecewise continuous on 0 < = t.
The graph of = f'(x) is given in the figure at right It f(20) = 150. estimate the maximum value attained by f(X) over 0 le x le 50 Each horizontal axis mark represents 5 units. Give a convincing argument..
The following table gives the emissions, E , of nitrogen oxides in millions of metric tons per year in the US1. Let t be the number of years since 1970 and E = f(t) . Year 1970 1975 1980 1985 1990 1995 2000 E 26.9 26.4 27.1 25.8 25.5 25.0.
The function V (t) = 2e3t ln(t + 17) models the speed of a particle for time t 0.
(a) Say briefly how you know whether V (t) grows or decays as t goes to infinity, without calculating or graphing. Justify your answer.
(b).
The function f(x) has two critical numbers 0 and 4 for which the derivative is 0. That is f'(0)=0 and f'(4)=0. Both critical numbers result in relative extrema. Also, f(0)=-2 and f(4)=6. Can we determine which is the relative maximum, -2 or 6? Explain why or why not..
The function f(x) = x3 describes the volume of a cube, f(x), in cubic inches, whose length, width, and height each measure x inches. If x is changing, find the average rate of change of the volume with respect to x as x changes from 1 inches to 1.1 inches..
The function y=sin(x) oscillates between a min value of y=-1 and a max value of y=1. Multiplying this function by a number A changes the min and max values, increasing the magnitudes if A>1 and decreasing the magnitudes if A<1. Give the min and max values of the function y=3sin(x)..
The cost (in dollars) of producing x units of a certain commodity is given below. C(x) = 1000 + 12x + 0.05x2
Find the instantaneous rate of change of C with respect to x when x = 100. (This is called the marginal cost.)
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The following statement is, in general, False for an object moving in more than one dimension: "Acceleration is the derivative of the speed. " As shown by the steps below, the equation of motion vector r(t) = cos t cap i + sin t cap j is a counterexample to.
The governing differential equation for the deflection of a cantilever beam subjected to a point load at its free end (Fig. 1) is given by: EI_zz d^2y/dx^2 = -Px where E is elastic modulus. I_zz is beam moment of inertia, y is beam deflection, P is the point load, and.
The force exerted by an electric charge at the origin on a charged particle at a point (x, y, z) with position vector
r =
x, y, z
is F(r) = Kr/|r|3
where K is a constant. Find.
The following series are geometric series or a sum of two geometric series.
Determine whether each series converges or not.
For the series which converge, enter the sum of the series. For the series which diverges enter "DIV" (without quotes)..
