Basic Math question and answers for November 13, 2024
- Q Park rangers released 4 fish into a pond in year 0 Each year there were three times as many fish as the year before How many fish were there after...
- Q The function y 100e 0 045t models the amount y of radioactive material remaining in grams as a function of time t in days Calculate the half life of this...
- Q 2 A company produces and sells electric cars The company s profit P in thousands of dollars changes based on the number of cars x they produce per month The...
- Q A coolant is injected into engine fluid causing the temperature of the engine fluid to decrease with respect to time at a rate that is proportional to the difference of...
- Q Find the general solution of the given differential equation.xy + xy = 4Give the largest interval over which the general solution is defined. (Think about the implications of any singular...
- Q Find an explicit solution of the given initial-value problem.x2dy/dx = y-xy, y(-1) = -6
- Q Consider the following differential equation and seek a power series solu-tion centered at ro = 0.(x+4)y" - xy + 5y = 0By putting the equation in standard form, we can...
- Q Find the first four nonzero terms in a power series expansion about x=0 for the solution to the given initial value problem.w" +5xw'-w=0; w(0)=4, w'(0) = 0
- Q Use implicit differentiation to find the tangent line of the function In(y) = x ln(x) at the point (2,4).
- Q For the differential equation dy/dx =e-x-3x:Part A: Find a general solution. Show all your work.Part B: Verify the solution. Show all your work.
- Q Solve the initial value problem x'(t) = Ax(1) for 120, with x(0)=(3,1) Classify the nature of the origin as an attractor, repeller, or saddle point of the dynamical system described...
- Q If f(x) = 2 +1, use the limit definition of the derivative to compute f'(z). You can use derivative rules to check your answer, but answers calculated without using the...
- Q 5. Consider differential equationdy/dx + (2/x) y = xy, y(1) = 1/2Find y(10) numerically using the following methods and h = 0.5, 0.25, 0.125 and calculatethe errors in each case....
- Q A jogger runs around a circular track of radius 65 ft. Let (x, y) be her coordinates, where the origin is the center of the track. When the jogger's coordinates...
- Q The rate of change of the number of raccoons N(t) in a population is directly proportional to 380 N(t), where t is the time in years. When t = 0,...
- Q Given the sets of system linear of differential equation;2x"+6x'+y" + 3y' = 12e ^-tx'+2x + y' = 0(a) Determine x(t) by using Elimination Method.(b) Determine y(t).(c) Check number of arbitrary...
- Q In drawing the slope field for the differential equation dy/dx= x+3y-4, I would draw a short line segment for different points on the x-y plane.What slope should I draw the...
- Q Solve the differential equation, such that the equation passes through the given point (x, y). (Remember to use absolute values where appropriate.)dy/dx = 5/x (1, 2)y = log(x5) +2
- Q Consider the autonomous first-order differential equation dy/dx = y - y and the initial condition y(0) = y?. Sketch the graph of a typical solution y(x) when y?, has thegiven...
- Q A 4-kg object's position, p, is changing with respect to time, t. The object experiences a force, F, that is proportional to the object's acceleration times its mass. What differential...
- Q The differential equation y' = 3x will produce which of the following? A. A slope field with parallel tangents along the diagonal B. A slope field that does not have...
- Q In 2012, the population of a city was 6.69 million. The exponential growth rate was 3.15% per year.a) Find the exponential growth function.b) Estimate the population of the city in...
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