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Calculus and Analysis

Demand Function

Research has indicated that the demand for heroin is given by the function q=100p^(-0.17) a) Find E b) Is the demand for heroin elastic or inelastic? Solve this problem, show all steps used to solve the equation, and explain the answer to receive credit for the solution.

arc length and differential equations

Please show all work with explanations. Thank you for your help. 4. Find 6. Find the arc length of the graph of the function over the interval . 18. Solve the differential equation

For what gross sales is Plan B better?

A car salesman has two choices for his salary. Plan A: A salary of $100 per week plus a commission of 3% of gross sales Plan B: A salary of $75 per week plus a commission of 5% of gross sales For what gross sales is Plan B better? Any help is appreciated!

Finding the equilibrium, quantity, and price

The quantity of watches demanded per month is related to the unit price by the equation: p = d(x) = 50/ (0.01x^2 + 1) (1 less than equal x less than equal 20) where p is measured in dollars and x is measured in units of a thousand. The supplier is willing to make x thousand watches available per month when the price

Differential Equation -Fourier transform distribution

Evaluate the fundamental solution of the equation u^(4) - 2u'' + u. More in general, evaluate the fundamental solution of u^(4) - (m+1)u'' + mu, where m>=0. Please note that you are not solving the equation set equal to zero. Since you are looking for the fundamental solution you set the equation equal to the delta distributi

Linear Functions Example Problems

For each of the relationships below, explain whether you think it is best described by a linear function or a non-linear function. Explain your reasoning thoroughly. a. The time is takes to get to work as a function of speed at which you drive. b. The probability of getting into a car accident as a function of the speed a

Properties of an Ellipse

Equation: x^2+9y^2-4x+54y+49=0 1. Identify the conic section represented by the equation. 2. Write the equation of the conic section in standard form. 3. Identify relevant key elements of your conic section such as center, focus/foci, directrix, radius, lengths of major and and or minor axes, equations of asymptotes

Maximum altitude attained by the rocket

1. If f is continuous at x= a and g is differentiable at x=a then: Lim x->a f(x)g(x) = f(a)g(a) (if true explain why true, if false, explain and give an example of why it is false) 2. Let f(x) = 2/3x^3 + x^2 â?" 12x + . Find the values of x for which: A f prime (x) = -12 B f prime(x) =o C f prime (x) = 12 3

Calculating stock price changes due to variations in beta: Example problem

Hard Hat Construction's stock is currently selling at an equilibrium price of $30 per share. The firm has been experiencing a 6 percent annual growth rate. last years earnings per share, was $4.00, and the dividend payout ratio is 40 percent. The risk-free rate is 8 percent, and the market risk premium is 5 percent. If systemati

Secant and Tangent Lines

Consider function f(x) = -x^2 +2x and points P1 = (0, 0), P2 = (1, 1) and P3 = (2, 0). Find equations of: - secant lines to f through every pair of these points (3 pairs), and - tangent lines to f at each of these points.

values of y and theta

The attached diagram shoes a lighthouse, L, 4.2 km from the nearest point, S, on a straight shoreline. The lighthouse beam rotates with a constant period of one complete rotation every 40 seconds. The beam makes an angle of theta with the line LS and the beam hits the shoreline a distance y km from S. At what rate is the beam

Proof involving non-autonomous differential equation

Let A be an n x n matrix. Let f(t; x0) be a solution to the initial value problem x' = Ax; x(0) = x0. Show that f(t2; f(t1; x0)) = f(t1 + t2; x0). Show by example that this is not true for a non-autonomous differential equation.

Arc length and surface area

Please show all your work with helpful explanations. 1. Find the length of the arc of the curve y = x^(3/2) from x=1 to x=2. 2. Find the length of the arc of the curve y = ln(sec x) from x=0 to x=PI/4. What is the length of the curve from x=0 to x=PI/2? 5. Find the surface area of the cone formed by rotating the line y = ax

Lebesque integral

A) Evaluate â?«R^2 xy ? {[0,1]Ã?[0,1]} dm *(x, y), (or if you prefer, â?«[0,1]Ã?[0,1] xydm*(x, y)). b) Evaluate â?«R^2 xy ?{[0,1]Ã?[0,1]â?'Q^2} dm* (x, y) The original problem is sent as PDF file attachment below. It is number 4 on the list.

Damped pendulum equation

For the damped pendulum equation: x"+cx'+kx=0 assume k = 9. (a) Write down a solution to the equation. When does the solution type change as c varies? (b) Classify the equilibrium at the origin as a "sink", "source", "spiral sink", "spiral source", "center", or "saddle".

The answer to Volume of solids

Please show all work. Explanations are very helpful. 1. Find the volume of the solid formed by rotating the ellipse (x/a)^2 + (y/b)^2 = 1 about the x axis. 12. The base of a solid is the region bounded by the parabola y = x^2 / 2 and the line y = 2. Each plane section of the solid perpendicular to the y axis is an

Uniform convergence of sequences of functions

1. Show that the sequence x^2 (e^-nx) converges uniformly on [0, infinity). 2. Show that if a is greater than zero then the sequence (n^2 x^2 (e^-nx)) converges uniformly on the interval [a, infinity) but does not converge uniformly on the interval [0, infinity). For problem 2 text gives a hint that if n is sufficiently larg

total mass of the lamina

1) A lamina has the shape region  in the xy-plane bounded by the graphs of y = (25-x^2)^(1/2) , y = 0, x = 3, x = 5 If the density (in kg/m^3) at each point P in  is inversely proportional to the square of the distance from P to the y-axis, with (5,0,0) = 1 kg/m^3. Find the mass of the lamina [Assume a constant thick

Example Differential Equation

Find the solution to the differential equation given below. y'=t*exp(3*t) - 2*y I can not arrive at the exact solution using separation of variables and integration. The exact solution makes use of convergence, y(t)=e^t .

Find the area using calculus

6. Find the area of a circle of radius r. 7. One strip of pink roses will be planted at the tip of the rose garden shown in the figure. Find the area of the strip of pink roses. Please refer to the attachment for more questions and mentioned figure. Please give suitable explanation along with answers that will help me u

Instantaneous Rate of Change of Demand with Respect to Price

Suppose that the demand for a product depends on the price (p) according to: D(P) = 40,000/p^3 - 1/4, p>0 where p is in dollars. Find and explain the meaning of the instantaneous rate of change of demand with respect to price when p = 50. Please provide a step by step help.

Solving differential equations.

Solve the following differential equations. 1a. 11x - 6y sqrt(x^(2)+1)*(dy/dx) = 0 w/ y(0) = 2 1b. Find f(x) if y = f(x) satisfies (dy/dx) = 160x^15 and the y-intercept if the curve y = f(x) is 5. 1c. ((x^2)-(y^(2)-8))*(dy/dx) = (1/2y) w/ y(1) = sqrt(9) 1d. 3e^(7x) * (dy/dx) = -49(x/y^(2)) w/ y(0) =

First-Order Differential Equations

Two Snowplows - Differential Equations (First-Order Differential Equations) One day it began to snow exactly at noon at a heavy and steady rate. A snowplow left its garage at 1:00pm, and another one followed in its tracks at 2:00pm. a)At what time did the second snowplow crash into the first? To answer this question, assum


Please show all woCarlos is blowing air into a soap bubble at the rate of 7 cm3/sec. Assuming that the bubble is spherical, how fast is its radius changing at the instant of time when the radius is 11 cm? cm/sec. How fast is the surface area of the bubble changing at that instant of time? cm2/sec. The Millers are plann

divergence and curl of the given vector field

Calculate the divergence and curl of the given vector field F. F(x,y,z)=3xi-2yj-4zk F(x,y,z)=(x^2 e^(-z) )i+(y^3 ln⁡〖x)〗 j+(z cosh y)k Evaluate ∫_C▒〖P(x,y)dx+Q(x,y)dy〗 P(x,y)=xy, Q(x,y)=x+y; C is part of the graph of y = x² from (-1,1) to (2,4) Show that the given line integral is i

Differential equation, Area of bounded region

1. Solve the following differential equation: -2yy' +3x^2 SQRT(4-y^2) =5x^2 SQRT(4-y^2) , -2 < y < +2 2. Let f(x) = ax^2 , a>0 , and g(x) = x^3 Find the value of a which yields an area of PI (i.e. 3.14159) for region bounded by figure, y-axis and line x=1.

Differential Equations Function for Region Bounded

1. Solve the following differential equation: -2yy' +3x² √(4-y²) =5x² √(4-y²) , -2< y<+2 2. A calculus instructor has determined that the arc of an individual diving into a swimming pool is defined by the function, f(x) = sin (.4x). Determine how far the diver has traversed in his dive as he passes thr