An elliptic curve can be written as y^2=x^3+ax+b. I need a proof for why x^3+ax+b either have 3 real roots or 1 real root and 2 complex roots. I don't have anything that I know about it prior to asking for help here at Brainmass.

Fixed Costs, Net Income, Capital Plan, & Utilization Reduction
Assume that Valley Forge hospital has only the following three payer groups:
Payer # of Admissions Avg. revenue/admission Variable cost/admission
PennCare 1,000 $5,000 ...

Show all work
1. Determine the exact value for each of the following limits:
a.
b.
2. Determine derivatives (with respect to x) for the following:
a.
b.
c.
d. Determine for
e. Determine the partial derivative with respect to x for
3. Integrate the following:
a.
b...

MATH 141 Homework Due Dec 2 Name :
Solve the following linear programming problem using a graphical method
A company makes two puddings, vanilla and chocolate. Each serving of vanilla pudding requires 2 teaspoons of sugar and 25 fluid ounces of ...

Name __________________________
Math 331
Fall 2015
DIRECTIONS: Show as much work as possible within each question as I grade on both the process and the final answer. TI-89's are wonderful calculators, but they don't show me if you know anything about calculus! Show all work.
1. (6 pts eac...

Question #1:
You used Pythagorus' theorem to determine whether or not a triangle was a right triangle. The sides of the triangle are:
a = sqrt(416), b = sqrt(601), and c = sqrt(1009) so that a2 + b2 did not equal c2. Thus it is not a right triangle. Let the α, β, γ be the angles of the tria...

In the attached problem, I am having trouble showing that the determinants are in the same form in the Lagrangian as the one in the implicit function theorem.

From what I have seen, the longest length of a repeating sequence for an irrational number is c-1 for a=b/c. This occurs when c is a prime. How does one prove this? Can you give mathematical proof for this?
Here is a link to the problem being discussed: http://boards.straightdope.com/sdmb/showth...

Please help with the following problem, providing step by step calculations in the solution.
Solve the differential equation subject to y(0)=2. An Euler approximation to y(x)=2. An Euler approximation to y(x) is given by setting h=x/h, solving the difference equation:
See attached file for eq...

Graph the function ƒ(x) = x3 - 4x + 2.
Let ƒ represent the position of an object with respect to time that is moving along a line. Identify when the object is moving in the positive and negative directions and when the object is at rest, showing all work.

Task:
Graph the f(x) = e^2x - 1/x
Verify the Limit x→0 f(x) meets the criteria for applying L'Hopital's Rule
Find the Limit x→0 f(x)
Explain why L'Hopital's Rule cannot be used to find the limit of Lim x→0 e^2x/x

This solution shows how to solve for various calculus problems, including differentiation of functions using the product rule, the quotient rule, and the chain rule, as well as how to calculate integrals.

Prove that any closed subset of compact metric space is compact by using Theorem 2.
Theorem 2: A subset of S of a metric space X is compact if, and only if, every sequence in S has a subsequence that converges to a point in S.

Prove that [0,1]^n is compact for any number (n e N) by using theorem 2. (see attached file)
Theorem 2: A subset S of a metric space X is compact if, and only if, every sequence is S has a subsequence that converges to a point in S.

I have been working on a general appraoch to partial fractions. And I wanted a proof for why the normal way of doing partial fractions always gives a consistent equation system for the constants in the partial fraction. Question is illustrated with an example and explained more in detail in the docu...

Consider the integral in the attachment. Using the trapezoidal method with n = 4 and n = 8, estimate the integral numerically. Calculate the integral exactly and compare this with your numerical results. Please see attached and show step by step, thanks.

Line Integrals
Please see the attached. Please do the problem(s) in detail and show all work.
This question requires a line integral around the rectangle defined by the points (1,-1), (1,1), -1,1), (-1,-1) and with the function given. This defines 4 integrals that have to be evaluated as describ...

I need help in answering this question:
A car is traveling down a road at 50 miles per hour. The car runs out of gas and drives allows the car to coast to a halt in order to get as close to the nearest gas station as possible. The car travels another 2.3 miles before continue to a stop.
a) find ...

An open topped box is constructed by removing a square from each corner of a flat piece of metal and folding up the resulting flaps. The piece of metal is 40 cm by 25 cm. What size square should be removed from each corner so as to maximize the enclosed volume of the box? What is that volume?

Please provide detailed answers for all questions as per the attached file.
These questions are from ESSENTIAL CALCULUS 2ND EDITION, BY WRIGHT-HURD-NEW.

Let z, w E C
a) Prove the following identities:
i) |z+w|^2 = |z|^2 + 2Re(zw) + |w|^2
ii) |z - w|^2 = |z|^2 - 2Re(zw) + |w|^2
b) Deduce that |z+w|^2 + |z-w|^2 = 2(|z|^2 + |w|^2).
c) Use (a)(i) to prove that |z+w| < |z-| + |w| and give necessary conditions for equality to hold.
d) Prov...

Find the derivatives of the following functions:
(i) f(x) = sqrt(x)*(2x^3-4) + 3x^(-1/4)
(ii) y(x) = (x(x^2-1))/(x^3-4)
(iii) g(u) = (4u^(1/3))*(sqrt(u^3+1))
Please see attached and show step by step, thanks.

I wonder how one can use a partial derivative with constrain slope dH= 0 in a general equation with two partial derivatives where dH=0 is not true. The problem is for the Joule-Thomson effect. The question is much better described in the attachment. This is a problem from chemistry but since it is j...

Below are the graphs of four functions. Which function is invertible?
Set up the integral for the length of the smooth arc y = e x on [0, 10].
What is the area of the triangle bounded by the lines x = 1, y = x − 1, and y = 3 − x ?
...