system of inequalities and foci of parabola and hyperbola

1. A person with no more the $2000 to invest plans to place the money in two investments, telecommunications investment and pharmaceuticals. the telecommunications investment is to be no more than 4 times the pharmaceuticals investment. Write a system of inequalities to describe the situation. Let x = amount to be invested in telecommunications and y=amount to be invested in pharmaceuticals.

2. A steel company produces two types of machine dies, part A and part B. The company makes a $2.00 profit on each part A that it produces and a $6.00 profit on each part B that it produces. Let X= the number of part A produced in a week and Y= the number of part B produced in a week. write objective function that describes the total weeky profit.

3. A refecting telescope has a parabolic mirror for which the distance from the vertex to the focus is 32 feet. If the distance across the top of the mirror is 70 inches, how deep is the mirror in the center.

4. Two LORAN stations are postioned 248 miles apart along a straight shore. A ship record a time difference of 0.00086 seconds between the LORAN signals. (The radio signals travel at 186,000 miles per seconds) Where will the ship reach shore if it were to follow the hyperbola corresponding to this time difference? If the ship is 200 miles offshore what position of the ship?

Solution Summary

The solution explains how to use the equations of parabola and hyperbola to solve real world problems.

Use completing the square to rewrite the equation in one of the standard forms for a conic and identify the conic.
1) x2 + 12x - y + 30 = 0
Find the equation of the parabola determined by the given information.
2) Vertex at the origin, focus at (0, 3)
Find the equation of the hyperbola.
3) Vertices at (0, 8) and (0, -8), fo

How do you find an equation for a hyperbola. Need list of steps taken to find an equation for a hyperbola. Solve the following to reinforce my understanding:
1) Vertices (+or-4, 0) and passing thru (8,3)
2) Foci (0,+-9)Center, directrices y = +-4
3) Center (1,-3), vertices (-4,3) and (2,3), foci (-6, 3) and (4,3)

1. Complete the square in order to put the equation into standard form. Identify the center and the radius or explain why the equation does not represent a circle.
2. Find the standard equation of the circle with endpoints of a diameter
(-3,7) and (1,5).
3. Find an equation of a parabola satisfying the given: Focus (0

What can the line graph, a parabola graph, a hyperbolaand an exponential graph be used for. In real life applications.
Example: A line graph can be used for instrument calibration

One of the civil engineers you interviewed for your article works for a company which specializes in bridge construction projects. In the process of designing suspension bridges, they must account for many variables in the modeling. Some of these variables include the bridge span; the force of the typical water currents wearing

Please help me with the attached pre-calculus questions.
1. Use mathematical induction to prove that 6 is a factor of n (n + 1)(n + 2).
2. Use mathematical induction to prove 1^2 + 3^2 + 5^2 + . . . + (2n - 1)^2 = n (4n^2 - 1) / 3.
3. Expand (2x - y)^6 using binomial coefficients and then evaluate each coefficient.
Ex

I need to graph the following hyperbolaand it has been several years since I have done this. Can you give me a step by step method of how to do this?
x^2 = 8(y-1)^2+1
I do not remember how to determine the foci or the vertices. Please assume that I know nothing other than the given equation. Once I know the method I will

1. 20x=y2
2. (x-3)squared =1/2(y+1)
3. y2+14y+4x+45=0
Find an equation of the parabola that satisfies the given conditions
Focus F(0-4), directrix y=4
Find the vertices, the fociand the equations of the asymptotes of the hyperbola.
1.y2divided by 49 minus x2 divided by sixteen =1
2.x2-2y2=8
Find an equat

A hyperbola is given the equation x^2/25 - y^2/9 = 1
A) Find the coordinates of the fociand the equations of the asymptotes.
B) Find the point of intersection with the line y=4-x
c) Graph the hyperbola, the line, and the point of intersection.
Please explain how to graph this because I dont understand it and