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1. From the concepts in the readings from Week Three, provide at least one real-world application of algebraic concepts as they would apply to one of the following areas: business, health and wellness, science, geometry or other math concepts, sports, or environmental science.2. Explain the four-steps for solving quadratic equations. Can any of these steps be eliminated? Can the order of these steps be changed? Would you add any steps to make it easier, or to make it easier to understand?3. Explain the five-steps for solving rational equations. Can any of these steps be eliminated? Can the order of these steps be changed? Would you add any steps to make it easier, or to make it easier to understand?4. Do all rational equations have a single solution? Why is that so?5. How are these concepts of direct, inverse, and joint variation used in everyday life? Provide examples for each.6. Other than those listed in the text, how might the Pythagorean Theorem and distance formula be used in everyday life? Provide examples of each.7. Quadratic equations, which are expressed in the form of ax2 + bx + c = 0, where a does not equal 0, may have how many solutions? Explain why.8. What is the quadratic formula? What is it used for? Provide a useful example, not found in the text.
Lena Dimock is saving for her college expenses. She sets aside $200 at the beginning of each three months in an account paying 8% annual interest, compounded quarterly. How much will Lena have accumulated in the account at the end of four years?
Let A be a real n x n matrix. Show that a linear subspace E of R^n is A-invariant if and only if E is e^{tA} -invariant for all t in R, where e^{tA} is the exponential matrix associated to A.
Prove that the statement "There exists a triangle with a sum of angles greater than 180 degrees" is true in spherical geometry.
Application of differential calculus in economics: Profit, Cost and Revenue function - What is the maximum profit if each item is sold for $7? (Assume you sell every thing you produce.)
Finding formulas for the volume enclosed by a hypersphere in n-dimensional space.
Perform the operation and make the result in standard form
How many solution sets do systems of linear inequalities have? Do solutions to systems of linear inequalities need to satisfy both inequalities? In what case might they not?
Two armies are advancing on two cities. The first army has 4 regiments and the second army has 3 regiments. At each city, the army that send more regiments to the city captures both the city and the opposing army regiment.
Determine the coefficient of restitution for each of the following objects dropped from a height of 2 meters onto a wooden floor.
A parcel of land is in the shape of a rectangle with length L (in feet). 65% of the length is waterfront and 70 feet of the length is not waterfront. Write and solve an equation to find the lenght of the parcel of land.
Consider the following LPP Without using artificial variable(s), solve the given LPP (do not solve the dual problem). Write the dual of the above problem.
At what time does the stone hit the ground? C. What is the velocity of the stone when it hits the ground?
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