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College Algebra
Individual Project
Solve the following algebraically. Trial and error is not an appropriate method of solution. You must show all your work.
Solve algebraically and check your potential solutions:
x = -4 does not satisfy the equality. So the answer is only x = 5
Show the steps that you would take to solve the following algebraically:
Show your work here:
c) What potential solution did you obtain? Explain why this is not a solution.
This is not a solution because it makes the original equation indefinite. It makes the denominator zero.
The following function computes the cost, C (in millions of dollars), of implementing a city recycling project when x percent of the citizens participate.
a)
Using this model, find the cost if 60% of the citizens participate?
Answer:
million dollars
b)
Using this model, determine the percentage of participation that can be expected if $4 million is spent on this recycling project. Set up an equation and solve algebraically. Round to the nearest whole percent.
Answer: 74%
4)
a)
If
, fill in the following table for x = 0,1,2,3,4. Round to three decimal places where necessary.
x y
0
-2
1
-1
2
-0.586
3
-0.268
4
0
b)
Explain why no negative values are chosen as values to substitute in for x.
Answer: Squareroot is not defined for negative values.
c) Graph in MS Excel or another web-based graphing utility and paste your graph here. Read the information in the assignments list to learn more about how to graph in MS Excel.
Answer:
5) A water tank is h feet high. Water is flowing from this water tank with a velocity V feet per second. The model representing the relationship between the velocity and height is given by V = 6?h
(a). find the height of a water tank that provides a water flow of 60 feet per second.
V = 60, substitute this in the original function above we get
60 = 6?h
60/6 = ?h h = 10
Square both sides we get
Answer: h = 100 feet
(b) find the velocity of the water flow when the height is 130 feet. Round answer to two decimal places.
h = 130, substitute this in the original function V = 6?h we get
V = 6?h
V = 6?130
V = 6*11.40175425
V = 68.41 feet/sec
College Algebra Graphing Transformations a) Given the function f (x) = x^2 complete the following table. Must show all work for full credit. f (x) Show Work: When x = 0, f (x) = f (0) = (0)^2 = 0. When x = 1, f (x) = f (1) = (1)^2 = 1. When x = 4, f (x) = f (4) = (4)^2 = 16. When x = 9, f (x) = f (9) = (9)^2 =
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Algebra Like many other languages and sciences, Algebra can be useful in the explanation of real-world experiences. Linear algebra, in particular, holds a high level of relevancy in the solution of real world problems like physics equations. Since the key point of physics is to explain the world in proven observations, linear algebra is an ideal mode for discussion. Many real-world situations can be explained by algebra; for example, how does
By observing x on the graph, then we make the connection that the slope of x on the graph represents rate of change of the linear function. Once we have done this, it is then possible to move to the development of a quadratic equation and see what the impact of the increase (or perhaps decrease) means to the data. Have we proven that the rate of change is linear?
Algebra, Trig Algebra-Trig Find the slope of the line that goes through the following points: (-4, 6), (-8, 6) Slope: m = (y2 -- y1) / (x2 -- x1) = (6 -- 6) / (-8 -- (-4)) = 0 / (-4) = 0 m = 0. Determine whether the given function is even, odd or neither: f (x) = 5x^2 + x^ To test a function for even, odd, or neither property, plug in -- x
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