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Composite functions are useful when one quantity depends on a second quantity, and in turn that second quantity depends on a third quantity. This is an extremely general situation with lots of real-world applications.
1. The cost of getting new life insurance depends on how old you are, and how old you are depends on what year you were born. Provide an example a composite function using these variables.
2. The amount of time it takes to get to work depends on how much traffic there is, and the amount of traffic there is depends on what time of day it is. If we call the amount of traffic C and the time of day t, then C is a function of t. If we call the time it takes to get to work W, then W is a function of C. Provide an example of a composite function using these variables.
3. Make up your own example of a composite function. Be sure to explain (1) what your variables are, (2) how they are represented in the function, and (3) which elementary functions are combined to form the composite function.
The surface area of a pyramid is 189 cm squared The area of the square base is 49 cm squared. What is the area of one triangular face of the lateral surface? Show the steps of your solution and explain your work.
Construct a 95% confidence interval estimate of the difference between the mean response times for Company A and Company B. Interpret your interval in context of the original claim.
A person receives $212 per year in simple interest from 3 investments totalling $2500. Part is invested at 7%, part at 8%, and part at 9%. There is $1100 more invested at 9% than 8%. Find the amount invested at each rate.
A consulting engineer's time is billed at $60 per hour, and her assistant's is billed at $10 per hour. A customer received a bill for $765 for a certain job. If the assistant worked 4 hours less than the engineer, how much time did each bill on th..
Seawater has density 1025 kg/m3 and flows in a velocity field v = y i + x j, where x, y, and z are measured in meters and the components of v in meters per second. Find the rate of flow outward through the hemisphere x2 + y2 + z2 = 144, z ≥ 0.
Explain Description of Isomorphism, We are working on the proof of showing G (the group of rigid motions of a regular dodecahedron) is isomorphic to the alternating group A_5.
Select an ordered pair from the choices below that is a solution to the following system of inequalities.
In a rooted binary tree with 16 vertices, there must be a path of length 4. No tree has a Hamilton path.
In a school of 160 students, 44 students are in the band, 100 students are on sports teams, and 24 participate in both activities. How many students are involved in band or sports.
What if we settled for an approximation? Do some research on methods for finding approximate solutions of equations. Write up at least one such method and discuss its advantages
The new daily payroll is $1540. How many were originally employed at each rate?
Let M be a two by two matrix for which each element is a real number, and let S be the set of all such matrices. Consider the mapping f of S to the real numbers R defined by the relation f(M) = determinant of M.
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