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1. Systems of equations can be solved by graphing, using substitution, or elimination. What are the pros and cons of each method?
2. What is the difference between intersecting and perpendicular lines? Can two lines exist that are not intersecting or parallel? Explain your answer.
Let G be a group and H be a non-empty subset of G. We define H^2 as the set of elements of G which can be written in the form h_1 h_2, with h_1 ,h_2∈H.
Let V be the space of all functions from R to R. It was stated in the discussion session that this is a vector space over R. Prove axioms (VS1)=For all x,y, x+y=y+x (commutativity of addition),
How do I go about solving and then graphing the following system?
Check that N(t) = t/(1 +ct) is a solution of the differential equation dN/dt = N^2/t^2. Treat c as an unspecified constant.
Problem on speed.
Let p represent a statement having a truth value T, q represent a statement having a truth value F, and r represent a statement having a truth value T. Find the truth value for the following:
Calculate a 95 percent confidence interval for the population mean
Two sides of an isoceles triangle each measure 10 cm, and the vertex angle measures 132 degrees, Find the length of the altitude to the base. Find the length of the base.
Evaluate the matrix of transformation
Use the disk method to find the volume of the solid of revolution formed by revolving the region about the x-axis. Solid region is a semi circle from 0,4 to 16,0 find the solid amount between 5,0 and 6,0
A number (a) is called a fixed point of a function (f) if f(a)=a. Prove that, if f'(x) does NOT equal 1 for all real numbers (x), then f has at most one fixed point.
Consider the function f(x)=kx/(100-x), where f(x) is the cost incurred to remove x% of a pollutant from an environment. Examine the behavior near the vertical asymptote, and discuss the ramifications behind this.
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