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How many solutions exist for aquadratic equation? explain
How do we determine whether the solutions are real or complex?
By a line, a great circle on the sphere is referenced. Is it still true that two points determine a unique line? Is it still true that two distinct lines either meet in a single point or do not meet at all?
Recall that if z=x+iy then, x=(z + zbar)/2 and y=(z-zbar)/2. By formally applying the chain rule in calculus to a function F(x,y) of two real variables, derive the expression
Hamilton Quaternions : Kernels and Images, Show that the map phi: H->M_2(C) defined by phi(a+bi+cj+dk)=(a+b(sqrt -1),c+d(sqrt-1);-c+d(sqrt-1),a-b(sqrt-1)) is a ring homomorphism
Derive the Boolean Expression and construct the switching circuit for the truth table stated
Direct Products of Groups, Conjugate Subgroups, Homomorphisms and Isomorphisms, Assume that K is a cyclic group, H is an arbitrary group and f1 and f2 are homomorphisms from K into Aut(H) such that f1(K) and f2(K) are conjugate subgroups of Aut(H)
Let G be finite abelian group with this property: For each positive integer m such that m | |G|, there are exactly m elements in G with order dividing m. Prove that G is cyclic.
Show that if R is a ring with identity element and x is an element in R, then Rx = {rx: r in R} is the principal left ideal generated by x. Similarly,
Write a method to calculate the area of a circle. Return the area and write a method to calculate the circumference of a circle.
The following pairs of functions, graph each one together in Desmos, show on your graph and find the area between them bounded by the given values of x.
Find the critical value for this hypothesis test.
Find the slope of the line passing through the points (1990, 3.5) and (2005, 5.15). Interpret the slope as a rate of change.
Provide probability distribution, histogram, and find the expected value of a coin that is tossed 3 times
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