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a) Define a rooted tree and the root of such a tree.
b) Define the parent of a vertex and a child of a vertex in a rooted tree.
c) What are an internal vertex, a leaf, and a sub tree in a rooted tree?
d) Draw a rooted tree with at least 10 vertices, where the degree of each vertex does not exceed 3. Identify the root, the parent of each vertex, the children of each vertex, the internal vertices, and the leaves
Let f (x,x',x"). Be a function of independent variables x, its first derivative x', and its second derivative xo. Write down an Euler-Lagrange expression for this function.
A ball of mass 0.1 kg is whirled in a horizontal circle of radius 1 m by means of a string at an initial speed of 10 r.p.m. Keeping the radius constant, the tension in the string is reduced to one quarter of its initial value. Find the new speed o..
A bag contains two red marbles, four green ones, one lavender one, three yellows, and five orange marbles. How many sets of five marbles include either the lavender one or exactly one yellow one but not both colors?
What is Diane's current monthly mortgage payment? What is Diane's current outstanding principal?
How would you find the definite integral for the following functions: f(X) = 67 over the interval [0,1]
The Forbes article titled Abandon Email as a Customer Service Channel at Your Peril discusses the channels of customer service that consumers prefer to use. What do you feel are the customer service channels people are most willing to use to resolv..
Two chemicals A and B are combined to form a chemical C. The rate of the reaction is proportional to the product of the instantaneous amounts of A and B not converted to chemical C.
An urn contains 6 balls numbered 1 through 6. Suppose you draw a ball from the urn, observe its number, replace the ball, draw a ball again, and observe its number. How many outputs are in the sample space?
Jim is helping Tom put up a fence diagonally across his 20 square foot backyard. What will be the length of the fence in radial form?
high-level computer languages are created to be understood by humans. as a result the keywords and the commands of
Derive polar parametric equations for the following: A circle with radius d and A spiral with equation at(cos(ωt),sin(ωt)).
What are the 4 stages of the business cycle? Like when a business begins, grows, ends, etc. How do you know what stage a business is in?
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