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A clique is the complete subgraph. Prove that the size (number of vertices) of the largest clique is a reconstructable property.
Who proved that the graph of any quadratic equation is a conic section?
In 628 AD this mathematician and astronomer wrote Brahmasphutuaiddhanta (The Opening of Universe). In this work he first introduced idea of zero by considering what takes place when number is subtra
Write down the following two statements in symbollic form and find out whether they're logically equivalent. Include truth table and a few words explaining how the truth table supports your answer.
If 5 integers are selected from the set {1,2,3,4,5,6,7,8}, should there be at least two integers with the property that the larger minus the smaller is 2?
Write down the following two statements in symbolic form and find out whether they are logically equivalent. Comprise a truth table and few words describing how the truth table suports your answer.
Discuss those statements with logic symbols and tell about if they are true or false. For every whole number apllies if the number is lower than 9 its lower than 10.
The inverse of a matrix A can be defined as the matrix X whose columns xj solve the equations Axj = ej, where ej is the jth column of the identity matrix.
There're two unbalanced coins loaded in a way such that, when they are tossed, one comes up a head with probability 1/3 and the other 3/7 . You are offered the following game:
Compute the present value of following cash flows, rounding to the nearest dollar: A single cash inflow of $12,000 in five years, discounted at the 12% rate of return.
Make a program which finds out the definite integral from 0 to 1 of any function of the form x^n using the Monte Carlo method. The user should supply the power of x (n), and number of trials. The o
Determine a recurrence relation which counts the number of off-diagonal elements of an n+1 x n+1 matrix. Solve this recurrence relation for an expression of the number of off diagonal entries as a f
Compare the mathematical contributions of Descartes and Fermat. Who was more influentialutions?
Determine the equation of motion for the weight. Find out the maximum displacement above the equilibrium that the weight will attain?
Employ techniques (possibly synthetic division) to find out all the zeros of the polynomial. (Hint: i is a zero). Write the function in factored form, including any complex factors.
Employ what you know regarding addition or subtraction in your explanation. You must discuss how you knew whether to add or subtract. You must discuss the strategy you employed when you added or sub
An amusement park consists of 11 rides. Every pair of rides is directly connected by either exactly one track (part of the monorail system) or exactly one walking path, but not both. Each path o
An apple pie in a 9.50 inch diameter plate is placed on the rotating tray. Then, the tray is rotated such that rim of the pie plate moves through a distance of 258 inches.
Two pizza restaurants, Brothers Pizza and Pizza Palace, compete for customers in small village. The typical pizza customer in village purchases pizza from one of these two restaurants once a week. E
Suggest a 5x10 grid divided up in squares of dimension 1 unit by 1 unit. Let A denote the lower left hand corner and B denote upper right hand corner. Any shortest path from A to B will be of length
John bought the new computer for $1,650. He paid the $160 down payment and financed the rest for one year at an interest rate of 7%. Determine the total interest paid on the given amortized loan ass
Please prove directly from definition of inverse that a square matrix A is invertible if and only if it has full rank, without talking about the connection between determinants and inverses.
If a child is chosen a random from group of 20 junior high school students including four 12 year olds, six 13 year olds and ten 14 year olds and this child doesn't have a cavity, determine the prob
A field E is said to be extension field of field F if there exists subfield F' of E such that F is isomorphic to F'. Prove that the field of complex numbers under complex addition and multiplicatio
Suggest the following all-integer linear program: Max 5x1 +8x2 s.t. 6x1 + 5x2 <30, 9x1+4x2<36,1x1+2x2<10, x1,x2 > 0 and integer.