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if 4x49x464 then the maximum value of x2y2 is solution from the eq finding the value of x2 and putting it in x2 y2we get 2nd eqdifferentiating that
a polynomial satisfies the following relation fxf1x fxf1x f2 33 find f3ans the required polynomial is x5 1this polynomial satisfies the condition
suppose a fluid say water occupies a domain d r3 and has velocity field vvx t a substance say a day is suspended into the fluid and will be
26000 is spended for two years in the first year it gets interest at 83 pa compounded semi annually in the same year the rate of interest changes to
consider the solow growth model as given in the lecture notes using the cobb-douglas production functionyt ak1-alphat lalphata set up the underlying
a drug is administrated once every four hours let dn be the amount of the drug in the blood system at the nth interval the body eliminates a certain
a well-known simple model applicable for analysing boom-bust cycles in agriculture but extendable to analysing boom-bust cycles in many different
one of the well-known class of models that involve a simple difference equation are models of mean reversion these models typically take the formyt1
a determine the matrix that first rotates a two-dimensional vector 180deg anticlockwise and then per- forms a horizontal compression of the resulting
a assume that a is a m1timesm2 matrix and b is a m2timesm3 matrix how many multiplications are required to calculate the matrix product abb given
problem you are given an undirected graph g ve in which the edge weights are highly restrictedin particular each edge has a positive integer weight
this problem involves the question of computing change for a given coin system a coin system is defined to be a sequence of coin values v1 lt v2 lt
a word on an alphabet is any arrangement of the letters in the alphabet for exampleodd dod doo ddd are three-letter words on the alphabet do how many
a how many equivalence relations on a b c d e f haveb how many arrangements are there ofc how many triangles are resolute by the vertices of
a let v f1 2 7g and define r on v by xry iff x - y is a multiple of 3 you should know by now that r is an equivalence relation on v suppose
let r be the relation on z defined by arb iff gcda b 1 that is a and b have no common divisors greater than oneexplain whether r is reflexive
let r be the relation on s 1 3 6 9 27 defined by arb iff aba write down the matrix of rb draw the digraph of rc explain whether r is reflexive
let r be the relation on s 1 2 3 4 5 defined byr 13 1 1 3 1 1 2 3 3 4 4b write down the matrix of rc draw the digraph of rd explain whether r is
a let n abc7 prove that n equiv a b c mod 6b use congruences to show that 432n - 1 for all integers n ge
let a0 a1 be the series recursively defined by a0 1 and an 3 an-1 for n ge 1a compute a1 a2 a3 and a4b compute a formula for an n ge 0c use
find the number of six-digit positive integers that can be formed using the digits 12 3 4 and 5 every of which may be repeated if the number must
in a collection of 30 dissimilar birds 15 eat worms 18 eat fruit and 12 eat seeds accurately 8 eat worms and seeds 8 eat worms and fruit 7 eat fruit
how many ways can six men and three women form a line if no two women may stand behind each
for complex number z the minimum value of z z - cosa - i sinaz - 2cosa i sina is solution z z-eia z-2eia we seeoigin eia 2eia forms a
what is the value of integration limit n-gt infinity nn to the power nto the power 1nsolution limit n--gtinf 1 n-nnnn1n e limit