Let ABC be a right triangle with ∠B = 90◦. Let E and F be respectively the mid-points of AB and AC. Suppose the incentre I of triangle ABC lieson the circumcircle of triangle AEF. Find the ratio BC/AB.6. Find all real numbers a such that 3
Let A be a m x m matrix with eigenvalues . Show that
[tr(A)] = tr(A) + 2
please provide detailed explanation how
[tr(A)] = ??? then becomes the final answer?
let a1 = 2, a(n+1) = (5*a(n) – 4) / a(n) for n>=1. Show that (1 <= a(n) <= a(n+1) <= 4) for n>=1
Given,A(n+1) = 5*A(n) -4/A(n) A(n+1) = 5 – [4/A(n)]That can be written as[A(n+1) – 1]/4 = 1 – [1/A(n)]Putting A(1) = 2A(2)> 1From A(2) ,A( 3) >1This tells that A(n) > 1A(n+1)…
Let (a; b) represent an interval (or range) of values x such that a <=x<= b . Consider an array X =<
a1,b1,a2,b2,…, an, bn > of 2n numbers representing n intervals (ai, bi) , where ai = X[2i-1] and bi =
X[2i] and ai <= bi . an algorithm called Simplify-Intervals(X) that takes an arrayX representing n
intervals, and simplifies X in-place. The “simplification” of a set of intervals X is a minimal set of intervals
representing the union of all the intervals in X . Notice that the union of two disjoint intervals can not be
simplified, but the union of two partially overlapping intervals can be simplified into a single interval. For
example, a correct solution for the simplification ofX =< 3, 7, 1, 5, 10, 12, 6, 8 > isX =< 10, 12, 1, 8 > .
An array X can be shrunk by setting its length (effectively removing elements at the end of the array).
In this example, length(X) should be 4 after the execution of the simplification algorithm. Analyze the
complexity of Simplify-Intervals .
let a1 = 1, a(n+1) = 3*a(n) + 2 for n>=1. show that a(n) = 2*3^(n-1) – 1 for n>=1
Given A(1) =1A(N+1) = 3*A(N)+2 A(N+1) – A(N) = 2 A(N) +2 [A(N+1)+1] – [A(N)+1] = 2 *(A(N) +1)Defining new series B(N) = A(N) +1 B(N+1)- B(N) = 2*B(N) B(N+1) = 3B(N) [B(N+1)/B(N)] = 3So B(N)…
Let A,B,C be events.(a)Write each of these events in terms ofA,B,C using intersections, unions,and complements:(i) None of A,B,C occurs.(ii) At least two of A,B,C occur.(iii) Exactly one of A,B,C occurs.(iv) Exactly two of A,B,C occurs.(v) Exactly three of A,B,C occur.
Let a random sample be taken of size n = 100 from a population with a known standard deviation of σ
= 20. Suppose that the mean of the sample is = 37. Find the 95% confidence interval for the mean, μ
, of the population from which the sample was drawn. (Answer in CI format and round the values to whole numbers.)
5
19
20
1
What will be the first item the burglar should choose? (Please show your work by stating your reason.)
a. Item 1
b. Item 2
c. Item 3
d. Item 4
e. Item 5
Solve question 1 Advanced Linear Algebra related to Vector spaces , Range and Null space . Try to give the solution with detailed necessary steps. Thank u.
1 . Let A : R" — RM defined by an m X 12 – matrix such that A : VH AV .( 1) Show that the range R ( A ) is the span of the column vectors of A ;( 2) Show that the mull space N ( A ) = 10; if and only if the column vectors of A arelinearly independent .
Let A = p∨q∨¬r, B = p∨¬q∨¬s, C = p∨¬r∨¬s, D = ¬p∨¬q∨¬s, and E = p∨q∨¬s, where p, q, r, and s represent meaningful statements. Determine whether A∧ B∧C ∧ D∧E is a tautology. Explain your answer
I have tried to use the and truth table. I got stuck cause there are 4 meaningful statements. Many thanks!
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