find a linear combination for gcd(259,313). use extended euclidean algorithm.

what is inverse of 259 in z subscript 313?

what is inverse of 313 in z subscript 259?

prove that for x is an odd, positive integer, 3x ≡−1 (mod 4). I'm not sure how to approach the problem. I thought to assume that x=2a+1 and then show that 3^x +1 is divisible by 4 and thus congruent to 3x=-1(mod4) but I'm stuck.

Show that  "f(x) = x^3" is continuous on all of ℝ

The Fibonacci numbers are recursively dened by F1 = 1; F2 = 1 and for n > 1; F_(n+1) = F_n + F_(n-1): So the rst few Fibonacci Numbers are: 1; 1; 2; 3; 5; 8; 13; 21; 34; 55; 89; 144; : : : There are numerous properties of the Fibonacci numbers.

a) Use the principle of Strong Induction to show that all integers n > 1 and m > 0

F_(n-1)F_(m )+ F_(n)F_(m+1) = F_(n+m):

Solution. (Hint: Use induction with respect to m. First verify the formula the base case,for m = 1 case (here use again induction on n) the assume that it is true for m = 1;m = 2; ;m = k then prove that it remains true if m = k + 1 (still with the use of induction on n)

A rectangular box without a lid is to be made from 12 m^2 of cardboard. Find the maximum volume of such a box

Find the general solution using REDUCTION OF ORDER. and the Ansatz of the form y=uy1 = y=ue^-x

(2x+1)y'' -2y' - (2x+3)y = (2x+1)² ; y1 = e^-x

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Provide an example:

1) A sequence with infinitely many terms equal to 1 and infinitely many terms that are not equal to 1 that is convergent.

2) A sequence that converges to 1 and has exactly one term equal to 1.

3) A sequence that converges to 1, but all of its terms are irrational numbers.

Diane has decided to play the following game of chance. She places a $1 bet on each repeated play of the game in which the probability of her winning $1 is .6. She has further decided to continue playing the game until she has either accumulated a total of $3 or has lost all her money. What is the probability that Diane will eventually leave the game a winner if she started with a capital of $1? Of $2?

Find the work done in moving a particle once around an ellipse C in the XY- plane if the ellipse has a center at the origin with semi-major axis p and semi-minor axis 2p and if the force field is given by F= (3x - 4y + 2z)i + (4x +2y - 3z^2)j + (2xz - 4y^2+z^3)k . where p=4

Prove that the covariant derivative of an arbitrary tensor is a tensor of which the covariant order exceeds that of the original by one.

Here are five different functional models that might represent the growth of the number of Zika cases, where x represents the week number, and y represents the number of cumulative cases.

1. Linear y = 258.74x

2. Logarithmic y=937.37ln(x)-202.03

3. Quadratic y = 31.357x ^(2 )+ 134.93x − 122

4. Power y = 55.278x ^2.0101

5. Exponential y=47.399e^(0.6737x)

For each function model listed, create a graph for 1 ≤ x ≤ 5, along with the Zika case data from Step 2. Be sure your graphs clearly label the function and the actual data.

Step 2 that the question is referring to is

Below is data of the weekly number of suspected Zika cases in French Polynesia in 2013.Plot the data on the graph below.