Give an algebraic proof for the triangle inequality vw v w +≤+ . draw a sketch. [hint: expand 2 vw vw vw + ≤+ ⋅+ ( )( ) . then use the cauchy-schwartz inequality ( vw v w ⋅ ≤ ).]

Find the greatest common factor of the polynomial: 10x^5+15x^4-25x^3 10x^5 x^3 5x^3 5

Exclude leap years from the following calculations. (a) compute the probability that a randomly selected person does not have a birthday on october 4. (type an integer or a decimal rounded to three decimal places as needed.) (b) compute the probability that a randomly selected person does not have a birthday on the 1st day of a month. (type an integer or a decimal rounded to three decimal places as needed.) (c) compute the probability that a randomly selected person does not have a birthday on the 30th day of a month. (type an integer or a decimal rounded to three decimal places as needed.) (d) compute the probability that a randomly selected person was not born in january. (type an integer or a decimal rounded to three decimal places as needed.)

A+b= 17, ab=70, find the value of |a-b|