Math
posted by ANR on .
1)let k and w be two consecutive integers such that k<x<w. If log base 7 of 143 = x, find the value of k+w
2) if 7 and 1 are two of the solutiosn for x in the equation 2x^3 +kx^2 44x+w=0, find the value of k+w
3) from an ordinary deck of 52 cards, two cards are selected at random (without replacement). find the probability that both cards were hearts. express your answer as a common fraction reduced to lowest terms.

1. if log_{7} 143 = x
then 7^x = 143
but 7^2 = 49 and 7^3 = 343
so k=2 and w = 3
then k+w = 5
2. let f(x) = 2x^3 + kx^2  44x + w
if 7 is a solution then f(7) = 0
2(343) + 49k  308 + w = 0
49k + w = 378
if 1 is a solution, then f(1) = 0
2(1) + k + 44 + w = 0
k + w = 42
subtract them:
48k = 336
k = 7
in k+w=42, 7+w = 42 > w = 35
and k+w = 42
3) prob(2 hearts) = (13/52)(12/51) = 1/17 
thank you!