Provide the GCF for the monomials 34s^2t and 96st^2.
Answer: the directional derivative value of the pressure function at Kearney moving toward Sioux City is - 0.09 mb/km
Step-by-step explanation:
Let’s assume P represents the pressure function
The calculation for the directional derivative of pressure at Kearney directed towards Sioux City will be denoted as DuP
The line connecting Kearney to Sioux City starts on the level curve representing a pressure of 1000mb
and ends on the level curve representing a pressure of 972 mb
thus letting X1 = 1000 mb
X2 = 972 mb
the distance between Kearney and Sioux is d = 300 km
So to approximate the directional derivative DuP at Kearney towards Sioux City, we assess the average rate of pressure change between both locations
therefore DuP = (X2 - X1) / d
= (972 - 1000) / 300
= -28 / 300
= - 0.09 mb/km
Thus, the directional derivative value of the pressure function at Kearney in the direction of Sioux City is - 0.09 mb/km
Answer: the boy won 10 games
Step-by-step explanation:
Let's denote B for the games won by the boy, and F for the games the father won.
We know that there are a total of 26 games:
B + F = 26.
For each game the boy wins, he gains 8 cents, while for each game lost to his father, he loses 5 cents. Since at the conclusion of the 26 games his total earnings net to zero, we have:
B*8 + F*(-5) = 0.
Now we form a system of equations:
B + F = 26
8*B - 5*F = 0.
Our first move is to isolate one variable. We'll start by expressing F in terms of B using the first equation:
B + F = 26
F = 26 - B.
Now substituting this into the second equation gives us:
8*B - 5*F = 0
8*B - 5*(26 - B) = 0
8*B + 5*B - 5*26 = 0
13*B = 5*26
B = 5*26/13 = 5*2 = 10
Thus, the boy emerged victorious in 10 games (the father won the remaining 16 games).
