Question

Suppose functions are defined as follows.

Answer 1

U(x) = x² + 7
w(x) = √(x + 4)

(w · u)(5) = (√(5 + 4))((5)² + 7)
(w · u)(5) = (√(9))(25 + 7)
(w · u)(5) = (3)(32)
(w · u)(5) = 96

(u · w)(5) = ((5)² + 7)(√(5 + 4))
(u · w)(5) = (25 + 7)(√(9))
(u · w)(5) = (32)(3)
(u · w)(5) = 96

Answer 2

The equation to find the ground speed of an airplane is
Vg = Va + Vw  where Vg is the ground velocity, Va is the velocity through the air, and Vw is the velocity of the wind.
So, first we find the ground speed of each. This is done by dividing the number of miles by the number of hours.
2370 ÷ 3 = 790 miles per hour
7630 ÷ 7 = 1090 miles per hour
Next, we set them both equal to the equation, making sure that the wind velocity of the first equation is subtracted, because the plane is flying against the wind.
790 = Va - Vw
1090 = Va + Vw
Finally, we have to find the speed of both the wind and the jet. We know that it has to be higher than 790, but lower than 1090. So, logically, it would make sense to find the speed that is perfectly in the middle of the two, because adding or subtracting the same number would equal either speed.
To find this, we do a little subtraction, division, and then addition and subtraction.
1090 - 790 = 300
This means there's a 300 mph difference between the two speeds.
300 ÷ 2 = 150
Half of 300 is 150, so it would make sense that the wind speed is 150 mph, either added or subtracted to the final speed.
790 + 150 = 940
1090 - 150 = 940
Because the two match, that means we've found the speed of both the jet plane, and the wind.
The rate (speed) of the jet is 940 miles per hour (mph), and
The rate of the wind is 150 mph.