Answer:
The rate at which the distance between them is changing at 2:00 p.m. is approximately 1.92 km/h
Step-by-step explanation:
At noon the location of Lan = 300 km north of Makenna
Lan's direction = South
Lan's speed = 60 km/h
Makenna's direction and speed = West at 75 km/h
The distance Lan has traveled at 2:00 PM = 2 h × 60 km/h = 120 km
The distance north between Lan and Makenna at 2:00 p.m = 300 km - 120 km = 180 km
The distance West Makenna has traveled at 2:00 p.m. = 2 h × 75 km/h = 150 km
Let 's' represent the distance between them, let 'y' represent the Lan's position north of Makenna at 2:00 p.m., and let 'x' represent Makenna's position west from Lan at 2:00 p.m.
By Pythagoras' theorem, we have;
s² = x² + y²
The distance between them at 2:00 p.m. s = √(180² + 150²) = 30·√61
ds²/dt = dx²/dt + dy²/dt
2·s·ds/dt = 2·x·dx/dt + 2·y·dy/dt
2×30·√61 × ds/dt = 2×150×75 + 2×180×(-60) = 900
ds/dt = 900/(2×30·√61) ≈ 1.92
The rate at which the distance between them is changing at 2:00 p.m. ds/dt ≈ 1.92 km/h
I think this would be (y = -2x + 9). Let me know if it is right!
So the problem is asking you to combine equations, in this case the Y factor will cancel out so you will be left with the X factor and the total after you add both of the totals together,
6x-4y=16
5x+4y=6
6x-5x=x
16+6=22
x=22
To answer this first we will subtract d amount of dollars Boy had by d amount of dollars he had left in d end. den we will divide d amount of dollars he used by d amount of books he bought. den d answer will be d amount of money each book cost. Lets do it:-
$266 - $18 = 248
$248 ÷ 6 books = 41.33333.....
So, 1 book costs about 41.50.
Hope I helped ya!! xD
