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
Answer:
y=5x-12
Step-by-step explanation:
The general equation of a line is <em>y=mx+b</em>.
The equation you currently have is <em>y=5x+b</em>.
Plug in the point (3,3) which will get you <em>3=5(3)+b</em>.
Solve the equation by solving what the y-intercept (b) is to create the new final equation.
3=5(3)+b
3=15+b
b=3-15
b=-12
y=5x-12
Answer:
$640 is how much she will make in in regular hours.
Step-by-step explanation:
Create an equation from the word problem and solve.
1 km=0.621mi
xkm=106 mi
x=106/0.621=170.66
b is the answer
