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
70 people are in the band
10 flute players
20 trombone players
10 drummers
30 trumpet players
let's factorise :
now, there are two cases :
case 1 :
case 2 :
Answer:
<u>See below:</u>
Step-by-step explanation:
Let the angles be 5x , 4x , 3x.[Since the angles are in ratio 5:4:3 ] respectively.
We know that sum of all angles of a triangle is 180°.
So,
Now Find the value of x of this equation.
Now,
Multiply each ratio given by 15 which is the value of x we got.
That is;
Hence,the measurements of the angles of the triangle would be 75°[First Angle],60°[Second angle],and 45° [Third Angle].
I hope this helps!
Let me know if you have any questions.
