Answer:
b=8.5cm
Step-by-step explanation:
tanx (this represents tan theta, it's just easier to type) is equal to 0.6 and since the tanx ratio is opp/adj, we know that opp/adj = 0.6
To find what b is (adjacent as it is adjacent to the angle being used and it is not the hypotenuse), we just have to rearrange.
0.6=5.1/adj
to solve for adj, we can switch 0.6 and adj. (This works because to get adj by itself on one side you would multiply it to the other side and then divide 0.6 from both sides --> simple algebra)
so then you have
adj=5.1/0.6
adj=8.5cm
(if you want to check your solution you can use pythagoeran theorem, a^2+b^2=c^2) and sub everything in and make sure all the numbers equal the right thing!
The correct answer is 77 degrees
ANSWER:
b) No
c) Yes
EXPLANATION:
b)
3 (-8 + 1) = 3 x -8 + 3
(3 x -8) (3 x +1) = 3 x -8 + 3 (just put left and right sides into calcu separately)
-72 = -21
Both sides are not equal and therefore it isn't a solution.
c)
3 (0.5 + 1) = 3 x 0.5 + 3
(3 x 0.5) (3 x +1) = 3 x 0.5 + 3
4.5 = 4.5
Both sides are equal and thereofre it IS a solution.
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
The answer to your question is c
