The sum of the angles of a triangle must add up to 180 degrees.
180 = 35 + 70 + x
180 = 105 + x
180 - 105 = x
75 = x
Option B is your answer.
Answer:
16 and 48
Step-by-step explanation:
let the 2 integers be x and 3x ← ratio 1 : 3
Then
3x - x = 32 ← difference between the integers
2x = 32 ( divide both sides by 2 )
x = 16
and 3x = 3 × 16 = 48
Since magnitude of difference is 32
We can also express the difference as
x - 3x = 32
- 2x = 32 ( divide both sides by - 2 )
x = - 16
and 3x = 3 × - 16 = - 48
The 2 integers are 16 and 48 or - 16 and - 48
Hopefully this helps, and sorry I didn't do 8 I'm limited on time
Answer: the rate at which the distance between the boats is increasing is 68 mph
Step-by-step explanation:
The direction of movement of both boats forms a right angle triangle. The distance travelled due south and due east by both boats represents the legs of the triangle. Their distance apart after t hours represents the hypotenuse of the right angle triangle.
Let x represent the length the shorter leg(south) of the right angle triangle.
Let y represent the length the longer leg(east) of the right angle triangle.
Let z represent the hypotenuse.
Applying Pythagoras theorem
Hypotenuse² = opposite side² + adjacent side²
Therefore
z² = x² + y²
To determine the rate at which the distances are changing, we would differentiate with respect to t. It becomes
2zdz/dt = 2xdx/dt + 2ydy/dt- - - -- - -1
One travels south at 32 mi/h and the other travels east at 60 mi/h. It means that
dx/dt = 32
dy/dt = 60
Distance = speed × time
Since t = 0.5 hour, then
x = 32 × 0.5 = 16 miles
y = 60 × 0.5 = 30 miles
z² = 16² + 30² = 256 + 900
z = √1156
z = 34 miles
Substituting these values into equation 1, it becomes
2 × 34 × dz/dt = (2 × 16 × 32) + 2 × 30 × 60
68dz/dt = 1024 + 3600
68dz/dt = 4624
dz/dt = 4624/68
dz/dt = 68 mph
