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
Answer:
v ≥ -17
Step-by-step explanation:
-82 ≤ 5v + 3
-82 - 3 ≤ 5v
5v ≥ -85
v ≥ -17
The order of the scale drawings from smallest to largest is
Smallest
1 in to 1 ft
Second smallest
1 in to 1 yd
Largest
1 in to 1 m
Given the following scales:
1 in to 1 ft
1 in to 1 m
1 in to 1 yd
We are to arrange the scales from smallest to largest.
Since 1 in is used as the base conversion for all the scales, we can convert the other scales to yards for consistency's sake.
Convert 1m to yards
1m = 1.1yards (From the question)
Convert 1ft to yards. According to conversion factor;
1 feet = 0.333333 yards
Ordering the scales from smallest to largest will give
0.33333yard (1 in to 1 ft), 1 yard (1 in to 1 yd), 1.1yards (1 in to 1 m)
Learn more here: brainly.com/question/14348682
X is 57
That means y is 36.
Sorry, I’m gonna try not explain it because I’m rlly bad at explaining and all I’m going to do is confuse you even more...
