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
Hello, 3Coli here!
Here is the answer to your question:
The variable B stands for the area of the base.
In this prism, B equals 38.5 in.^2
The variable H stands for height.
In this prism, h is 9 in.
The volume of the prism is 346.5 in.^3
Hopefully, this helps! :D
Good luck with your assignment.
Answer: 12 9/10 and 10 7/8
Step-by-step explanation:
5 8/10 plus 7 1/10 equals 12 9/10
8 5/8 plus 2 2/8 equals 10 7/8
In order to answer this you’d have to find how much does a membership cost monthly first !
Answer:
2x - 2y
Step-by-step explanation:
Multiply by 1
combine like terms
Combine the second
rearrange terms
Then you should come up with the sloution 2x - 2y
