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
1 lb / 0.45 = 2.22
so approximately 2.22 kilograms per pound
divide price per pound by kilometers per pound
1.44 / 2.22 = 0.648
round to 0.65, so it costs $0.65 per kilogram
Answer:
2.80
Step-by-step explanation:
Take the cost and divide by the number of padlocks
25.20/9
2.80
Each padlock costs 2.80
If you need further help on how they got the answer, this equation will take more time, but it will also help you understand these types of problems. Part÷Whole=Percent÷100
Part= X because it is what you are trying to find.
Whole=250 because it is what you are taking the percentage of.
Percent=80
Now you have:
X÷250=80÷100
Set this up in fraction form and cross multiply.
You get:
100x=250×80
250×80=20,000
100x=20,000
X=200
