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
-3x-5+2x=6
2x-3x-5=6
-1x-5=6
-x-5=6
-x=11
x=11
an equivilent equaiton is x=11
Answer: the mathematical equation in very probomatic the answer is already a solution to your equtivented question. 15 miles in 45 minutes then the fortentea of 60 minutues, for mathematical troduction the answer 15/45^)60)=567/(}9}10ths of a mile}xtimes the matter of 67} over 56|=34x4milespersecound-34.=4r%~times the sectation matter
Step-by-step explanation:
59,424.77 rounded to the nearest square mile is 59,425.
Answer:
your answer is going to be -158
Step-by-step explanation:
(5)-(3)^2+7×-22=-158
