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
9514 1404 393
Answer:
(x, y) → (-∞, -∞), (+∞, +∞)
Step-by-step explanation:
The expression is of odd degree with a positive leading coefficient. It will have a generally upward slope (/). That is, the sign of f(x) will match the sign of x for large-magnitude values of x:
x → -∞, f(x) → -∞
x → ∞, f(x) → ∞
Answer is C because it's less than.
Answer:
30cm
Step-by-step explanation:
Assuming that the thickness of the books is 2cm (This is a reasonable assumption, as books are almost always longer and wider than they are thick, and assuming that the books are stacked flat on top of one another, faces up or down, and not sideways, the question becomes 'What is the height of 15 books stacked on top of one another, if each book is 2cm thick?' The answer to this question is 15*2 or 30.
