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
It is the last answer choice
Answer:
4 1/3 as an improper fraction is 13/3
Answer:
$541.63
Step-by-step explanation:
To find the balance of Gurindas, we need to break down our values.
Checking Balance = $532.14
Checks = $-46.19 + $-138.32 = $-184.51
Deposit = $200
Service Charge = $-6
Now to find her new balance, we simply add them all together.
New Balance = 532.14 + -184.51 + 200 + -6
New Balance = $541.63
Answer:
The coordinates of point S are (6, 2).
Step-by-step explanation:
(x, y) where x is horizontal and y is vertical.
Point P's coordinates are (6, -4). Point S is 6 units above point P. This means we need to add 6 to point P's y value; -4.
-4 + 6 = 2
The y value is 2 for point S. The x value stays the same because we are not moving point S to the left or right of point P. The coordinates of point S are (6, 2).
Hope this helps,
♥<em>A.W.E.</em><u><em>S.W.A.N.</em></u>♥
