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
<u><em>Answer:</em></u>
575% as a mixed number is 
<u><em>Explanation:</em></u>
575% is equivalent to 
which is equal to 5.75
5.75 = 5 + 0.75
0.75 can be written as 
. This value can be simplified by dividing both the numerator and the denominator by 25. This would give us 
<u>Back to our number:</u>
Hope this helps :)
Answer:
D) C': ( -3, -2), D': ( -4, 1), E': ( -1, -2)
Step-by-step explanation:
Formula for this equation:
(x - 5, y - 3)
C:
(2, 1)
(x - 5, y - 3)
C': ( -3, -2)
E:
(4, 1)
(x - 5, y - 3)
E': ( -1, -2)
D:
(1, 4)
(x - 5, y - 3)
D': ( -4, 1)
Answer:
The exact value of
sin
(
30
)
sin(30) is
1
2
12.
15
⋅
1
2
15⋅12
Combine
15
15 and
1
2
12.
15
2
152
The result can be shown in multiple forms.
Exact Form:
15
2
152
Decimal Form:
7.5
7.5
Mixed Number Form:
7
1
2
712
Step-by-step explanation:
