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
Answer:
178.3 mm²
Step-by-step explanation:
Surface area = Base area + 3 x side triangles area
Sₐ = 43.3 + 3 x (1/2 x (10 x 9)) = 43.3 + (3 x 45) = 178.3
Step-by-step explanation:
6:36 = 6/36 = 1/6
3:18 = 3/18 = 1/6
therefore this ratios are equivalents...
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Answer:
Andres has 12 stars.
Step-by-step explanation:
- 3 stars - 1 goal
- -3/4 stars - Missed goal
- Scored 5
- Missed 4
3 * 5 = 15
He has 15 stars but then misses 4 goals.
3/4 * 4 = 3
He loses 3 stars becuase he missed 4 goals.
15 - 3 = 12
He ends with 12 stars.
