Koalagirl133 I think this is the answer I don't know if it is 9,540,000× 10 = 94, 500, 000
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
The number of orders Michael, Rafael and Amanda served are 16.8, 33.6, and 41.6 servings
respectively.
<h3>Equation</h3>
- Michael = x
- Rafael = 2x
- Amanda = 2x + 8
- Total servings = 92 orders
x + 2x + (2x + 8) = 92
3x + 2x + 8 = 92
5x = 92 - 8
5x = 84
x = 84/5
x = 16.8 servings
Therefore,
Michael = x
= 16.8 servings
Rafael = 2x
= 2(16.8)
= 33.6 servings
Amanda = 2x + 8
= 33.6 + 8
= 41.6 servings
Learn more about equation:
brainly.com/question/4344214
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The correct answer should be y=4x + 1d where x equals the number of personal pizzas, and d equals the number of drinks.
She didn't account for the number of drinks ordered for more than one meal.
