I don’t know if you meant off or of but I will do both
25% OFF: $150
25% OF: $50
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
To find the biggest or close number say 70 is close to 75 or 70 the answer would be 70 I think but not sure
<h3>
Answer: w^2 + 3w - 10</h3>
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Work Shown:
Let x = w-2
This will allow us to replace the (w-2) with x to get...
(w-2)(w+5)
x(w+5)
x*w + x*5 ... distribute
w(x) + 5(x)
Now replace x with w-2 and distribute again
w(x) + 5(x)
w(w-2) + 5(w-2)
w*w + w*(-2) + 5*w + 5*(-2)
w^2 - 2w + 5w - 10
w^2 + 3w - 10
