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
With the 3 colors - red=1, yellow=2 and green=5 - adding up to 8, that is one quarter the total of 32. Multiply each by 4 and you'll have - 4:8:20.
Answer:
I don't really know but one triangle is 180 degrees so two added together is 360 degrees...
but ohh I remembered
a=c+d (since a+b=180 and c+d+b=180)
e=g+h (since e+f=180 and g+h+f= 180)
and the fact is that c+d+g+h+b+f=the angle sum of quadrilateral PQRS
a+e+b+f= the angle sum of quadrilateral PQRS (by substitutions)
a+e+b+f=360 (four angles are from one origin so it's 360 degrees )
Answer:
=6 units squared
Step-by-step explanation:
area=1/2h(a+b)
=1/2×2(4+2)
=6
