3*4*3-2*4^2 = 36-32 = 4
hope helped
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
Since the basis is from year 1 to year 2, calculate first for the difference of their percentages. That would be:
Difference = year 2 - year 1
Difference = 2.32% - 1.1% = 1.22%
We apply this same value of percentage increase from year 2 to year. Thus, the percentage for year 3 is:
% Year 3 = % Year 2 + percentage increase
% Year 3 = 2.32% + 1.22%
% Year 3 = 3.54%
It isn't proportional because 3/4 is proportional to 9/16 not 9/15.
Answer:
2√2
Step-by-step explanation:
compare this equation with the standard equation of a circle centered at (h, k) with radius r:
(x - h)^2 + (y - k)^2 = r^2
(x - 5)^2 + (y + 7)^2=8
Clearly, r^2 = (radius)^2 = 8, and so the radius, r, is √8, or 2√2
