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
9/-5 ÷ -3/8 = 9/5 ÷ 3/8 = 27/8/5= [8•5=40] = 27/40
Answer: 27/40
Use -a/b= a/-b= a/b to rewrite the
fraction. -
Simplify the complex fraction
Simplify the complex fraction( yes again)
Answer:diameter of circle A is
(2r - 10) centimeters while Answer:diameter of circle B is 2r
Step-by-step explanation:
Diameter = radius/2
Circle A has a radius that is 5 centimeters less than the radius of Circle B. It means that if the radius of circle B is 5 centimeters, then the radius of circle A would be (r - 5) centimeters. Also,
The diameter of circle B would be
2 × r = 2r centimeters
Therefore, the diameter of circle A would be expressed as
2(r - 5) = (2r - 10) centimeters
Draw 12 squares, and shade 3 in
