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
$10.50a + $3.75b = $2,071.50
It is given that b = 82
Therefore - $10.50a + ($3.75)(82) = $2,071.50
or $10.50a + $307.50 = $2,071.50
$10.50a = $2,071.50 - $307.50 = $1,764.00
Therefore - a (number of adult tickets sold) = $1,764.00/$10.50 = 168 tickets
Answer:
statement: 2. both pairs of parallel lines are congruent
reason: 2. def. of a parallelogram
and that should be all you need
Answer:
268
Step-by-step explanation:
please give brainliest
ANSWER: 312 3/8
So Volume is Length • Width • Height
So first we would put it into this formula:
8.5 • 5.25 • 7= 312.375, or, 312 3/8
