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
Answer:
2/3
Step-by-step explanation:
1. add all the beads up together:
20+10+30= 60
2. add the blue and yellow beads up:
10+30= 40
3. put 40 over 60
40/60 which equals 2/3
4. the final answer:
2/3
33 Million dollars have been made.
Answer:
1) x= 3/2= 1 1/2
2) x= 2/3
Step-by-step explanation:
1)How many times as heavy as Whiskers is Piglio?
a) Write a multiplication equation for the question.
2 2/3 kg * [x]= 4kg
b) Write a division equation for the question.
4/ 2 (2/3) = x
c) Is the answer greater than 1 or less than 1?
Ans) Greater than 1
d) Find the answer
4/ 8/3= x
x= 3/2= 1 1/2
Pigilo is 1 1/2 times as heavy as whiskers
2)How many times as heavy as Piglio is Whiskers?
a) Write a multiplication equation for the question.
4 kg * [x]= 2 2/3 kg
b) Write a division equation for the question.
2 (2/3)/4 = x
c) Is the answer greater than 1 or less than 1?
Ans) Less than 1
d) Find the answer
8/3/4= x
8/3 * 1/4= x
2/3= x
Whiskers is 2/3 times as heavy as Pigilo.
