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
4. Using the given formula, replace t with 8 seconds and multiply:
343 x 8 = 2,744 meters.
5. Domain is the X value, replace x with 1/4 and solve:
1/4^2 + 2 = 2 1/8
y= 2 1/8
The last one is the answer. GD is similar to MJ, and DE is similar to JK. While DE is similar to ML as well, it is more so to JK because they are facing the same way
Answer:
You can also just find the area and times that by 4
If you want I can do that, just spam tell me and I'll figure the area out and tell u the answer in comments.
Step-by-step explanation:
She will pay $1.50 for the hairbrush and her mum paid $1.50 as well
