Answer:
c = 6d
Step-by-step explanation:
c = change in y/change in x times days
According to the graph: c = 12/2d
Simplify
c = 6d
Answer:
288
Step-by-step explanation:
took the quiz
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
Let's assume there's a fourth place too, and fourth place is the one where it's no prize.
4 3 2 1 (4 3 X X)
4 3 1 2 (^ but 3rd and 4th digit exchanged)
4 2 3 1 (4 2 X X)
4 2 1 3 etc.,.
4 1 2 3
4 1 3 2
As you can see, there are six possibilities assuming first swimmer was fourth.
Now, there would be six possibilities if the first swimmer was third, and same goes for second and first.
Thus, 6 x 4 = 24, there are 24 possibilities to award the 3 prizes (plus 1 no-prize)
Simple Mathematical Way:
4 x 3 x 2 x 1 = 4! = 24
There are 24 ways.
Y= 3x+2/p
y-(2/p)=3x
(y-(2/p))/3=x
