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
The expression for g(x) is wrong, you skipped some signs and, apparentely, some parentheses. The rigtht expression for g(x) should be g(x) = 3(x+1) + 4. Note that g(x) = 3(x+1) + 4 it is the same that f(x+1) + 4. When you add a number to the argument, the graph of function is shifted that number of units to the left; and when you add a number to the function the graph shifts that number of units up. Therefore, the steps that will translate f(x) = 3x to g(x) = 3(x+1) + 4 is shift f(x) one unit to the left and four units up.
For the answer to the question on w<span>hich steps will translate f(x) = 3x to g(x) = 3x + 1 + 4? The answer to this question is
</span>f(x) = 3x one unit to the left and four units up
Answer:
1.66666667 <-- repeatedly is your answer
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
16 dollars in all- we can assume the dollars are paid per mile.
4 miles- 16/4 = 4 dollars per mile
Answer:
e,compound transformation
Step-by-step explanation:
