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:I think the answer is
1. x=8
Step-by-step explanation:
1. X=8
2. X=1⅓
3. 0x=-12
4. -8x=0
5. 0x=24
0.04 is multiplied 10 times to get 0.004
Answer:
69
Step-by-step explanation:
by eliminating 20 from 84 we get 64 then add the 3 to get 67 and then we know that we always add 2 to our answers and therefore get 69
Answer:
Step-by-step explanation:
(g-f)(x) = 9x³ - 4x² + 10x - 55 - [ 4x³ +3x² - 5x + 20]
To remove the parenthesis, take - inside, multiply f(x) by -1
= 9x³ - 4x² + 10x - 55 - 4x³ - 3x² + 5x - 20
Now, bring like terms together,
= 9x³ - 4x³ - 4x² - 3x² + 10x + 5x - 55 - 20
= 5x³ - 7x² + 15x - 75
