Answer: Answer: A
Explanation:
Just plug in numbers since you know the unknown values,
x + r = 4 + 5
4 + 5 = 9
Step-by-step explanation:
Number one is none of them
2) c
3) d
4) a
5) d
6) c
7) a
8) b
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:
Y'=3xy-3x-12
Y'=F(-2,-1)=0
Step-by-step explanation:
The function of the equation at the point (-2,-1)
is where the equation make the function go to zero:
Y'=3xy-3x-12
Y'=F(-2,-1)=[3(-2)(-1)]-[3(-1)]-12
F(-2,-1)=[6]-[-6]-12
F(-2,-1)=6+6-12
F(-2,-1)=12-12
F(-2,-1)=0
Solving for y
3xy-3x-12=0
y=4/x+x
Making y=0
So the values make the function go to zero
