The answer is C
Hope this helped
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: No, because ABC is not a right angle.
Step-by-step explanation: In triangle ABC, the three angles add up to 180
So angle B = 180 - 48 - 47 = 85.
Answer:
(x² − 2x + 2) (x − 1)
Step-by-step explanation:
Use grouping.
x³ − 3x² + 4x − 2
x³ − 3x² + 2x + 2x − 2
x (x² − 3x + 2) + 2 (x − 1)
x (x − 2) (x − 1) + 2 (x − 1)
(x (x − 2) + 2) (x − 1)
(x² − 2x + 2) (x − 1)
Answer:
you switch 8x and 4y by subtracting 8x to 4y + 16 and substracting 4y to 8x.
This gives you the equation -4y = -8x+16
Then you divide each side by -4
To give you your slope-intercept form which is y = 2x-4.
