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
108/4 = 27 pieces you multiply 36 x 3 = 108 and the denominator stays the same so 108/4 equals to 27 pieces
Answer:
3x + 1y = $163
2x + 3y =$174
Step-by-step explanation:
Adult tickets to space amusement park cost x dollars children’s tickets cost y dollars.
Henson family bought 3 adults and 1 child's tickets for $163
x + y = 163
3x + 1y = 163
The Garcia family bought 2 adults and 3 child’s ticket for $174.
x + y = $174
2x + 3y = $174
Therefore the equations representing both families cost are
Henson family
3x + 1y = $163
Garcia family
2x + 3y = $174
Answer:
A
Step-by-step explanation:
for a right angled triangle, the sum of the square of the two sides should be equal to the square of the hypotenuse. If this rule does not hold, the dimensions do not represent the side of a right angled triangle.
The Pythagoras theorem : a² + b² = c²
where a = length
b = base
c = hypotenuse
4² + 10² ≠ 16²
6² + 12² = 13²
7² + 24² = 25²
8² + 15² = 17²
Both answers are not the same. You are correct and your friend is wrong. The situation your teacher gave could have only one other interpretation that would be acceptable and that would be 8t+3 because it is the same number just in a different order.
