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 answer for t is 4 and the proportional relationship is 9
Soooooo sorry but I only understood part a and c.
sorry
Answer:
see explanation
Step-by-step explanation:
(a)
To find the first 4 terms substitute n = 1, 2, 3, 4 into the n th term formula.
a₁ = 1 + 5 = 6
a₂ = 2 + 5 = 7
a₃ = 3 + 5 = 8
a₄ = 4 + 5 = 9
For the 10 th term substitute n = 10, that is
a₁₀ = 10 + 5 = 15
The first 4 terms are 6, 7, 8, 9 and the 10 th term is 15
(b)
Substitute n = 1, 2, 3, 4 and 10 into the n th term formula
a₁ = 2(1) - 1 = 2 - 1 = 1
a₂ = 2(2) - 1 = 4 - 1 = 3
a₃ = 2(3) - 1 = 6 - 1 = 5
a₄ = 2(4) - 1 = 8 - 1 = 7
a₁₀ = 2(10) - 1 = 20 - 1 = 19
The first 4 terms are 1, 3, 5, 7 and the 10 th term is 19
