The employees of the company marked a grid on the floor and set the robot at left parenthesis 2 comma 3 right parenthesis(2,3). They programmed the robot to walk 33 yards east and 55 yards north each minute. What will the robot's location be after 7 minutes? Answer problems

The robot's location from its initial location after 7 minutes is (233, 386)

Distance moved from initial location = 451.56 yards < 59.2°  North-East

Step-by-step explanation:

Since the robot moves 33 yards east and 55 yards north each minute, the distance it moves east in 7 minutes is 33 yards/minute × 7 minutes = 231 yards.

The distance it moves north in 7 minutes is 55 yards/minute × 7 minutes = 385 yards.

The robot's location from its initial location after 7 minutes is (2 + 231, 3 + 385) = (233, 388)

The distance moved from the initial location is

r = √(231² + 385²)

= √(53361 + 150544)

= √203905

= 451.56 yards

Its direction is gotten from tanθ = distance moved north/distance moved east = 388/231 = 1.680

θ = tan⁻¹(1.680) = 59.23° ≅ 59.2°

Hi there!
The question gives us the rule A(n) = -14 + (n - 1)(2). We are asked to find the ninth term of the arithmetic sequence. To find this, all we have to do is plug in 9 for n. This gives us A(9) = -14 + (9 - 1)(2). Now, just simplify. 
A(9) = -14 + (9 - 1)(2)
A(9) = -14 + 16
A(9) = 2
Therefore, the ninth term in this arithmetic sequence is 2. Hope this helped and have a phenomenal day!