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9966 [12]
2 years ago
7

COMPLETE THE TABLE PICTURED: A robot is put into a maze, it can only go N, E, S, and West. The value i represents the north, and

the magnitude is equal to 1. I have figured out that N= i, East= 1, South= -i, and West= -1. When programming the robot, let the complex number d represent the direction the robot is facing. As the robot changes direction, the value of d will also change; so, the value of d is dependent on where the robot is in the maze. When the robot makes a turn, it would be useful to have an operation to perform on d to represent this turn. This is because after making a turn, the new value of d will depend on the old value of d. Complete the table for the new values of d if the robot is turning left or right. Then determine an expression in terms of d that will give the new position if the robot turns left and another expression if the robot turns right. Type these expressions in the last row of the table.

Mathematics
2 answers:
jonny [76]2 years ago
6 0

Step-by-step explanation:

\boxed{\begin{array}{c|c|c} \underline{Intial -d} & \underline {Left-turn} & \underline{Right-turn} \\ -1 & -i & i \\ 1 & i & -i \\ i & -1 & 1\\ -i & 1 & -1 \\ d & di & -di \end{array}}

Dmitry_Shevchenko [17]2 years ago
5 0

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

A right turn represents a clockwise rotation of the direction vector by 90°. It is equivalent to multiplying the complex number representation by -i.

A left turn represents a counterclockwise rotation of the direction vector by 90°. It is equivalent to multiplying the complex number representation by i.

The attached table shows the desired values and expressions.

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Answer:

Step-by-step explanation:

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Step-by-step explanation:

(4b^2+3)(4b^2-3)

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Ad libitum [116K]

The transformation of a function may involve any change. The correct option is D.

<h3>How does the transformation of a function happen?</h3>

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

  • Left shift by c units, y=f(x+c) (same output, but c units earlier)
  • Right shift by c units, y=f(x-c)(same output, but c units late)

Vertical shift

  • Up by d units: y = f(x) + d
  • Down by d units: y = f(x) - d

Stretching:

  • Vertical stretch by a factor k: y = k \times f(x)
  • Horizontal stretch by a factor k: y = f(\dfrac{x}{k})

Given the function f(x)=2ˣ, while the h(x)=-3(2ˣ), therefore, the function f(x) is a reflection and a translation of a function. Hence, the correct option is D.

Learn more about Transforming functions:

brainly.com/question/17006186

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