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.
Answers
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.
Step-by-step explanation:
[tex]\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}}[/tex]
Related Questions
Can someone solve please? An explanation with it would help as well!
Answers
Take triangle PQM and find all sides and angles to get the length of the hypotenuse for right triangle RQM. Then use the Pythagorean Theorem to solve fo side RQ:)
The sum of three consecutive intgers is 72 find the smallest integer
Answers
23 is the answer
Step-by-step explanation: 23 is the answer
23+24+25=72
hiii please help me 20ptss
Answers
Answer:
I think it's the second answer, The head of state is always chosen by the citizens.
Step-by-step explanation:
I hope this helps!
Answer:
I think it is the first one but im not too sure sry if its wrong
Step-by-step explanation:
How many 3 2/3 ounce bottles of perfume can be filled from a jug containing 64 ounces?
Answers
Answer:
24 bottles would fill the jug
Step-by-step explanation:
Given
[tex]Bottles = 3\frac{2}{3}[/tex]
[tex]Jug = 64[/tex]
Required
Determine the number of bottles in a jug.
To do this, we simply divide the given measurements of jug and the bottle.
In other words,
[tex]Number = \frac{Jug}{Bottle}[/tex]
[tex]Number = \frac{64}{3\frac{2}{3}}[/tex]
Convert fraction to improper
[tex]Number = \frac{64}{\frac{8}{3}}[/tex]
[tex]Number = 64/\frac{8}{3}[/tex]
[tex]Number = 64*\frac{3}{8}[/tex]
[tex]Number = 8 * 3[/tex]
[tex]Number = 24[/tex]
Hence, 24 bottles would fill the jug
Given the system of equations, solve for x
2x - 3y = -19
4x + 5y = 17
Answers
Answer:x=-2
Step-by-step explanation: First, you need to multiply 2 for the first equation. The first equation becomes 4x-6y=-38. Then you have to subtract the first equation from the second equation, so it becomes 11y=55. 55/11=5, so y =5. We can plug 5 into the equation, and from there, we can draw out the conclusion that x=-2. You can also verify this by plugging -2 into the equation, which I did.
estimate then divide 75578÷53
Answers
the school office orderd 24 boxes of pen there total cost was 191.52 what was the cost of 1 box of pen
Answers
Answer:
$7.98 per box
Step-by-step explanation:
Divide 191.52 by 24
If a population doubles every 5 years, how many years will it take for the population to increase by 10 times
its original amount?
Answers
Answer:
25 years
Step-by-step explanation:
I need help answering this question
Answers
Answer:
[tex] x = 53 [/tex]
Step-by-step explanation:
[tex] 65 = x + 12 [/tex] (alternate interior angles are congruent)
Subtract 12 from each side
[tex] 65 - 12 = x + 12 - 12 [/tex]
[tex] 53 = x [/tex]
[tex] x = 53 [/tex]
Use the figure below to answer the question below.
A. If each square represent one square unit, estimate the area of the shaded figure in square units.
B. Estimate percent of the larger square that is shaded.
Answers
Answer:
Part A : 4pi OR 12.56637
Part B : 34.9%
Step-by-step explanation:
helppppp please will give brainliest
Answers
Answer:
The answer is A
Step-by-step explanation:
so who's going to do this aka the queen / King Master
Answers
Help ASAP thank you!! And show work !
Answers
Answer:
c. -2
Step-by-step explanation:
Since f(x) is the regular graph. Since the inverse function flips the x and y coordinates, f inverse of 4 is actually where y=4, not x=4. so the x coordinate where y is 4 is -2.
What is the greatest common factor of 6,27, and 30
Answers
Answer:
the GCF is 3 because 6/3= 2 27/3=9 30/3=10True or False
Unit rate is a ration with denominator 2 example 100words in 2 minutes
True
False
Answers
Answer:
The Answer Is True
Step-by-step explanation:
What's the range of this function graph
Answers
Answer:
[2,∞)
Step-by-step explanation:
The range is the y intercept and the function starts at 2 and continues going up causing the range of the function to be [2,∞)
The highest temperature in Fairbanks Alaska was 15.7 degrees Fahrenheit one day that night the temperature fell 38.4 degrees what was the lowest temperature for the night?
Answers
Answer:
-22.7 degrees Fahrenheit
Step-by-step explanation:
Subtract change in temperature from the original temperature. 15.7 - 38.4 = -22.7. Hope this helps!!
Divide.
(15x +9x² +24x – 13) + (5x2–2x)
Your answer should give the quotient and the remainder.
Quotient:
1
Remainder:
X Х
?
Answers
Answer:
14x2+37x−13
Step-by-step explanation:
15x+9x2+24x−13+5x2−2x
=15x+9x2+24x+−13+5x2+−2x
Combine Like Terms:
=15x+9x2+24x+−13+5x2+−2x
=(9x2+5x2)+(15x+24x+−2x)+(−13)
=14x2+37x+−13
30 POINTS IF U GET IT RIGHT
The original price of a chair was $545.00. The store had a sales tax of 4.5%. What is the exact price of the chair, including tax?
Answers
explanation: 545 x 1.045 to add the 4.5% increase in tax
find the equation of the line m=6 and b=-7 in slope intercept form
Answers
Answer:
y = 6x - 7
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y- intercept )
Here m = 6 and b = - 7 , thus
y = 6x - 7 ← equation of line
Matt is helping to set up drinks and snacks for a luncheon.
Matt has 4.8 liters of iced tea. He is going to pour this into pitchers that can each only hold 0.8 liters of iced tea.
If Matt pours an equal amount of iced tea into each pitcher, how many pitchers does he fill?
Answers
Answer:
he will fill 6 pitchers
Step-by-step explanation:
4.8÷0.8=6
20!! points see the image please help as fast as possible please 20!
Answers
Answer:
67.7Step-by-step explanation:
perimeter = semicircle (x2) + rectangle side (x2)
= 1/2 π 12 (x2) + 15 (x2)
= 37.7 + 30
= 67.7
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Answers
h(x)=4x+4 find h(3b)
Answers
Answer:
h(3b)=12b+4
another answer
h(3b)=4(3b+1)
Step-by-step explanation:
h(x)=4x+4
h(3b)=4(3b)+4
h(3b)=12b+4
if need to simplify..then:
h(3b)=4(3b+1)
Evaluate:
20
5.2-^3
Answers
Answer:
3 37 over 41
Step-by-step explanation:
Lauren is replacing a door that measures 80 inches by 39. What is the distance between opposite corner of the door
Answers
Answer:
Step-by-step explanation:
x² = 80² + 39²
x² = 6400 + 1521
x² = 7921
x = 89 inches
Graph the line that contains the point (-3,1) with a slope of 2/3
Answers
Answer:
The graph of the line that contains the point [tex](-3,1)[/tex] with a slope of 2/3.
Step-by-step explanation:
As the line contains the point (-3, 1) with a slop 2/3
Given the slop-intercept form of the line equation
y = mx+b
Here,
m = slopeb = y-interceptSubstituting the values in the slop-intercept form of the line equation
[tex]y = mx+b[/tex]
[tex]1 = \frac{2}{3} (-3) + b[/tex]
[tex]1 =- 2 + b[/tex]
switching sides
[tex]-2+b=1[/tex]
[tex]b=3[/tex]
Now Substituting the value of [tex]b=3[/tex] in the slop-intercept form of the line equation
[tex]y = mx+b[/tex]
[tex]y=\frac{2}{3} x+3[/tex]
Hence, the line of the equation will be: [tex]y=\frac{2}{3} x+3[/tex]
Therefore, the graph of the line that contains the point [tex](-3,1)[/tex] with a slope of 2/3.
The manager of an ice cream shop found that the probability of a new customer ordering vanilla ice is 7\9. What are the odds against a new customer ordering vanilla ice cream?
Answers
Answer:
The odds-against a new customer ordering a vanilla ice cream are: 2/7 or 2 to 7
Step-by-step explanation:
Odds-against is the ratio of probability of non-occurrence of an event to the probability of occurrence of an event.
Let p be the probability that the new customer will order vanilla
Then
[tex]p = \frac{7}{9}[/tex]
Let q be the probability that the new customer will not order vanilla
[tex]q = 1-p\\= 1 - \frac{7}{9}\\= \frac{9-7}{9}\\=\frac{2}{9}[/tex]
Now the odds against formula is:
[tex]\frac{Probability\ of\ non-occurrence}{Probability\ of\ occurrence}= \frac{q}{p}\\=\frac{\frac{2}{9}}{\frac{7}{9}}\\=\frac{2}{9} * \frac{9}{7}\\=\frac{2}{7}[/tex]
Hence,
The odds-against a new customer ordering a vanilla ice cream are: 2/7 or 2 to 7
Find the QUOTIENT of 0.4452 and 0.06.
Answers
Answer:
7.42
Step-by-step explanation:
When you divide by something smaller than 1, the answer becomes bigger because you are trying to see how many times 0.06 can fit in 0.4452. Hope this helps
Are integers closed under addition? Justify your answer.
Answers
Answer:
The set of integers is closed under addition, subtraction, and multiplication because when I add, subtract, or multiply any integers, the result is always an integer.
Step-by-step explanation:
Answer:
The integers are "closed" under addition, multiplication and subtraction.
Step-by-step explanation:
But can not be used doing division or A fraction involving two integers.