MATHEMATICS HIGH SCHOOL

When navigating the maze, the robot will only need to go north, south, east, and west. It can be useful to use the complex plane to represent these directions. When using the complex plane this way, we use numbers such that their magnitude is equal to 1. If we let the value i represent the robot facing due north, what values represent the robot facing east, south, and west?
When navigating the maze, the robot will only need to - 1

Answers

Answer 1
Answer:

Answer:

East = 1

South = - i

West = -1

Step-by-step explanation:

We are given that, the robot can only go north, south, east and west.

Assuming that the north-south axis corresponds to the y-axis and west-east axis corresponds to x-axis.

Now, it is provided that the ' i ' represent that robot is facing north.

So, if the robot turns and faces south, it can be seen that he will be facing in the opposite direction of ' i '.

Since, the values on y-axis are negative in that direction.

Hence, South will be represented by ' - i ' .

Moreover, it is given that we use only the numbers whose magnitude is 1. As, west-east axis represents x-axis.

So, the value that represents East will be 1 ( as it is on the positive x-axis ).

Since, west is in the opposite direction of east.

So, West will be represented by -1.

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The numbers on a football field indicate 10 yard increments. You walk around the perimeter of a football field between the pylons. You walk a distance of 306 and 2/3 yards. Find the area and perimeter of the indicated regions. Write your answers as mixed numbers, if necessary. One end zone

Answers

Answer: 126.67 is the perimeter walked

Step-by-step explanation:

Given data:

Distance walked on the field = 306 2/3 yards.

Increments on the field = 10 yards.

Solution:

We know a pitch has 4 sides let make it A, B,C,D = 306.67yards.

each has an increment of 10

= 10 x 10 + 10 x 10 = 200

Therefore

= 306.67 yards – 200

= 106.67 yards.

For both end zones Perimeter

= 106.67 + 10 + 10

= 126.67 yards

Final answer:

The area of the end zone is 6400 square yards and the perimeter is 326 and 2/3 yards.

Explanation:

To find the area and perimeter of the end zone of a football field, we need to know the dimensions of the end zone. If the end zone has a width of 53 and 1/3 yards, we multiply the width by the length of the field, which is 120 yards, to find the area. So the area of the end zone is (53 and 1/3) x 120 = 6400 square yards. The perimeter is found by adding the dimensions together, so the perimeter of the end zone is (2 x 53 and 1/3) + (2 x 120) = 326 and 2/3 yards.

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Which graph represents the linear function y=-2x+3

Answers

The coordinates will be (0, 3) and (1.5, 0), and mark these points on the paper and make a straight line.

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A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.

The linear function is given below.

y = -2x + 3

Then the graph of the equation will be

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Put y = 0, then the value of x will be

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Evaluate the Riemann sum for (x) = x3 − 6x, for 0 ≤ x ≤ 3 with six subintervals, taking the sample points, xi, to be the right endpoint of each interval. Give three decimal places in your answer.

Answers

Hello,

Reminders:
$\sum_(i=1)^(n) i= (n(n+1))/(2)$
$ \sum_(i=1)^(n) i^2= (n(n+1))/(2)$
$ \sum_(i=1)^(n) i^3= (n^2(n+1)^2)/(4) $

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The perimeter of a basketball court is 114 meters and the length is 6 meters longer than twice the width. What are the length and the width?

Answers

ok first list everything you know (what they told us) about this basketball court because this will come in handy. 

perimeter (p)=114 (they told us that this is the perimeter)
p=2w+2L  (using what we know about perimeters we can infer that this is the formula for a perimeter. this is just another way of writing p= w+L+w+L)
L=6+2w ("L" is length. they say that the length is 6 MORE, hence the plus sign, than 2 TIMES the width)

now lets put all this together. we want to find the length and width. we already have an idea of what the length is so we can plug that into our "p" formula...

p= 2w+ 2(6+2w).. now do a little simplifying 
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we know what "p" is so we can also plug that in
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Great we just found what the width is BUT we aren't finished. we have to find the length. for this you just plug "w" back into your "p" formula. 

p= 2(17)+2L
remember that p=114
114= 34+2L
get "L" to one side
114-34=2L
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make sure you check your answers. simply plug "w" and "L" into your "p" formula if it equals 114 you did it right !!
let width be x then
L = 6 + 2x (as per the question)
therefore perimeter = 2(L+B)
P=2(6+2x+x)
P=2(6+3x)
P=12+6x
acc. to question P=114 m
144 = 12 + 6x
6x=114-12
6x=102
x=(102)/(6)
x=17
therefore width = 17 meters
then , length = 6 + 2x
where x=17 m
L=6+2(17)
L=6+34
L=40
therefore length and breadth of the basketball court is 17 m and 40 m respectively...

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Answers

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Answers

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