1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Morgarella [4.7K]
3 years ago
5

The position vector of p (relative to the origin) is op = (x, y). if the magnitude of op is 5 units, find the set of all possibl

e values of (x, y), with x, y E z​
Mathematics
1 answer:
Firdavs [7]3 years ago
7 0

Answer:

S = {(0, 5), (0, - 5), (3, 4), (3, -4), (-3, 4), (-3, -4), (4, 3), (4, -3), (-4, 3), (-4, -3), (5,0), (-5, 0) }

Step-by-step explanation:

Remember that the distance between two points (a, b) and (c, d) is given by:

distance = \sqrt{(a - c)^2 + (b - d)^2}

So, here we have that the distance between the point (x, y) and the origin, (0, 0) must have a magnitude of 5 units, then we want to solve:

5 = \sqrt{(x - 0)^2 + (y - 0)^2} \\5 = \sqrt{x^2 + y^2}

If we square both sides, we get

5^2 = (\sqrt{x^2 + y^2} )^2\\25 = x^2 + y^2

Now we want to find all the points (x, y) that meet this condition, suc that:

x ∈ Z

y ∈ Z

So both x and y must be integers.

So here we can just play with different values of x and y.

For example, if we define:

x = 0 we get:

25 = 0^2 + y^2

25 = y^2

√25 = y

Then we can have y = 5 or  y = -5

from this we got two points:

(0, 5) and (0, - 5)

if x = 1 we have:

25 = 1^2 + y^2

25 - 1 = y^2

24 = y^2

There is no integer such that its square is equal to 24, so we can stop here.

if x = 2 or - 2, we have:

25 = 2^2 + y^2

25 = 4 + y^2

25 -4 = 21 = y^2

Again, there is no integer such that its square is equal to 21, so we can stop here.

if x = +3 or -3, we have:

25 = 3^2 + y^2

25 = 9 + y^2

25 - 9 = 16 = y^2

√16 = y

then we can have y = 4 or y = -4

from this we got four points:

(3, 4)

(-3, 4)

(3, -4)

(-3, -4)

And for symmetry, if x = 4 or -4 we have the points:

(-4, 3)

(4, 3)

(-4, -3)

(4, -3)

finally, again for symmetry, if we take x = 5 or x = -5 we have the points:

(5,0)

(-5, 0)

Concluding, the set of all possible values (x, y) is:

S = {(0, 5), (0, - 5), (3, 4), (3, -4), (-3, 4), (-3, -4), (4, 3), (4, -3), (-4, 3), (-4, -3), (5,0), (-5, 0) }

You might be interested in
Given the function, f(x)=10x-3, <br> what is the value of the function when x=-1/2
Mandarinka [93]
-8

f(-1/2)=10(-1/2)-3
f(-1/2)=(-5)-3
f(-1/2)=-8
6 0
2 years ago
Identify the inequality that describes this graph​
enyata [817]

Answer:

B

Step-by-step explanation:

The direction of the greater than/equal to signs dictates which direction the graph is shaded.

6 0
3 years ago
Iron has a density of 7.87 g/cm^3. What is the mass of a block of iron that is 2cm x 10cm x 5cm?
Rufina [12.5K]

Answer:

2x10x5

V = 100 cm3

D = 7.87 g/cm3

M = 7.87x100

= 787g

3 0
2 years ago
How much percent of 200 miles is in 150 miles
satela [25.4K]
❅ 300%
You can do this by multiplying
Then converting that into a decimal
Then multiplying that by 150
❅Hope this helps!❅
4 0
3 years ago
Read 2 more answers
A Runway is 3100 ft long and 65 ft wide what is the area of the runway in feet squared​
ivolga24 [154]

Answer:

201, 500ft²

Step-by-step explanation:

The formula for calculating area in this case is;

<em>A = w × l</em>

This means we're going to take the width of the runway (65ft) and multiply it by the length of the runway (3100ft).

(To make it easier on paper, you can swap the two numbers around, so the higher number is on top, and the smaller number is on the bottom - 3100 × 65. It won't change the answer, but it will make it quicker and easier to get to the result, and lessens the chances making a mistake.)

So the equation you need to do is;

<em>3,100 × 65 = 201, 500.</em>

Add on the units, and there's your answer;

201, 600ft²

<h2>Hope this helped!</h2>
6 0
3 years ago
Other questions:
  • Jessica walks 7 times as far to school as Taylor does . Jessica walks 5 miles. How many miles does Taylor walk?
    12·1 answer
  • HURRY!!!!!!! Which symbol replaces ? to make the statement true? 16÷4+12 ? 4+24÷2 A.&lt; B.= C.&gt;
    10·2 answers
  • Can u give me the solution step by step
    15·1 answer
  • This recipe will serve 12 pancakes.
    8·1 answer
  • Find the range of the function f(x) = 4x - 7,
    8·1 answer
  • If an object is propelled upward from a height of 48 feet at an initial velocity of 96 feet per second, then its height after t
    8·1 answer
  • I need help (–
    11·1 answer
  • Please help, When do you need to approximate an irrational number with a rational value? Explain your understanding and give an
    8·1 answer
  • Find the area of this right triangle and explain how you got the answer ​
    13·1 answer
  • Emily sells her books through Amazon. She makes a profit of $3 per book sale, however, she needs to pay $6 to Amazon Pay in fees
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!