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
I am Lyosha [343]
3 years ago
13

Determine two pairs of polar coordinates for the point (4, -4) with 0° ≤ θ < 360°.

Mathematics
1 answer:
umka2103 [35]3 years ago
5 0
A polar coordinate is that which can be written as (r, θ) where r is the radius and θ is the angle. 

The radius, r, is also the hypotenuse of the right triangle that can be formed. Hence, it can be calculated through the equation,
    
                   r² = x² + y²
If we are to simplify this for the r alone, we have,
                     r = sqrt (x² + y²)

Substituting the known values,
               r = sqrt ((4)² + (-4)²) = 4√2

The x and y can be related through the trigonometric function, tangent. 
      tan θ = y/x
To solve for θ
   θ = tan⁻¹(y/x) = tan⁻¹(-4/4) = -45° = 315°

Hence, the polar coordinate is <em>(4√2, 315°)</em>
You might be interested in
Can someone answer this for me
Mekhanik [1.2K]

The answer is B, 162

4 0
3 years ago
A four-digit number N leaves a remainder of 10 when divided by 21, a remainder of 11 when divided by 23, and a remainder of 12 w
aksik [14]

Answer:

  16

Step-by-step explanation:

There may be a formal way to solve simultaneous Diophantine equations, but I don't know what it is. So, I addressed this by solving them 2 at a time.

First of all, we want to find a relation between integers p and q such that ...

  21p+10 = 23q +11

  21p -23q = 1 . . . . . . subtract 23q+10

Using the extended Euclidean algorithm or trial and error or astute observation, we find that (p, q) = (11, 10) is a solution to this equation. Then we can write p and q as ...

  • p = 23n+11
  • q = 21n+10

for some integer n.

Then our original numbers become ...

  21p+10 = 21(23n+11)+10 = 483n +241 . . . . for some integer n

For this to be a 4-digit number, we must have n such that

  1000 ≤ 483n +241 ≤ 9999

  1.6 < n < 20.2

__

Modulo 25, the number (483n+241) is ...

  8n +16

and we want that value to be 12:

  (8n +16) mod 25 = 12

  (8n +4) mod 25 = 0 . . . . . subtract 12

  4(2n+1) mod 25 = 0 . . . .  factor out 4

For this to be true, we must have 2n+1 be a multiple of 25. The only value of n that is in the required interval [2, 20] is n=12.

__

When n=12, 483n+241 = 6037. The sum of digits of 6037 is 16.

3 0
3 years ago
On Monday, Deborah ran 3 2− 5miles and on Tuesday she ran 4 1− 5miles. How many miles did she run on these two days together?
notsponge [240]

Mixed fraction:

3 2/5 = 17/5

4 4/5 = 24/5

Miles she ran:

17/5 + 24/5

= 41/5 miles or 8.2 miles

6 0
2 years ago
Type the equation for the following pattern.<br> Please Help!!
mash [69]

Answer:8

Step-by-step explanation: Every time the x goes down, the y goes up 3. Since you are trying to find the y intercept, when setting x to zero you will get 3+5 which equals 8. Hope this helps! (Can I please have brainliest?)

7 0
3 years ago
Read 2 more answers
Will give brainliest please help <br><br>4b + 7b +5 <br><br>i need help simplifying.​
vitfil [10]

Answer:

11b+5

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Other questions:
  • How would i write 2.318 with the 18 repeating? and how would i show my work?
    7·1 answer
  • Given the points J(4,-7) and L(-2, 13) find the coordinates of point K on line JL such that the ratio of JK to JL 1:4
    10·1 answer
  • I don't get 7/8n-3=5/8n+12??
    7·2 answers
  • Help me please!!!!!!!!!
    13·1 answer
  • What numbr must be subtracted from -20 to obtain 15?
    5·1 answer
  • What is the simplest from for 12/36
    9·2 answers
  • What is an 1 equation of the line that passes through the points (-2,1) and (6, – 7)?
    9·1 answer
  • Suppose Carson worked as a babysitter for '8' hours one week. What is the minimum number of full hours he would need to work at
    9·2 answers
  • - 1/5(y-x) please help on this !!!!
    6·1 answer
  • Help with geometry question please
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!