Answer:
(3 square root of 2 , 135°), (-3 square root of 2 , 315°)
Step-by-step explanation:
Hello!
We need to determine two pairs of polar coordinates for the point (3, -3) with 0°≤ θ < 360°.
We know that the polar coordinate system is a two-dimensional coordinate. The two dimensions are:
- The radial coordinate which is often denoted by r.
- The angular coordinate by θ.
So we need to find r and θ. So we know that:
(1)
x = rcos(θ) (2)
x = rsin(θ) (3)
From the statement we know that (x, y) = (3, -3).
Using the equation (1) we find that:
Using the equations (2) and (3) we find that:
3 = rcos(θ)
-3 = rsin(θ)
Solving the system of equations:
θ= -45
Then:
r = 3\sqrt{2}[/tex]
θ= -45 or 315
Notice that there are two feasible angles, they both have a tangent of -1. The X will take the positive value, and Y the negative one.
So, the solution is:
(3 square root of 2 , 135°), (-3 square root of 2 , 315°)
Answer:
1350
Step-by-step explanation:
Hope this helps!
Answer:
Step-by-step explanation:
The graph shows the solution (-6,2)
i.e at x= -6 y=2
Analysis of each of the answers, since we can't write the equation of a straight line with only that information i.e the single point
Then,
Option 1
1. 2x - 3y = -6
x= -6 y=2
Then let insert x=-6 and y =2
2(-6)-3(2)
-12-6
-18.
Since -18 ≠ -6, then this is not the equation of the line and doesn't make up the system
Option 2
2. 4x - y = 26
Inserting x=-6 and y=2
4(-6)-(2)
-24-2
-26
Since -26 ≠ 26, then this is not the equation of the line and doesn't make up the system
Option 3
3. 3x + 2y = -14
Inserting x=-6 and y=2
3(-6)+2(2)
-18+4
-14
Since -14 ≠ -14 then this is the equation of the line and it make up the system.
Option 4
x-y = -2
Inserting x=-6 and y=2
(-6)-(2)
-6-2
-8
Since -8≠ -2, then this is not the equation of the line and doesn't make up the system
Option 5
5. x+y=-4
Inserting x=-6 and y=2
(-6)+(2)
-6+2
-4
Since -4 ≠ -4, then this is the equation of the line and it makes up the system.
Then, there are two option that make up the system
3. 3x + 2y = -14
And
5. x+y=-4
Step-by-step explanation:
Domain x belongs to [-4 , 0]
Range y belongs to [-4 , 4]
The answer to this problem is x - 17.
