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:
$75
Step-by-step explanation:
First, we will find how many hours he worked. 8:00-12:00 is 4 hours, and 12:00-2:00 is 2 hours, so he worked a total of 6 hours.
Next, we have to multiply the hours worked by his hourly wage.
12.50*6=75
Answer:
Sum=720 x=105 degrees Angle H=110 degrees Angle I= 100 degrees Angle K= 135
Step-by-step explanation:
*A hexagons angles add up to 720
*This is a hexagon
*No matter how the hexagon is shaped, it's still going to add up to 720
- Combine all of the angles (known and unknown) into an equation to equal 720
- 140+105+(x+30)+130+(x-5)+(x+5)=720
- remove parentheses
- 140+105+x+30+130+x-5+x+5=720
- Combine like terms and simplify
- 3x+405=720
- subtract 405 from both sides
- 3x=315
- divide by 3 on both sides
- 3x/3=315/3
- x=105
- Angle H = x+5
- Plug in x
- 105+5=110
- Angle H= 110 degrees
- Angle I = x-5
- pug in x
- 105-5=100
- Angle I= 100 degrees
- Angle K= x+30
- plug in x
- 105+30=135
- Angle K= 135 degrees
let's put value of t in equation.
x = 2√t
x = 2√y
x/2 = √y
(x/2)^2 = y
y = x^2 /4
now let's differentiate it with respect to x.
dy/dx = 2x/4 = x/2
differentiating again wrt to x
d^2y/dx^2 = 1/2
