Answer:
![r^2 sin2\theta = 12](https://tex.z-dn.net/?f=r%5E2%20sin2%5Ctheta%20%3D%2012)
Step-by-step explanation:
Given
![xy = 6](https://tex.z-dn.net/?f=xy%20%3D%206)
Required
Get polar equivalent
Polar coordinate
and rectangular coordinate
are related in such a way that:
and ![y = rsin\theta](https://tex.z-dn.net/?f=y%20%3D%20rsin%5Ctheta)
So, substitute
and
in ![xy = 6](https://tex.z-dn.net/?f=xy%20%3D%206)
![rcos\theta * rsin\theta = 6](https://tex.z-dn.net/?f=rcos%5Ctheta%20%2A%20rsin%5Ctheta%20%3D%206)
This can be rewritten as:
![r * cos\theta * r * sin\theta = 6](https://tex.z-dn.net/?f=r%20%2A%20cos%5Ctheta%20%2A%20r%20%2A%20sin%5Ctheta%20%3D%206)
Reorder
![r * r * cos\theta * sin\theta = 6](https://tex.z-dn.net/?f=r%20%2A%20r%20%2A%20cos%5Ctheta%20%2A%20sin%5Ctheta%20%3D%206)
![r^2 * cos\theta * sin\theta = 6](https://tex.z-dn.net/?f=r%5E2%20%2A%20cos%5Ctheta%20%2A%20sin%5Ctheta%20%3D%206)
Multiply both sides by 2
![2 * r^2 * cos\theta * sin\theta = 6 * 2](https://tex.z-dn.net/?f=2%20%2A%20r%5E2%20%2A%20cos%5Ctheta%20%2A%20sin%5Ctheta%20%3D%206%20%2A%202)
![2 * r^2 * cos\theta * sin\theta = 12](https://tex.z-dn.net/?f=2%20%2A%20r%5E2%20%2A%20cos%5Ctheta%20%2A%20sin%5Ctheta%20%3D%2012)
Reorder
![r^2 * 2 * cos\theta * sin\theta = 12](https://tex.z-dn.net/?f=r%5E2%20%2A%202%20%2A%20cos%5Ctheta%20%2A%20sin%5Ctheta%20%3D%2012)
![r^2 * 2cos\theta sin\theta = 12](https://tex.z-dn.net/?f=r%5E2%20%2A%202cos%5Ctheta%20sin%5Ctheta%20%3D%2012)
In trigonometry:
![sin2\theta = 2sin\theta cos\theta = 2cos\theta sin\theta](https://tex.z-dn.net/?f=sin2%5Ctheta%20%3D%202sin%5Ctheta%20cos%5Ctheta%20%3D%202cos%5Ctheta%20sin%5Ctheta)
So, the expression becomes
![r^2 * sin2\theta = 12](https://tex.z-dn.net/?f=r%5E2%20%2A%20sin2%5Ctheta%20%3D%2012)
![r^2 sin2\theta = 12](https://tex.z-dn.net/?f=r%5E2%20sin2%5Ctheta%20%3D%2012)
Hence, the equivalent of
is ![r^2 sin2\theta = 12](https://tex.z-dn.net/?f=r%5E2%20sin2%5Ctheta%20%3D%2012)
Answer: The Answer would be 13.
Step-by-step explanation:
I think the one that is true about the way you should value your financial goals is : As you progress through life, your values and financial possibilities will gradually change, which leads to an evolution of your financial goals over time.Possibilities tend to be wider on younger age and the humanity value tend to increase as you got older.
Perimeter is adding all sides so the answer will be 12(pi) + 46, hope this helps!!
Answer: Choice A
f(x) = (x + 2)^2 - 11
=========================================================
Work Shown:
y = x^2 + 4x - 7
y+7 = x^2 + 4x
y+7+4 = x^2 + 4x + 4
y+11 = x^2 + 4x + 4
y+11 = (x + 2)^2
y = (x + 2)^2 - 11
f(x) = (x + 2)^2 - 11
In the third step, I added 4 to both sides to complete the square for the x^2+4x portion. Notice that (x+2)^2 = x^2+4x+4. So I added 4 to fill in the missing piece needed to complete the square.
Put another way the '4' added to both sides is because we first divided the x coefficient 4 in half to get 4/2 = 2. Then you square it to get 2^2 = 4.
--------------------
Alternative Method (optional)
y = x^2 + 4x - 7 is in the form of y = ax^2+bx+c
where: a = 1, b = 4, c = -7
Plug those a,b values into the formula below
h = -b/(2a)
h = -4/(2(1))
h = -2
This is the x coordinate of the vertex.
Use it to find the y coordinate of the vertex.
y = x^2 + 4x - 7
y = (-2)^2 + 4(-2) - 7
y = -11
The vertex is located at (h,k) = (-2,-11)
We have the template y = a(x-h)^2 + k update to y = (x + 2)^2 - 11 after plugging in a = 1, h = -2, and k = -11.