Answer:
![y=\frac{-1}{4}(x-1)^2-2](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-1%7D%7B4%7D%28x-1%29%5E2-2)
Step-by-step explanation:
Given : focus of (1, -3) and a directrix of y= -1
The distance between focus and directrix is 2p
The distance between (1,-3) and y=-1 is 2
So 2p = 2 and p =1
Vertex (h,k) lies inbetween the focus and directrix
focus is (h, k-p)
given focus is (1,-3)
so h=1 and k-p = -3 ( we got p =1)
So k-1= -3 , k= -2
Hence, vertex is (1,-2), h=1 and k = -2
![a=\frac{1}{4p} =\frac{1}{4}](https://tex.z-dn.net/?f=a%3D%5Cfrac%7B1%7D%7B4p%7D%20%3D%5Cfrac%7B1%7D%7B4%7D)
Here focus at the bottom and directrix at the top
so parabola opens down
hence a= -1/4
Plug it in the equation
![y=a(x-h)^2+k](https://tex.z-dn.net/?f=y%3Da%28x-h%29%5E2%2Bk)
![y=\frac{-1}{4}(x-1)^2-2](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-1%7D%7B4%7D%28x-1%29%5E2-2)
Value of cos(x+π) = ![\bold{\frac{\sqrt{3} }{2}}](https://tex.z-dn.net/?f=%5Cbold%7B%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B2%7D%7D)
Given cosine of x = ![-\frac{\sqrt{3} }{2}](https://tex.z-dn.net/?f=-%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B2%7D)
i.e., cos(x) = ![-\frac{\sqrt{3} }{2}](https://tex.z-dn.net/?f=-%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B2%7D)
Also cos(
) =
. So x =
.
We need to find cos(x+π) = cos(
).
But its value is not easy to find. So we use trigonometric formulas.
We have the trigonometric formula, cos (x+π) = - cos(x) = -
= ![\bold{\frac{\sqrt{3} }{2}}](https://tex.z-dn.net/?f=%5Cbold%7B%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B2%7D%7D)
Cos(x+π) lies in the 3rd quadrant. So there cosine has negative values. That is why, cos (x+π) = - cos(x).
Learn more about Cos(x+π) trigonometric formula at brainly.com/question/12243383
#SPJ4
Answer:
a = 0
Step-by-step explanation:
The cube root (radical) is equivalent to x^(1/3). When that is divided by x^(1/3), the result is ...
(x^(1/3))/(x^(1/3)) = x^(1/3 -1/3) = x^0
Comparing that to x^a, we find a=0.
_____
The applicable rules of exponents are ...
![\sqrt[n]{x^m}=x^{\frac{m}{n}}\\\\\dfrac{x^a}{x^b}=x^{a-b}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%5Em%7D%3Dx%5E%7B%5Cfrac%7Bm%7D%7Bn%7D%7D%5C%5C%5C%5C%5Cdfrac%7Bx%5Ea%7D%7Bx%5Eb%7D%3Dx%5E%7Ba-b%7D)
Answer:
$580
Step-by-step explanation:
{371x(100-34)/100}+371=580