Answer:
Hey is your ans
Step-by-step explanation:
Hope it helps you
Tq
Answer: 1. x = -2(y - 4)² + 1
2. x = -y² + 5
3. y = -5(x + 1)² + 2
<u>Step-by-step explanation:</u>
Notes: The vertex formula of a parabola is x = a(y - k)² + h or y = a(x - h)² + k
- (h, k) is the vertex
- p is the distance from the vertex to the focus
![\bullet\quad a=\dfrac{1}{4p}](https://tex.z-dn.net/?f=%5Cbullet%5Cquad%20a%3D%5Cdfrac%7B1%7D%7B4p%7D)
1)
![\text{Vertex}=(1,4)\qquad \text{Focus}:\bigg(\dfrac{7}{8},4\bigg)\\\\\text{Given}: (h,k)=(1,4)\\\\\\p=focus-vertex=\dfrac{7}{8}-\dfrac{8}{8}=\dfrac{-1}{8}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{-1}{8})}=\dfrac{1}{-\frac{1}{2}}=-2](https://tex.z-dn.net/?f=%5Ctext%7BVertex%7D%3D%281%2C4%29%5Cqquad%20%5Ctext%7BFocus%7D%3A%5Cbigg%28%5Cdfrac%7B7%7D%7B8%7D%2C4%5Cbigg%29%5C%5C%5C%5C%5Ctext%7BGiven%7D%3A%20%28h%2Ck%29%3D%281%2C4%29%5C%5C%5C%5C%5C%5Cp%3Dfocus-vertex%3D%5Cdfrac%7B7%7D%7B8%7D-%5Cdfrac%7B8%7D%7B8%7D%3D%5Cdfrac%7B-1%7D%7B8%7D%5C%5C%5C%5C%5C%5Ca%3D%5Cdfrac%7B1%7D%7B4p%7D%3D%5Cdfrac%7B1%7D%7B4%28%5Cfrac%7B-1%7D%7B8%7D%29%7D%3D%5Cdfrac%7B1%7D%7B-%5Cfrac%7B1%7D%7B2%7D%7D%3D-2)
Now input a = -2 and (h, k) = (1, 4) into the equation x = a(y - k)² + h
x = -2(y - 4)² + 1
***********************************************************************************
2)
![\text{Vertex}=(5,0)\qquad \text{Directrix}:x=\dfrac{21}{4}\\\\\text{Given}: (h,k)=(5,0)\\\\\\p=vertex-directrix=\dfrac{20}{4}-\dfrac{21}{4}=\dfrac{-1}{4}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{-1}{4})}=\dfrac{1}{-1}=-1](https://tex.z-dn.net/?f=%5Ctext%7BVertex%7D%3D%285%2C0%29%5Cqquad%20%5Ctext%7BDirectrix%7D%3Ax%3D%5Cdfrac%7B21%7D%7B4%7D%5C%5C%5C%5C%5Ctext%7BGiven%7D%3A%20%28h%2Ck%29%3D%285%2C0%29%5C%5C%5C%5C%5C%5Cp%3Dvertex-directrix%3D%5Cdfrac%7B20%7D%7B4%7D-%5Cdfrac%7B21%7D%7B4%7D%3D%5Cdfrac%7B-1%7D%7B4%7D%5C%5C%5C%5C%5C%5Ca%3D%5Cdfrac%7B1%7D%7B4p%7D%3D%5Cdfrac%7B1%7D%7B4%28%5Cfrac%7B-1%7D%7B4%7D%29%7D%3D%5Cdfrac%7B1%7D%7B-1%7D%3D-1)
Now input a = -1 and (h, k) = (5, 0) into the equation x = a(y - k)² + h
x = -1(y - 0)² + 5 → x = -y² + 5
***********************************************************************************
3)
![\text{Vertex}=(-1,2)\qquad \text{Directrix}:y=\dfrac{41}{20}\\\\\text{Given}: (h,k)=(-1,2)\\\\\\p=vertex-directrix=\dfrac{40}{20}-\dfrac{41}{20}=\dfrac{-1}{20}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{-1}{20})}=\dfrac{1}{-\frac{1}{5}}=-5](https://tex.z-dn.net/?f=%5Ctext%7BVertex%7D%3D%28-1%2C2%29%5Cqquad%20%5Ctext%7BDirectrix%7D%3Ay%3D%5Cdfrac%7B41%7D%7B20%7D%5C%5C%5C%5C%5Ctext%7BGiven%7D%3A%20%28h%2Ck%29%3D%28-1%2C2%29%5C%5C%5C%5C%5C%5Cp%3Dvertex-directrix%3D%5Cdfrac%7B40%7D%7B20%7D-%5Cdfrac%7B41%7D%7B20%7D%3D%5Cdfrac%7B-1%7D%7B20%7D%5C%5C%5C%5C%5C%5Ca%3D%5Cdfrac%7B1%7D%7B4p%7D%3D%5Cdfrac%7B1%7D%7B4%28%5Cfrac%7B-1%7D%7B20%7D%29%7D%3D%5Cdfrac%7B1%7D%7B-%5Cfrac%7B1%7D%7B5%7D%7D%3D-5)
Now input a = -5 and (h, k) = (-1, 2) into the equation y = a(x - h)² + k
y = -5(x + 1)² + 2
Answer:
People who live alone or with families of their own
Step-by-step explanation:
2 to the first is 2 because there is only one 2
Answer:
The population of this country in 11 years will be 76972702.82
Step-by-step explanation:
The population of this country in 11 years can be calculated using the formula
Population in 11 years = Starting population x ![(1+growth rate)^{period}](https://tex.z-dn.net/?f=%281%2Bgrowth%20rate%29%5E%7Bperiod%7D)
Thus
Population in 11 years =50000000×
=76972702.82