Answer:
D
Step-by-step explanation:
From any point (x, y) on the parabola the focus and directrix are equidistant
Using the distance formula
= | y + 1 |
Squaring both sides
(x + 5)² + (y - 5)² = (y + 1)^2 , that is
(y + 1)² = (x + 5)² + (y - 5)² ← subtract (y - 5)² from both sides
(y + 1)² - (y - 5)² = (x + 5)² ← expand left side and simplify
y² + 2y + 1 - y² + 10y - 25 = (x + 5)²
12y - 24 = (x + 5)² ← factor left side
12(y - 2) = (x + 5)² ← divide both sides by 12
y - 2 = (x + 5)² ← add 2 to both sides
y = (x + 5)² + 2
or
f(x) = (x + 5)² + 2 → D
Answer:
25/13
Step-by-step explanation:
Multiply the denominator x the whole number
Add the numerator
13 * 1 = 13 + 12 = 25
Keep the original denominator
Answer:
- length 100 ft
- height 30 ft
Step-by-step explanation:
The center is 40 ft from the focus, so the wall is 40+10 = 50 ft from the center. From wall to wall must be 2×50 ft = 100 ft.
The length is 100 ft.
__
Assuming the gallery has an elliptical vertical cross section, the distance from the focus to the center ceiling is the same as half the length of the gallery, so we can use the Pythagorean theorem to find the height:
50² = 40² + h²
h = √(2500 -1600) = √900 = 30
The height of the ceiling at the center is 30 feet.
_____
<em>Comment on the geometry</em>
We expect the gallery to have an elliptical floor plan, rather than an elliptical vertical cross section. In the latter case, the focus would have to be above the floor for it to work, so the ceiling at center would have to be higher than 30 ft. by the distance that the focus is above the floor.
x-32.2= 18.5
Add 32.2 to both sides
x-32.2+32.2 = 18.5 + 32.2
x = 50.7
I hope that's help !
Check your answer
replace x by its number
50.7-32.2= 18.5
18.5 = 18.5
so the answer is good .
Please let me know if you have question(s) !
Ok So, 5+3=8x2=16-6=10 :)