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
The volume of a sphere is (4/3) (pi) (radius cubed).
The volume of one sphere divided by the volume of another one is
(4/3) (pi) (radius-A)³ / (4/3) (pi) (radius-B)³
Divide top and bottom by (4/3) (pi) and you have (radius-A)³ / (radius-B)³
and that's exactly the same as
( radius-A / radius-B ) cubed.
I went through all of that to show you that the ratio of the volumes of two spheres
is the cube of the ratio of their radii.
Earth radius = 6,371 km
Pluto radius = 1,161 km
Ratio of their radii = (6,371 km) / (1,161 km)
Ratio of their volumes = ( 6,371 / 1,161 ) cubed = about <u>165.2</u>
Note:
I don't like the language of the question where it asks "How many spheres...".
This seems to be asking how many solid cue balls the size of Pluto could be
packed into a shell the size of the Earth, and that's not a simple solution.
The solution I have here is simply the ratio of volumes ... how many Plutos
can fit into a hollow Earth if the Plutos are melted and poured into the shell.
That's a different question, and a lot easier than dealing with solid cue balls.
Answer:
sorry
Step-by-step explanation:
I can't see the picture
Answer:
five-number summary
Step-by-step explanation:
y = ( 48 *2 ) / 6
Step-by-step explanation:
If y varies directly as x they are directly proportional, which means they relate to each other in the same way....
2 : y = 6: 48
what is y if x = 2?
The value of y can be found if you write it a two fracrions
2 : y = 6 : 48
2 / y = 6 / 48
cross multiply the fractions gives
6*y = 48 *2
divide left and right of the = sign by 6 gives the answer:
y = ( 48 *2 ) / 6
(if you solve it you get y = 12 but that was not the question).
Other method:
multiply left and right of the = sign by y
2 * y/y = y *6 / 48
6y / 48 = 2 * 1
multiply left and right of the = sign by 48
6y * 48/48 = ( 48 *2 )
6y = ( 48 *2 )
divide left and right of the = sign by 6
6/6* y = ( 48 *2 )/6
y = ( 48 *2 ) / 6
(if you solve it you get y = 12 but that was not the question).
