Remember the shortcut way for graphing quadratic equations
- A quadratic function has graph as parabola
- Hence on both sides of vertex the parabola is symmetric and axis of symmetry is vertex x values .
- y on both sides for -x and +x is same
#1
Vertex
As a is positive parabola facing upwards
Find y for same x distance from vertex
I took 3-1=2 and 3+1=4
- f(2)=2(2-3)²-1=2(-1)²-1=2-1=1
- f(4)=2(4-3)²-1=1
Now plot vertex and these two points (2,1) and (4,1) on graph then draw a parabola by freehand
#2
- y=(x-2)(x+4)
- y=x²+4x-2x-8
- y=x²+2x-8
Convert to vertex form
Vertex at (-1,-9)
Same take two equidistant x values
Let's take -1-1=-2 and -1+1 =0
- f(-2)=(-2+1)²-9=1-9=-8
- f(0)=(1)²-9=-8
Put (-1,-9),(-2,-8),(0,-8) on graph and draw a freehand parabola
#3.
Yes it can be verified by finding the coordinate theoretically on putting them on function then can be verified through putting them on graph whether they matches or not
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:
x is vertical *laying down* y in upward also (x,y) so ifthe first on would be anywhere on the y axis
