The length of the rectange is 20ft and width of the 5ft.
<u>Step-by-step explanation:</u>
Let us consider a rectangle and its area is known to be 100 sq ft.
We are given the information that the length of the rectangle is 10ft longer than twice its width.
⇒Length l = 2w+10.
Where w is the width of the rectangle.
The formula for area of the rectangle A = length × width.
A= (2w+10)×w.
100 = 
.
0=
.
Thus it forms an quadratic equation we have to solve for the solution.
0=(2w-10)(w+10).
2w-10=0. w+10=0.
2w=10. w=-10. (negative value cannot be choosed.)
w=
.
w=5ft.
Thus width is is 5 ft.
Length = 2(5)+10.
=10+10.
=20ft.
Thus the length is 20ft.
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:
Grades 6 and 8
Step-by-step explanation:
If the relationship of girls to boys in two different grades are proportional, <u>they must have the same ratio</u>. To tackle this problem, we can find the <u>ratios</u> of genders in each grade and compare them.
Step 1, finding ratios:
Finding ratios is just like <u>simplifying fractions</u>. We will reduce the numbers by their<u> greatest common factors</u>.
<u>Can't be simplified!</u>
<u />
Step 2:
Notice how grades 6 and 8 both had a ratio of 3:4. We can conclude that these two grades have a proportional relationship between girls and boys.
<em>I hope this helps! Let me know if you have any questions :)</em>
<u />
Answer:
18.85 feet
Step-by-step explanation:
Determine the arc length of SR
Arc length = θ/360 × 2πr
r = 9 feet
θ =120°
Arc length = 120/360 × 2 × π × 9
= 18.849555922 feet
Approximately = 18.85 feet
Therefore, the arc length of SR = 18.85 feet
