Vbox-vspheres
vbox=, I assume we are dealing with l=w=h
so
v=lwh=12^3=1728
vsphere=(4/3)pir^3
r=3
vsphere=(4/3)pi3^3=4pi9=36pi
8 of them so
8 times 36pi=288pi or about 904.7786842338604526772412943845 cubic inches
vbox-sphere=1728-904.7786842338604526772412943845=823.2213157661395473227587056155
space filled by packing beads is about 823.22 cubic inches
beads percent is 823.2213157661395473227587056155/1728 times 100=47.64% filled by beads
Let
rA--------> radius of the circle A
rB-------> radius of the circle B
LA------> <span>the length of the intercepted arc for circle A
</span>LB------> the length of the intercepted arc for circle B
we have that
rA/rB=2/3--------> rB/rA=3/2
LA=(3/4)<span>π
</span>
we know that
if <span>Both circle A and circle B have a central angle , the ratio of the radius of circle A to the radius of circle B is equals to the ratio of the length of circle A to the length of circle B
</span>rA/rB=LA/LB--------> LB=LA*rB/rA-----> [(3/4)π*3/2]----> 9/8π
the answer is
the length of the intercepted arc for circle B is 9/8π
5/4 = 75/g....cross multiply because this is a proportion
5g = 300
g = 300/5
g = 60
so in 2nd semester, there were 75 students in art class and 60 students in gym class....for a total of 135 students.
1st semester....ratio was 2:7...added = 9
art : 2/9(135) = 270/9 = 30 <=== art class had 30
gym: 7/9(135) = 945/9 = 105 <=== gym class had 105
I will explain step by step how to solve for x
Remove the parenthesis using distributive property
1.5(x + 4) - 3 = 4.5(x - 2)
1.5(x) + 1.5(4) = 4.5(x) - 4.5(2)
1.5x + 6 = 4.5x - 9
Combining like-terms. Move the terms whose variable x to the left side, and move constants to the right side. Plus sign will become substract sign after being moved.
1.5x + 6 = 4.5x - 9
1.5x - 4.5x = -9 - 6
-3x = -12
Move -3 to the right side to solve for x. Multiplication becomes division after being moved to the other side
-3x = -12
x = -12/-3
x = 4
The value of x is 4
