Answer:
523 cm^3
Step-by-step explanation:
The volume of a sphere is
V = 4/3 pi r^3
V = 4/3 (3.14) (5)^3
V = 523.33333
Rounding to the nearest whole number
V = 523
to do it in mental math: you can ignore the zeroes in 400 for now.
4*14 = 4*10 + 4*4 = 40 + 16 = 56
now add the zeroes back on: 5600m
Answer:
59.03° is greater than 56.31°' This means that the sliding pole that rises 5 feet for every 3 feet of run making an angle of inclination of 59.03° is steeper than the angle of inclination made by a sliding pole that rises 3 feet for every 2 feet run.
Step-by-step explanation:
Step 1
Express the angle of inclination as follows;
Tan∅=H/R
where;
∅=angle of inclination
H=vertical rise
R=distance of run
Step 2
Determine the angle inclination when;
H=3 feet
R=2 feet
replacing;
Tan∅=(3/2)=1.5
∅=Tan^(-1)(1.5)
∅=56.31°
Determine the angle inclination when;
H=5 feet
R=3 feet
replacing;
Tan∅=(5/3)=1.67
∅=Tan^(-1)(1.67)
∅=59.03°
59.03° is greater than 56.31°' This means that the sliding pole that rises 5 feet for every 3 feet of run making an angle of inclination of 59.03° is steeper than the angle of inclination made by a sliding pole that rises 3 feet for every 2 feet run.
Let the number of men and women in the room be represented by an arbitrary constant, x and y respectively.
x + y = 96
y = 96 - x
When one man leaves, we get: x - 1
When one woman replaces the man, we get: y + 1
So, y + 1 = 3(x - 1)
Substituting y = 96 - x, we get:
96 - x + 1 = 3x - 3
97 + 3 = 4x
100 = 4x
x = 25
Thus, there were 25 men and 41 women in the room originally.
Y = 2x - 3
y = -x+ 9
2x-3 = -x+9
2x+x = 9+2
3x = 12
x = 12/3
x = 4
y = 2(4)-3
y = 8-3 = 5
Mark on (4,5) & draw the line from origin.
Hope this helps!