Answer:
To check if a given value is a solution to an equation:
Evaluate the left-hand side expression at the given value to get a number.
Evaluate the right-hand side expression at the given value to get a number.
See if the numbers match.
Step-by-step explanation:
radius of sphere, rs
radius of cylinder, rc
height of cylinder, h
given: h = rs = rc =r..eq1
volume of cylinder, vc = 27pi ft...eq2
volume of cylinder, vc = pi × rc^2 × h...eq3
volume of sphere, vs = 4/3(pi×rs^3)...eq4
subst for h & rs from eqn 1 in eqn 3...
vc = pi x r^2 x r= pi x r^3...eqn 5
subst for vc from eqn 2 in eqn 5...
=> 27 pi ft = pi x r^3
=> 27 = r^3
=> r = 3ft...eqn 6
subst for rs from eqn 1 in eqn 4
vs = 4/3 (pi x r^3)...eqn7
subst for pi x r^3 from eqn 5 in eqn 7
vs = 4/3 vc = 4/3 (27pi ft) = 36 pi ft
29). The 'six' is the same as (6 x 5) = 30 fifths.
So six and three fifths = (30 + 3) fifths = thirty-three fifths.
30). The 'eight' is the same as (8 x 6) = 48 sixths.
So eight and five sixths = (48 + 5) fifths= fifty-three sixths.
31). Twenty-seven of the thirds are the same as (27/9) = 3 .
That leaves a remainder of 2 thirds.
So twenty-nine thirds are the same as 3 and 2/3 .
32). Thirty-two of the fourths are the same as (32/4) = 8 .
That leaves a remainder of one fourth.
So thirty-three fourths are the same as 4 and 1/4 .
In this case if x<100 George will be losing money. So he will only earn a profit when he sells more than 100 DVDs. Essentially (x-100) represents his break-even point.
Y = -2x + 4
substitute the value of x = 1 to the equation:
y = -2 · 1 + 4 = -2 + 4 = 2
Answer: a. 2
