Answer:
6.51 cm
Step-by-step explanation:
Since the sphere causes the water level in the cylindrical container to rise and thus increase by its own volume, the volume of the sphere is V = 4πr³/3 where r = radius of sphere. The volume rise of the container is thus V' = πR²h where R = radius of base of cylinder = 7 cm and h = height of water level = 7.5 cm.
Since V = V',
4πr³/3 = πR²h
dividing through by π, we have
4r³/3 = R²h
multiplying both sides by 3/4, we have
r³ = 3R²h/4
taking cube-root of both sides, we have
r = ∛(3R²h/4)
Substituting the values of the variables into the equation, we have
r = ∛(3(7 cm)² × 7.5 cm/4)
r = ∛(3 × 49 cm² × 7.5 cm/4)
r = ∛(1102.5cm³/4)
r = ∛(275.625 cm³)
r = 6.508 cm
r ≅ 6.51 cm to 2 decimal places
900 is the answer of 2 squared times 15 squared
3x+4=10
Subtract 4 from both sides
3x=6
Divide both sides by 3
X=2
Sides = 10,10,5
Problem 5. 4x+1=29
Subtract 1 from both sides
4x=28
X=7
Answer:
Infinite number of solutions
Step-by-step explanation:
Since the equations are both the same, we have an infinite number of solutions! The solutions lie on the graph y = -2x+5.
