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
Answer:
JM
Step-by-step explanation:
A tangent line is a line that only intersects a circle at one point.
LG and CJ are not lines, and GH intersects the circle twice (at point G and point H), so JM is the tangent line.
1/7+2x/3=(15x-3)/21 make all terms have a common denominator of 21
3+14x=15x-3 subtract 3 from both sides
14x=15x-6 subtract 15x from both sides
-x=-6 divide both sides by -1
x=6
*Notice the use of parentheses in this format to make it clear what the numerators and denominators are...
Answer:
Step-by-step explanation:
(X,Y)=(-55/2,-38