Commutaive property says
ab=ba or expanded to say
abc=cba

associative peropty =
a(bc)=(ab)c

so using that
first mix them up knowing that we can move the parenthaseese
all possible equivelnt ones are
4*(5*3)
(3*5)*4
3*(5*4)
(3*4)*5
3*(4*5)

4 0

2 years ago

Three balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom, and sides of the cylin

lianna [129]

We know the following:
Cylinder volume: V₁ = π r² h
Ball (sphere) volume:V₂ = $\frac{4}{3}$ π r³
where:
V - volume
r - radius of base of cylinder and diameter of ball
h - height of cylinder.

R = 13 cm ⇒ r = 13 ÷ 2 = 6.5
π = 3.14

a) Since balls touch all sides of cylinder (as shown in image), it can be concluded that height of cylinder is equal to sum of diameters of 3 balls and that radius of base of cylinder is equal to radius of ball:
h = 3 × r = 3 × 13 cm = 39 cm
r = 6.5 cm
So,
V₁ = π r² h
V₁ = 3.14 × (6.5 cm)² × 39 cm
V₁ = 5,173.9 cm³

b. The total volume of three balls is the sum of volumes of each ball:
Vₐ = 3 × V₂
Vₐ = 3 × $\frac{4}{3}$ π r³
Vₐ = 3 × $\frac{4}{3}$ 3.14 (6.5 cm)³
Vₐ = 3,449.3 cm³

c. Percentage of the volume of the container occupied by three balls ould be expressed as ratio of volume of three balls and volume of cylinder:
V = $\frac{ V_{1}}{ V_{a} }$ ×100
V = $\frac{3,449.3}{5,173.9}$ ×100
V = 0.6666 ×100
V = 66.66%

4 0

2 years ago

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Is y= x + 2 and y= -x + 3 perpendicular lines?

Vlad [161]

I believe y=x+2 and y=-x+3 are perpendicular lines.

8 0

3 years ago

Read 2 more answers