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poizon [28]
2 years ago
9

How do you multiply monomials with the same base?​

Mathematics
1 answer:
IrinaK [193]2 years ago
3 0

9514 1404 393

Answer:

  multiply their coefficients, use the base with the sum of exponents

Step-by-step explanation:

The coefficients multiply. The base gets an exponent that is the sum of the exponents of the factors.

  (a·x^b)(c·x^d) = ac·x^(b+d)

_____

If you remember that an exponent is simply an indicator of the number of times the base is a factor, this should be fairly clear. The usual associative and commutative properties of multiplication apply.

<u>Example</u>

  5x^2 · 7x^3= 5·x·x·7·x·x·x

  = 5·7·x·x·x·x·x

  = (5·7)(x^(2+3))

  = 35x^5

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Three balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom, and sides of the cylin
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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
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V₁ = <span>π r² h
</span><span>V₁ = </span>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 × <span>V₂ 
</span>Vₐ = 3 × <span>\frac{4}{3} π r³
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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%
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HELP DUE TODAY
Fudgin [204]
I think it is D
Hope my answer help you?
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