MATHEMATICS MIDDLE SCHOOL

A right prism has a base that is an equilateral triangle. The height of the prism is equal to the height of the base. If the volume of the prism is 81, what are the lengths of the sides of the base?

Answers

Answer 1

Answer:

Answer:

Lengths of the sides (there are 3 sides in an equilateral triangle) of the base of prism is5.72cm each.

Step-by-step explanation:

As the base of triangular prism is equilateral:

∴ Area of base = (√ 3 / 4)× (side)²

According to question:

height of prism = height (side) of base

Volume of prism = 81 cm³,

∴ Volume of prism = Area of base x height

⇒ 81 cm³ = (√ 3 / 4)× (side)² × height ∵ side = height

⇒ 81 cm³ = (√ 3 / 4)× (side)³

⇒ 81 × (4/√3) cm³ = side³

⇒ ∛(81 × (4/√3) cm = side

⇒ side = 5.72cm

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Answers

Answer:

$a_n=a_(n-1)+16$

Step-by-step explanation:

The given arithmetic sequence is

14,30,46,62

The first term of this sequence is

$a_1=14$

The common distance is obtained by subtracting a subsequent term from a previous term;

d=30-14

The common difference is

d=16

The recursive formula is given by:

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Step-by-step explanation:

What is the solution to the following equation? 4x^2-48x=-144

Answers

Answer:

x = 6

Step-by-step explanation:

Start off by reducing this equation: divide all three terms by 4. This yields:

x^2 - 12x + 36 = 0

This equation has the form (x - h)^2, the square of a binomial.

x^2 - 12x + 36 = 0, written as the square of the binomail x - 6, comes out to:

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