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Rus_ich [418]
3 years ago
10

Using long division to find the quotient, what changes do you first

Mathematics
1 answer:
lora16 [44]3 years ago
8 0

Answer:

\frac{125x^3 - 8}{5x - 2} = 25x^2 + 10x +4

Step-by-step explanation:

Given

Dividend = 125x^3 - 8

Divisor = 5x - 2

Required

Determine the quotient

See attachment for complete process.

First, divide 125x^3 by 5x

\frac{125x^3}{5x} =25x^2

Write 25x^2 at the top

Multiply 5x - 2 by 25x^2

= 125x^3 - 50x^2

Subtract from 125x^3 - 8

i.e.

125x^3 - 8 - (125x^3 - 50x^2) = 50x^2 - 8

Step 2:

Divide 50x^2 by 5x

\frac{50x^2}{5x} = 10x

Write 10x at the top

Multiply 5x - 2 by 10x

= 50x^2 - 20x

Subtract from 50x^2 - 8

i.e.

50x^2 - 8 - (50x^2 - 20x) = 20x - 8

Step 3:

Divide 20x by 5x

\frac{20x}{5x} = 4

Write 4 at the top

Multiply 5x - 2 by 4

= 20x - 8

Subtract from 20x - 8

i.e.

20x - 8 - (20x - 8) = 0

Hence:

\frac{125x^3 - 8}{5x - 2} = 25x^2 + 10x +4

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\displaystyle  \\ 
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<><><><><>

Answer: \boxed{\bold{-8}}

<><><><><>

Explanation: \downarrow\downarrow\downarrow

<><><><><>

[ Step One ] Follow PEMDAS Order Of Operations; Calculate Within Parenthesis

Note: \bold{PEMDAS: \ Parenthesis, \ Exponents, \ Multiply, \ Divide, \ Add, \ Subtract}

\bold{-6+8: \ 2}

[ Step Two ] Rewrite Equation

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[ Step Eight ] Rewrite Equation

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<><><><><><><>

\bold{\rightarrow Mordancy \leftarrow}

8 0
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The base diameter and the height of a cone are both<br> equal to x units.
Vera_Pavlovna [14]

Answer:

π x³ /12 is the volume of the cone if  A cone has a height of x and a diameter of x

Step-by-step explanation:

The base diameter and the height of a cone are both equal to x units

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=> Volume of cone =  (1/3)π (x/2)² * x

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