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3 years ago

Simplify the expression 3x^2y^5•(4xy^2)^3

Mathematics

1 answer:

zhannawk [14.2K]3 years ago

7 0

$3x^2y^5\cdot(4xy^2)^3 = 3x^2y^5\cdot(64x^3y^6) = \boxed{192x^5y^{11}}$

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3 years ago

Each side of a square is increasing at a rate of 6 cm/s. At what rate (in cm2/s) is the area of the square increasing when the a

My name is Ann [436]

36 cm²s⁻¹ is the rate at which the area of the square is increasing.

Given each side of the square is increasing at a rate of 6cm/s

Area, A = s², s is the side length

=> $\frac{dA}{dt} =\frac{dA}{ds}* \frac{ds}{dt} =2s*(\frac{ds}{dt} )$ {chain rule of differentiation}

$\frac{ds}{dt}$ = 6 cm/s

When A = 9 cm² => 9 = s²

=> s = √(9) => s = 3 cm

Hence, $\frac{dA}{dt}$ = 2 × 3 × 6 = 36 cm²s⁻¹

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3 years ago

1. Write an algebraic expression for the word phrase ; the quotient of r and 12.

oksano4ka [1.4K]

r ÷ 12 or r/12

<h3>Further explanation</h3>

Given the word phrase: the quotient of r and 12.

An algebraic expression for it is $\boxed{ \ r \div 12 \ or \ r/12 \ or \ \frac{r}{12} \ }$

<u>Notes:</u>

The quotient is the ratio of two quantities to be divided or the number obtained by division. Synonyms for the quotient are proportion, ratio, or fractions.

An algebraic expression for the quotient of a and b is $\boxed{ \ a \div b \ or \ a/b \ or \ \frac{a}{b} \ }$

'a' is called a dividend
'b' is called a divider
The quotient is the result derived after dividing the dividend by the divisor.

The quotient, a dividend, and a divisor represent the fundamental components of a division equation.

<u>Another example:</u>

A car requires 10 liters of fuel to travel 60 km. Determine the quotient of the distance of the car with fuel (in km/L).

The quotient (or ratio) is

$\boxed{ \ the \ distance \div fuel \ consumption \ }$

$\boxed{ \ 60 \ km \div 10 \ L \ }$

$\boxed{\boxed{ \ 6 \ km/L \ }}$

Consider the same method as follows.

$\boxed{ \ \frac{the \ distance}{fuel \ consumption} \ }$

$\boxed{ \ \frac{60 \ km}{10 \ L} \ }$

$\boxed{\boxed{ \ 6 \ \frac{km}{L} \ }}$

This means that the car can travel a distance of 6 km for every 1 L of fuel.

Kilometers per liter is a unit used to measure fuel economy and we see this as one example of the use of the quotient (or ratio).

<h3>Learn more</h3>

10 times as many as (blank) hundreds or 60 hundreds is (blank) thousands brainly.com/question/47704532
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Keywords: write an algebraic expression, for the word phrase, the quotient of r and 12, a dividend, a divisor, components of a division equation

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