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3 years ago

Select the correct answer. Which expression is equivalent to this polynomial? 9x^2 - 4

Mathematics

1 answer:

liberstina [14]3 years ago

3 0

Step-by-step explanation:

Given expression is :

$9x^2-4$

We can write it as :

$(3x)^2-2^2$

Now using identity : $a^2-b^2=(a-b)(a+b)$

Here, a = 3x and b = 2

So,

$(3x)^2-2^2=(3x-2)(3x+2)$

Hence, the given expression is equivalent to (3x - 2)(3x + 2) .

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Answer:

The total resistance of these three resistors connected in parallel is $1.7143\Omega$

Step-by-step explanation:

The attached image has the circuit for finding the total resistance. The circuit is composed by a voltage source and three resistors connected in parallel: $R_1=6\Omega$ , $R_2=3\Omega$ and $R_3=12\Omega$ .

<u>First step: to find the source current</u>

The current that the source provides is the sum of the current that each resistor consumes. Keep in mind that the voltage is the same for the three resistors ( $R_1$ , $R_2$ and $R_3$ ).

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The total current is:

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Now, replace $I_S$ by the previous expression and the total resistance would be:

$R_T=\frac{V_S}{V_S\cdot \frac{R_2\cdot R_3+R_1\cdot R_3+R_1\cdot R_2}{R_1\cdot R_2\cdot R_3}}$

Simplify the expression and you must get:

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The last step is to replace the values of the resistors:

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Thus, the total resistance of these three resistors connected in parallel is $1.7143\Omega$

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