QuestionFind $A$ in the equation: $A=\frac{4(3)^{4}-3(3)^{3}-1(3)^{2}-10(3)-4}{(3^{2}+1)^{2}}$ .

Studdy Solution

STEP 1

Assumptions1. The equation is given as $A=\frac{4(3)^{4}-3(3)^{3}-1(3)^{}-10(3)-4}{\left(3^{}+1\right)^{}}$ . We need to solve this equation to find the value of $A$ .

STEP 2

First, let's simplify the numerator of the fraction. We can do this by calculating the value of each term and then subtracting or adding them as indicated.
$umerator =4()^{4}-()^{}-1()^{2}-10()-4$

STEP 3

Now, calculate the value of each term in the numerator.
$umerator =(81)-3(27)-1(9)-10(3)-$

STEP 4

Now, perform the operations in the numerator.
$umerator =324 -81 -9 -30 -4$

STEP 5

Calculate the value of the numerator.
$umerator =324 -81 -9 -30 -4 =200$

STEP 6

Next, let's simplify the denominator of the fraction. We can do this by calculating the value of the term and then squaring it.
$Denominator = \left(3^{2}+1\right)^{2}$

STEP 7

Now, calculate the value of the term in the denominator.
$Denominator = \left(9+1\right)^{2}$

STEP 8

Now, perform the operation in the denominator.
$Denominator =10^{2}$

STEP 9

Calculate the value of the denominator.
$Denominator =^{2} =100$

STEP 10

Now that we have the values of the numerator and the denominator, we can substitute these values back into the equation to find the value of $A$ .
$A=\frac{umerator}{Denominator}$

STEP 11

Plug in the values for the numerator and the denominator to calculate the value of $A$ .
$A=\frac{200}{100}$

STEP 12

Calculate the value of $A$ .
$A=\frac{200}{100} =2$ So, the value of $A$ is2.

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