QuestionFind the value of $\frac{{[G(-1)]^{3} - [G(2)]^{2} + 4 \cdot G(-1)}}{10}$ given $G(-1) = 20$ and $G(2) = -10$ .

Studdy Solution

STEP 1

Assumptions1. The function $G(x)$ is given for two points $G(-1) =20$ and $G() = -10$ . . We need to substitute these values into the given expression and simplify.

STEP 2

First, let's substitute the given values of $G(-1)$ and $G(2)$ into the expression. $\frac{{[G(-1)]^{} - [G(2)]^{2} +4 \cdot G(-1)}}{10} = \frac{{[20]^{} - [-10]^{2} +4 \cdot20}}{10}$

STEP 3

Now, simplify the numerator of the fraction. $20^{3} =8000$ $-10^{2} =100$ $\cdot20 =80$
So, the expression becomes $\frac{{8000 -100 +80}}{10}$

STEP 4

Next, we simplify the numerator by performing the subtraction and addition operations.
$8000 -100 +80 =7980$
So, the expression becomes $\frac{7980}{10}$

STEP 5

Finally, we divide the numerator by the denominator to find the value of the expression.
$\frac{7980}{10} =798$
So, the value of the given expression is798.

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