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erastovalidia [21]
3 years ago
6

a) Let $\mathcal{R}$ be the region consisting of the points $(x,y)$ that satisfy \[-6 \le 3x - 5y \le 6\]and \[-3 \le x + 2y \le

3.\]Plot the region $\mathcal{R},$ and identify the vertices of polygon $\mathcal{R}.$ (b) Find the maximum value of $x + y$ among all points $(x,y)$ in $\mathcal{R}.$

Mathematics
2 answers:
jekas [21]3 years ago
8 0

Answer:

+ 2y \le 3.\]Plot the region $\mathcal{R},$ and identify the vertices of polygon $\mathcal{R}.$ (b) Find the maximum value of $x + y$ among all points $(x,y)$ in $\mathcal

Tems11 [23]3 years ago
6 0

First, we can solve the inequalities as if they were equalities, so we solve the equation 3x - 5y = -6 and x + 2y = 3.  Eliminating y, we get x = 3/11.  Then y = 15/11, so (x,y) = (3/11, 15/11) is one corner of the region R.  The inequalities are symmetric around the origin, so the region R is also symmetric around the region.  So R is the rectangle with vertices (-3/11, 15/11), (3/11, 15/11), (-3/11, 15/11), and (-3/11, -15/11).

The maximum value of x + y is then given by the corners of the rectangle R, so the maximum is 3/11 + 15/11 = 18/11.

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What is the product? startfraction x squared minus 16 over 2 x 8 endfraction times startfraction x cubed minus 2 x squared x ove
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The product of the given expression is \frac{x(x-1)(x-4)}{2(x+4)} OR \frac{x(x^{2} -5x+4)}{2x+8} OR \frac{x^{3} -5x^{2} +4x}{2x+8}

<h3>Simplifying fractions </h3>

From the question, we are to determine the product of the given expressions

The given expressions are

\frac{x^{2} - 16}{2x+8}\times \frac{x^{3}-2x^{2} +x}{x^{2} +3x-4}

\frac{(x+4)(x-4)}{2(x+4)}\times \frac{(x^{2} -x)(x-1)}{(x-1)(x+4)}

\frac{(x-4)}{2}\times \frac{(x^{2} -x)}{(x+4)}
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\frac{x(x-1)(x-4)}{2(x+4)}

OR

\frac{x(x^{2} -5x+4)}{2x+8}

OR
\frac{x^{3} -5x^{2} +4x}{2x+8}

Hence, the product of the given expression is \frac{x(x-1)(x-4)}{2(x+4)} OR \frac{x(x^{2} -5x+4)}{2x+8} OR \frac{x^{3} -5x^{2} +4x}{2x+8}

Learn more on Simplifying fractions here: brainly.com/question/27038950

Here is the complete and correct question:

What is the product? StartFraction x squared minus 16 Over 2 x + 8 EndFraction times StartFraction x cubed minus 2 x squared + x Over x squared + 3 x minus 4 EndFraction

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7 - 12 fry my brain too much to do.

Step-by-step explanation:

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