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3 years ago

Let x be a real number. Find the lowest possible value of |5x^2 - 16| + |10x - 2|.

1 answer:

4 0

Since the equations are for absolute value this means any negative number used the answer would become positive, so to get the lowest value possible x would need to equal 0, which would eliminate the x variable from the equations.

Replace x with 0 and solve:

|5(0)^2 - 16| + |10(0) - 2|

Simplify:

|0 - 16| + |0 - 2|

|-16| + |-2|

Combine:

|-18|

Absolute Value = 18

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You have D dollars to buy fence to enclose a rectangular plot of land (see figure at right). The fence for the top and bottom co

alex41 [277]

The perimeter of the rectangular plot of land is given by the expression below

$P=2x+2y$

On the other hand, since the available money to buy fence is D dollars,

$\begin{gathered} D=4(2x)+3(2y) \\ \Rightarrow D=8x+6y \\ D\rightarrow\text{ constant} \end{gathered}$

Furthermore, the area of the enclosed land is given by

$A=xy$

Solving the second equation for x,

$\begin{gathered} D=8x+6y \\ \Rightarrow x=\frac{D-6y}{8} \end{gathered}$

Substituting into the equation for the area,

$\begin{gathered} A=(\frac{D-6y}{8})y \\ \Rightarrow A=\frac{D}{8}y-\frac{3}{4}y^2 \end{gathered}$

To find the maximum possible area, solve A'(y)=0, as shown below

$\begin{gathered} A^{\prime}(y)=0 \\ \Rightarrow\frac{D}{8}-\frac{3}{2}y=0 \\ \Rightarrow\frac{3}{2}y=\frac{D}{8} \\ \Rightarrow y=\frac{D}{12} \end{gathered}$

Therefore, the corresponding value of x is

$\begin{gathered} y=\frac{D}{12} \\ \Rightarrow x=\frac{D-6(\frac{D}{12})}{8}=\frac{D-\frac{D}{2}}{8}=\frac{D}{16} \end{gathered}$ <h2>Thus, the dimensions of the fence that maximize the area are x=D/16 and y=D/12.</h2><h2>As for the used money,</h2> $\begin{gathered} top,bottom:\frac{8D}{16}=\frac{D}{2} \\ Sides:\frac{6D}{12}=\frac{D}{2} \end{gathered}$ <h2>Half the money was used for the top and the bottom, while the other half was used for the sides.</h2>

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1 year ago

What is the difference between constructing and drawing geometric figures? Give a real-world example of each.

Furkat [3]

<span>The difference between constructing and drawing geometric figures:
</span>Drawing Geometric Figures refers to drafting, in which you are trying to create or sketch geometric figures using ruler, paper, etc.
While constructing geometric figure refers to constructing or building a geometric figure with the use of compass, graph paper, etc.

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4 years ago

What does the slope of the function represent in this situation?

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Slope of a function is defined as the rate of change of a function. It determine the unit price of values or amount traveled in unit time.

<h3>Slope of a function</h3>

Slope of a function is defined as the rate of change of a function. It determine the unit price of values or amount traveled in unit time.

The formula for expressing the slope of a function is given as;

f'(x) = f(b)-f(a)/b-a

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The slope can also be expressed as a function of its coordinate (x, y)

Slope = y2-y1/x2-x1

Learn more on slope here: brainly.com/question/1884491

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Step-by-step explanation:

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