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3 years ago

Write the equation of a line that is perpendicular to x = -1 and that passes through the Point (8, -4).

Mathematics

1 answer:

pychu [463]3 years ago

7 0

Answer:

y = - 4

Step-by-step explanation:

x = - 1 is the equation of a vertical line parallel to the y- axis

The equation of a line perpendicular to it will therefore be a horizontal line parallel to the x- axis with equation

y = c

where c is the value of the y- coordinates the line passes through.

The line passes through (8, - 4 ) with y- coordinate - 4 , then

y = - 4 ← equation of perpendicular line

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3 years ago

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]

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

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