A line passes through the points (p, a) and (p, –a) where p and a are real numbers. If p=0, what is the y-intercept? Explain your reasoning.

p - as "x" never changes with the value of "y", so no matter what y is, x is always "p", so when y is 0, x = p 

slope of the line 
change in y over the change in x 
(-a - a) / (p - p) = infinity - or a vertical line 
equation of the line 
y = p 
slope of a line perpendicular to the given line 
inverse of the orig slope or (p - p)/(-a - a) = 0

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3 years ago

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A rectangular plot of land is to be enclosed by a fence. One side is along a river, and does not need to be enclosed. If the tot

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Answer:

Width 150 meters.

Length = 350 meters.

Step-by-step explanation:

Let us assume the width of the fence = k meters

So, both sides = k + k = 2k meters

Also, the TOTAL fencing length = 600 m

So, the one side length of the fence = (600 - 2 k) meters

AREA = LENGTH x WIDTH

⇒ A(k) = (600 - 2k) (k)

or, A = -2k² + 600 k

The above equation is of the form: ax² +bx + C

Here: a = - 2 , b = 600 and C = 0

As a< 0, the parabola opens DOWNWARDS.

Here, x value is given as: $x = \frac{-b}{2a}$

Solving for the value of k similarly, we get:

$k = \frac{-b}{2a} = \frac{600}{2(-2)} = 150$

Thus the desired width = k = 150 meters

So, the desired dimensions of the plot is width 150 meters.

And length = 650 - 2k = 650 - 300 = 350 meters.

5 0

3 years ago