What is the product?
1 answer:
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<span><span>The correct answers are:
</span><span>(1) The vertical asymptote is x = 0
(2) The horizontal asymptote is y = 0
</span><span>Explanation:
</span><span>(1) To find the vertical asymptote, put the denominator of the rational function equals to zero.
Rational Function = g(x) = </span></span>
<span>
Denominator = x = 0
Hence the vertical asymptote is x = 0.
(2) To find the horizontal asymptote, check the power of x in numerator against the power of x in denominator as follows:
Given function = g(x) = </span><span>
We can write it as:
g(x) = </span>
<span>
If power of x in numerator is less than the power of x in denomenator, then the horizontal asymptote will be y=0.
If power of x in numerator is equal to the power of x in denomenator, then the horizontal asymptote will be y=(co-efficient in numerator)/(co-efficient in denomenator).
If power of x in numerator is greater than the power of x in denomenator, then there will be no horizontal asymptote.
In above case, 0 < 1, therefore, the horizontal asymptote is y = 0
</span>
</span><span>(1) The vertical asymptote is x = 0
(2) The horizontal asymptote is y = 0
</span><span>Explanation:
</span><span>(1) To find the vertical asymptote, put the denominator of the rational function equals to zero.
Rational Function = g(x) = </span></span>
Denominator = x = 0
Hence the vertical asymptote is x = 0.
(2) To find the horizontal asymptote, check the power of x in numerator against the power of x in denominator as follows:
Given function = g(x) = </span>
We can write it as:
g(x) = </span>
If power of x in numerator is less than the power of x in denomenator, then the horizontal asymptote will be y=0.
If power of x in numerator is equal to the power of x in denomenator, then the horizontal asymptote will be y=(co-efficient in numerator)/(co-efficient in denomenator).
If power of x in numerator is greater than the power of x in denomenator, then there will be no horizontal asymptote.
In above case, 0 < 1, therefore, the horizontal asymptote is y = 0
</span>
The sum of the lengths of three sides of the rectangle, gives the length
of the fencing, while one third of the rectangle area is for the pavement.
Responses:
Project A: The formula for the length of the fencing is, L = 4·x - 1
Project B: Length of the fancy wall = 2·x + 1
<h3>Which method can be used to find the length and area of paving from the given equations?</h3>
Project A: Let QP and SR represent the longest sides of the rectangle, we have;
PQ = SR = 2·x + 1
Given parameters are;
Length of the rectangular plot = 2·x + 1
Width of the rectangular plot = x - 1
Vertices of the rectangular plot are; QPSR
Project A: Let QP and SR represent the longest sides of the rectangle, we have;
PQ = SR = 2·x + 1
Which gives;
SP = QR = x - 1
The length of the fencing, L = SP + PQ + QR = x - 1 + 2·x + 1 + x - 1 = 4·x - 1
- The formula for the length of the fencing is, L =<u> 4·x - 1</u>
Project B: The front side is SR
Therefore;
- Length of the fancy wall = <u>2·x + 1</u>
Project C:
Area, A = Length × Width
Area of the plot, A = (2·x + 1) × (x - 1) = 2·x² - x - 1
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