a.Write an equation for the area of the "dented square" if xx represents the length of the large square and yy represents the area of the square.

banganX 2021-08-09 Answered
Sheila is in Ms. Cai's class . She noticed that the graph of the perimeter for the "dented square" in problem 3-61 was a line . "I wonder what the graph of its area looks like ," she said to her teammates .
a. Write an equation for the area of the "dented square" if xx represents the length of the large square and yy represents the area of the square.
b. On graph paper , graph the rule you found for the area in part (a). Why does a 1st−quadrant graph make sense for this situation? Are there other values of xx that cannot work in this situation? Be sure to include an indication of this on your graph, as necessary.
c. Explain to Sheila what the graph of the area looks like.
d. Use the graph to approximate xx when the area of the shape is 20 square units.

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Expert Answer

Sally Cresswell
Answered 2021-08-10 Author has 3852 answers
(a) The are of the "dented square ” \(\displaystyle{y}={x}^{{{2}}}\) — 1 square units
(b) Graph the rule for the area using the table values
(c) The graph of the aren is a curve
(d) When the area of the shape is 20 square units so, \(\displaystyle{x}\approx{4.5}\)
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Sheila is in Ms. Cai's class . She noticed that the graph of the perimeter for the "dented square" in problem 3-61 was a line . "I wonder what the graph of its area looks like ," she said to her teammates .
a. Write an equation for the area of the "dented square" if xx represents the length of the large square and yy represents the area of the square.
b. On graph paper , graph the rule you found for the area in part (a). Why does a 1st−quadrant graph make sense for this situation? Are there other values of xx that cannot work in this situation? Be sure to include an indication of this on your graph, as necessary.
c. Explain to Sheila what the graph of the area looks like.
d. Use the graph to approximate xx when the area of the shape is 20 square units.
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