Each side of the first figure is one unit copy and complete the table then find the function rule for the relationship between t
he figures number and the parameter
1 answer:
Perimeter of a shape is the total length of its border
Figure 1, perimeter = 5 units
Figure 2, perimeter = 7 units
Figure 3, perimeter = 9 units
Figure 4, perimeter = 11 units
Notice that the perimeter is forming an Arithmetic sequence; 5, 7, 9, 11 with a common difference of 2
The general form of an Arithmetic sequence is
Where 'd' is a common difference and 'n' is the number of terms.
We have d = 2, and
zero term = the term before the first term = 3
⇒ This is the rule to find the perimeter of the next figures
Figure 1, perimeter = 5 units
Figure 2, perimeter = 7 units
Figure 3, perimeter = 9 units
Figure 4, perimeter = 11 units
Notice that the perimeter is forming an Arithmetic sequence; 5, 7, 9, 11 with a common difference of 2
The general form of an Arithmetic sequence is
Where 'd' is a common difference and 'n' is the number of terms.
We have d = 2, and
zero term = the term before the first term = 3
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This question is solved applying the formula of the area of the rectangle, and finding it's width. To do this, we solve a quadratic equation, and we get that the cardboard has a width of 1.5 feet.
Area of a rectangle:
The area of rectangle of length l and width w is given by:
w(2w + 3) = 9
From this, we get that:
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
.
This polynomial has roots such that
, given by the following formulas:
In this question:
Thus a quadratic equation with
Then
Width is a positive measure, thus, the width of the cardboard is of 1.5 feet.
Another similar problem can be found at brainly.com/question/16995958