Answer:
first four terms are 2, 7, 12, 17
Step-by-step explanation:
use this formula: =
+ (n - 1)· d
where 'n' equals the position in the sequence the term is in and 'd' is the common difference
if = 2 and d = 5 are given, plug those into formula
= 2
= 2 + (2 - 1)·5 = 2+5 = 7
= 2 + (3 - 1)·5 = 2+2(5) = 12
= 2+(4 - 1)·5 = 2+3(5) = 17
Answer:
width = 72 yards
length = 108 yards
Step-by-step explanation:
Given:
<u>Area of the field</u> with the given values:
To maintain the <u>same perimeter</u>, but <u>change the area</u>, either:
In geometry, length pertains to the <u>longest side</u> of the rectangle while width is the <u>shorter side</u>. Therefore, we should choose:
<u>Define the variables</u>:
Therefore:
Solve the inequality:
Therefore, as distance is positive only and the maximum width is 75 yd (since we are subtracting from the original width):
Therefore, to find the width and length of another rectangular field that has the same perimeter but a smaller area than the first field, simply substitute a value of x from the restricted interval into the found expressions for width and length:
<u>Example 1</u>:
⇒ Width = 75 - 3 = 72 yd
⇒ Length = 105 + 3 = 108 yd
⇒ Perimeter = 2(72 + 108) = 360 yd
⇒ Area = 72 × 108 = 7776 yd²
<u>Example 2</u>:
⇒ Width = 75 - 74 = 1 yd
⇒ Length = 105 + 74 = 179 yd
⇒ Perimeter = 2(1 + 179) = 360 yd
⇒ Area = 1 × 179 = 179 yd²