As stated the area of the circle is 85π ft2. The area of the sector BAC is a portion of this full circle area. the sector is made of 2 radii and arc that has rotated by 36°.
the magnitude of the central angle in the circle is 360°
Area for 360° central angle - 85π ft2
then the area for 1° = 85π ft2/360°
the area of 36° sector = 85π ft2/360° x 36°
= 8.5π ft2
Answer:
Length = 5p + 3
Perimeter = 26p + 6
Step-by-step explanation:
Given
Area = 40p² + 24p
Width = 8p
Solving for the length of deck
Given that the deck is rectangular in shape.
The area will be calculated as thus;
Area = Length * Width
Substitute 40p² + 24p and 8p for Area and Width respectively
The formula becomes
40p² + 24p = Length * 8p
Factorize both sides
p(40p + 24) = Length * 8 * p
Divide both sides by P
40p + 24 = Length * 8
Factorize both sides, again
8(5p + 3) = Length * 8
Multiply both sides by ⅛
⅛ * 8(5p + 3) = Length * 8 * ⅛
5p + 3 = Length
Length = 5p + 3
Solving for the perimeter of the deck
The perimeter of the deck is calculated as thus
Perimeter = 2(Length + Width)
Substitute 5p + 3 and 8p for Length and Width, respectively.
Perimeter = 2(5p + 3 + 8p)
Perimeter = 2(5p + 8p + 3)
Perimeter = 2(13p + 3)
Open bracket
Perimeter = 2 * 13p + 2 * 3
Perimeter = 26p + 6
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The prediction is 193.86 lb.
Substituting 73 for x, we have:
-102.3923 + 4.0582*73 = 193.86