Answer:
A = 82.53 in²
Step-by-step explanation:
We use the circumference equation C = 2πr and the area equation A = πr².
Using the first equation and the given circumference (32 in), we find the radius of the circle, and then use this result to find the area of the circle.
C 32 in
C = 2πr becomes r = ----------- and here r = ---------- = 5.10 in
2π 6.28
Then the area of the circle is A = πr², which here is A = 3.14(5.10 in)², which, when rounded off to two decimal places, is A = 82.53 in²
He could have scored 7, 14, 21, 28, 35, or 42 points (all multiples of 7 less than 45).
answer: B
Step-by-step explanation:
Given that,
The length of the shelf = 24 inches
The width of the shelf = 7 inches
Area of the shelf, A = 24 × 7
= 168 inch²
When the width of the shelf is doubles,
New width = 14 inch
New area, A' = 14×24
= 336 inch²
It means,
A' = 2(A)
So, the new area becomes 336 inch² i.e. twice the initial area.
(8/9)^2 is just 8/9 squared, or 8/9 * 8/9. This is 64/81, and cannot be reduced. This is therefore our answer.
The two enclosures will need three equal fences coming out from the wall and meeting another fence running parallel to the wall. If the fences coming out from the wall are x metres long the parallel fence will be (132 - 3x) metres long.
The area A = x(132 - 3x) = 132x - 3x^2
The derivative of A = zero when 132 - 6x = 0 which means the maximum area is when x = 22m
The maximum area = 22 x (132 - 3 x 22) = 1452 m^2
If you don’t know how to find derivatives then you could sketch the graph of y = x(132 - 3x).
This is an inverted parabola (hill) with x intercepts at 0 and 132/3 = 44.
The maximum point (top of the hill) is halfway between 0 and 44 I.e. 22m
Try any other value for x and the area will be smaller.
