Answer:
A. 346.19 square feet.
Step-by-step explanation:
We have been given that a contractor has been hired to install flooring for a bandstand in the shape of a circle that is 21 feet across.
To find the square feet of flooring required, we will find area of circle.
Since the length across the circle is 21 feet, so radius of circle will be half of 21 feet.
![\text{Radius}=\frac{\text{21 feet}}{2}](https://tex.z-dn.net/?f=%5Ctext%7BRadius%7D%3D%5Cfrac%7B%5Ctext%7B21%20feet%7D%7D%7B2%7D)
![\text{Radius}=\text{10.5 feet}](https://tex.z-dn.net/?f=%5Ctext%7BRadius%7D%3D%5Ctext%7B10.5%20feet%7D)
![\text{Area of circle}=\pi r^2](https://tex.z-dn.net/?f=%5Ctext%7BArea%20of%20circle%7D%3D%5Cpi%20r%5E2)
![\text{Area of circle}=\pi (\text{10.5 feet})^2](https://tex.z-dn.net/?f=%5Ctext%7BArea%20of%20circle%7D%3D%5Cpi%20%28%5Ctext%7B10.5%20feet%7D%29%5E2)
![\text{Area of circle}=3.14*110.25\text{ feet}^2](https://tex.z-dn.net/?f=%5Ctext%7BArea%20of%20circle%7D%3D3.14%2A110.25%5Ctext%7B%20feet%7D%5E2)
![\text{Area of circle}=346.185\text{ feet}^2](https://tex.z-dn.net/?f=%5Ctext%7BArea%20of%20circle%7D%3D346.185%5Ctext%7B%20feet%7D%5E2)
![\text{Area of circle}\approx 346.19\text{ feet}^2](https://tex.z-dn.net/?f=%5Ctext%7BArea%20of%20circle%7D%5Capprox%20346.19%5Ctext%7B%20feet%7D%5E2)
Therefore, 346.19 square feet of flooring will be required.
Answer:
(a) The maximum height of the ball is 16 feet at 1 seconds.
(b) The ball hits the ground at 2 seconds.
PART (A) :
Given function: h(t) = -16t² + 32t
Comparing to quadratic function: ax² + bx + c
In this function: a = -16, b = 32, c = 0
<u>To find the maximum height</u>, use the vertex formula:
![\sf x = \dfrac{-b}{2a}](https://tex.z-dn.net/?f=%5Csf%20x%20%3D%20%5Cdfrac%7B-b%7D%7B2a%7D)
<u>Insert values</u>
![\rightarrow \sf t = \dfrac{-32}{2(-16)} = 1](https://tex.z-dn.net/?f=%5Crightarrow%20%5Csf%20t%20%3D%20%5Cdfrac%7B-32%7D%7B2%28-16%29%7D%20%3D%201)
Then find h(t) = -16(1)² + 32(1) = 16 feet
Conclusion: The maximum height of the ball is 16 feet at 1 seconds.
PART (B) :
When the ball hits the ground, the height [h(t)] will be 0 ft
-16t² + 32t = 0
-16t(t - 2) = 0
-16t = 0, t - 2 = 0
t = 0, t = 2
The ball hits the ground at 2 seconds. Note: the other 0 seconds is for when the ball was launched at the beginning.
The two different ways of finding the area are,
Case 1 = assume horizontal rectangles,
Case 2 = assume vertical rectangles.
<h3>What is a rectangle?</h3>
the rectangle is a four-sided polygon whose opposites sides are equal and has an angle of 90° between its sides.
Here,
case 1,
As shown in the image
Area = sum of horizontal rectangles
Area = 10 * 3 + 2 * 5 + 2 * 1
Area = 30 + 10 + 2
Area = 42
Case II,
As shown in right figure,
Area of the vertical rectangles
Area = 3 * 5 + 5 * 3 + 2 * 6
Area = 15 + 15 + 12
Area = 42
Here, the area in case 1 is equal to case 2.
Thus, the two different ways of finding the area have shown above.
Learn more about rectangles here:
brainly.com/question/16021628
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50 is 40% of 125
You solve this by
X is the number that 50 is 40% of.
40/100 times x = 125
x = 50 times 100 divided by 40 = 125
40/100x125=50
Brainliest plz