Because 2 and 6 are corresponding
Answer:
![2489ft^{2}](https://tex.z-dn.net/?f=2489ft%5E%7B2%7D)
Step-by-step explanation:
The pool are is divided into 4 separated shapes: 2 circular sections and 2 isosceles triangles. Basically, to calculate the whole area, we need to find the area of each section. Due to its symmetry, both triangles are equal, and both circular sections are also the same, so it would be enough to calculate 1 circular section and 1 triangle, then multiply it by 2.
<h3>Area of each triangle:</h3>
From the figure, we know that <em>b = 20ft </em>and <em>h = 25ft. </em>So, the area would be:
![A_{t}=\frac{b.h}{2}=\frac{(20ft)(25ft)}{2}=250ft^{2}](https://tex.z-dn.net/?f=A_%7Bt%7D%3D%5Cfrac%7Bb.h%7D%7B2%7D%3D%5Cfrac%7B%2820ft%29%2825ft%29%7D%7B2%7D%3D250ft%5E%7B2%7D)
<h3>Area of each circular section:</h3>
From the figure, we know that
and the radius is
. So, the are would be calculated with this formula:
![A_{cs}=\frac{\pi R^{2}\alpha}{360\°}](https://tex.z-dn.net/?f=A_%7Bcs%7D%3D%5Cfrac%7B%5Cpi%20R%5E%7B2%7D%5Calpha%7D%7B360%5C%C2%B0%7D)
Replacing all values:
![A_{cs}=\frac{(3.14)(30ft)^{2}(2.21radians)}{6.28radians}](https://tex.z-dn.net/?f=A_%7Bcs%7D%3D%5Cfrac%7B%283.14%29%2830ft%29%5E%7B2%7D%282.21radians%29%7D%7B6.28radians%7D)
Remember that ![360\°=6.28radians](https://tex.z-dn.net/?f=360%5C%C2%B0%3D6.28radians)
Therefore, ![A_{cs}=994.5ft^{2}](https://tex.z-dn.net/?f=A_%7Bcs%7D%3D994.5ft%5E%7B2%7D)
Now, the total are of the figure is:
![A_{total}=2A_{t}+2A{cs}=2(250ft^{2} )+2(994.5ft^{2})\\A_{total}=500ft^{2} + 1989ft^{2}=2489ft^{2}](https://tex.z-dn.net/?f=A_%7Btotal%7D%3D2A_%7Bt%7D%2B2A%7Bcs%7D%3D2%28250ft%5E%7B2%7D%20%29%2B2%28994.5ft%5E%7B2%7D%29%5C%5CA_%7Btotal%7D%3D500ft%5E%7B2%7D%20%2B%201989ft%5E%7B2%7D%3D2489ft%5E%7B2%7D)
Therefore the area of the symmetrical pool is ![2489ft^{2}](https://tex.z-dn.net/?f=2489ft%5E%7B2%7D)
Rick would lose 1,248 points if he did all of the corrections.
Answer:In 8 years the tree will have the same height.
Step-by-step explanation:
Step 1:
Let x = the number of years when the two trees will be the same height.
For the 2ft tree, you can express its height in x years as:
2+1(x)
And for the 6ft. tree...
6+0.5(x)
Step 2:
2+x = 6+0.5x Subtract 0.5x from both sides.
2+0.5x = 6 Now subtract 2 from both sides.
0.5x = 4 Finally, divide both sides by 0.5
x = 8