Answer:
Step-by-step explanation:
<u>Sum of interior angles of a polygon:</u>
- (n - 2)180 = 160n
- 180n - 360 = 160n
- 20n = 360
- n = 18
Answer is A
Step-by-step explanation:
hope that helps
Answer:
<h2>a) 0.5367feet</h2><h2>b) 0.5223feet</h2><h2>c) 0.7292feet</h2>
Step-by-step explanation:
Given the rate at which an eucalyptus tree will grow modelled by the equation 0.5+6/(t+4)³ feet per year, where t is the time (in years).
The amount of growth can be gotten by integrating the given rate equation as shown;

a) The number of feet that the tree will grow in the second year can be gotten by taking the limit of the integral from t =1 to t = 2
![\int\limits^2_1 {0.5 + \frac{6}{(t+4)^{3} } } \, dt = [0.5t-3(t+4)^{-2}]^2_1\\= [0.5(2)-3(2+4)^{-2}] - [0.5(1)-3(1+4)^{-2}]\\= [1-3(6)^{-2}] - [0.5-3(5)^{-2}]\\ = [1-\frac{1}{12}] - [0.5-\frac{3}{25} ]\\= \frac{11}{12}-\frac{1}{2}+\frac{3}{25}\\ = 0.9167 - 0.5 + 0.12\\= 0.5367feet](https://tex.z-dn.net/?f=%5Cint%5Climits%5E2_1%20%7B0.5%20%2B%20%5Cfrac%7B6%7D%7B%28t%2B4%29%5E%7B3%7D%20%7D%20%20%7D%20%5C%2C%20dt%20%3D%20%5B0.5t-3%28t%2B4%29%5E%7B-2%7D%5D%5E2_1%5C%5C%3D%20%5B0.5%282%29-3%282%2B4%29%5E%7B-2%7D%5D%20-%20%5B0.5%281%29-3%281%2B4%29%5E%7B-2%7D%5D%5C%5C%3D%20%5B1-3%286%29%5E%7B-2%7D%5D%20-%20%5B0.5-3%285%29%5E%7B-2%7D%5D%5C%5C%20%3D%20%5B1-%5Cfrac%7B1%7D%7B12%7D%5D%20-%20%5B0.5-%5Cfrac%7B3%7D%7B25%7D%20%5D%5C%5C%3D%20%5Cfrac%7B11%7D%7B12%7D-%5Cfrac%7B1%7D%7B2%7D%2B%5Cfrac%7B3%7D%7B25%7D%5C%5C%20%20%20%3D%200.9167%20-%200.5%20%2B%200.12%5C%5C%3D%200.5367feet)
b) The number of feet that the tree will grow in the third year can be gotten by taking the limit of the integral from t =2 to t = 3
![\int\limits^3_2 {0.5 + \frac{6}{(t+4)^{3} } } \, dt = [0.5t-3(t+4)^{-2}]^3_2\\= [0.5(3)-3(3+4)^{-2}] - [0.5(2)-3(2+4)^{-2}]\\= [1.5-3(7)^{-2}] - [1-3(6)^{-2}]\\ = [1.5-\frac{3}{49}] - [1-\frac{1}{12} ]\\ = 1.439 - 0.9167\\= 0.5223feet](https://tex.z-dn.net/?f=%5Cint%5Climits%5E3_2%20%7B0.5%20%2B%20%5Cfrac%7B6%7D%7B%28t%2B4%29%5E%7B3%7D%20%7D%20%20%7D%20%5C%2C%20dt%20%3D%20%5B0.5t-3%28t%2B4%29%5E%7B-2%7D%5D%5E3_2%5C%5C%3D%20%5B0.5%283%29-3%283%2B4%29%5E%7B-2%7D%5D%20-%20%5B0.5%282%29-3%282%2B4%29%5E%7B-2%7D%5D%5C%5C%3D%20%5B1.5-3%287%29%5E%7B-2%7D%5D%20-%20%5B1-3%286%29%5E%7B-2%7D%5D%5C%5C%20%3D%20%5B1.5-%5Cfrac%7B3%7D%7B49%7D%5D%20-%20%5B1-%5Cfrac%7B1%7D%7B12%7D%20%5D%5C%5C%20%20%3D%201.439%20-%200.9167%5C%5C%3D%200.5223feet)
c) The total number of feet grown during the second year can be gotten by substituting the value of limit from t = 0 to t = 2 into the equation as shown
![\int\limits^2_0 {0.5 + \frac{6}{(t+4)^{3} } } \, dt = [0.5t-3(t+4)^{-2}]^2_0\\= [0.5(2)-3(2+4)^{-2}] - [0.5(0)-3(0+4)^{-2}]\\= [1-3(6)^{-2}] - [0-3(4)^{-2}]\\ = [1-\frac{1}{12}] - [-\frac{3}{16} ]\\= \frac{11}{12}+\frac{3}{16}\\ = 0.9167 - 0.1875\\= 0.7292feet](https://tex.z-dn.net/?f=%5Cint%5Climits%5E2_0%20%7B0.5%20%2B%20%5Cfrac%7B6%7D%7B%28t%2B4%29%5E%7B3%7D%20%7D%20%20%7D%20%5C%2C%20dt%20%3D%20%5B0.5t-3%28t%2B4%29%5E%7B-2%7D%5D%5E2_0%5C%5C%3D%20%5B0.5%282%29-3%282%2B4%29%5E%7B-2%7D%5D%20-%20%5B0.5%280%29-3%280%2B4%29%5E%7B-2%7D%5D%5C%5C%3D%20%5B1-3%286%29%5E%7B-2%7D%5D%20-%20%5B0-3%284%29%5E%7B-2%7D%5D%5C%5C%20%3D%20%5B1-%5Cfrac%7B1%7D%7B12%7D%5D%20-%20%5B-%5Cfrac%7B3%7D%7B16%7D%20%5D%5C%5C%3D%20%5Cfrac%7B11%7D%7B12%7D%2B%5Cfrac%7B3%7D%7B16%7D%5C%5C%20%20%20%3D%200.9167%20-%200.1875%5C%5C%3D%200.7292feet)
Q) 145+ (-15) + (-188) = ?
→ 145+ (-15) + (-188)
→ {145 - 15} - 188
→ 130 - 188
→ -58 is the solution.
Answer:
An example that may contradict the definition is that if you are trying to find chords, they wont be the same distance as finding the radius. The way that you can change this definition is by saying that "A circle is the set of all points in a plane that are the same distance from a fixed point called the center."
Hope this helps you!