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;
![\int\limits {0.5 + \frac{6}{(t+4)^{3} } } \, dt \\= \int\limits {0.5} \, dt + \int\limits\frac{6}{(t+4)^{3} } } \, dx } \, \\= 0.5t +\int\limits {6u^{-3} } \, du \ where \ u = t+4 \ and\ du = dt\\= 0.5t + 6*\frac{u^{-2} }{-2} + C\\= 0.5t-3u^{-2} +C\\= 0.5t-3(t+4)^{-2} + C](https://tex.z-dn.net/?f=%5Cint%5Climits%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%5C%5C%3D%20%5Cint%5Climits%20%7B0.5%7D%20%5C%2C%20dt%20%2B%20%5Cint%5Climits%5Cfrac%7B6%7D%7B%28t%2B4%29%5E%7B3%7D%20%7D%20%20%7D%20%5C%2C%20dx%20%7D%20%5C%2C%20%5C%5C%3D%200.5t%20%2B%5Cint%5Climits%20%7B6u%5E%7B-3%7D%20%7D%20%5C%2C%20du%20%5C%20%20where%20%5C%20u%20%3D%20t%2B4%20%5C%20and%5C%20du%20%3D%20dt%5C%5C%3D%200.5t%20%2B%206%2A%5Cfrac%7Bu%5E%7B-2%7D%20%7D%7B-2%7D%20%2B%20C%5C%5C%3D%200.5t-3u%5E%7B-2%7D%20%2BC%5C%5C%3D%200.5t-3%28t%2B4%29%5E%7B-2%7D%20%2B%20C)
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)
Answer:
2
Step-by-step explanation:
trust me bc im black:)
Well you can put 4/5 in a decimal form by dividing it
which is 0.8
Complement adds to 90
complement of A is 90-A
supplement is adds to 180
supplemetn of A is 180-A
2(90-A) is -40+180-A
2(90-A)=-40+180-A
2(90-A)=140-A
distribute
180-2A=140-A
add 2A to both sides
180=140+A
minus 140 both sides
40=A
A=40 degres
Answer: ANSWER DOWN BELOW
Step-by-step explanation: