US<br> Find the measure of 48.<br> 48<br> 97/83<br> 97<br> 48 = [?]<br> Enter

After a long study, tree scientists conclude that a eucalyptus tree will grow at the rate of 0.5 6/ (t+4)3 feet per year, where

kipiarov [429]

Answer:

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;

$\int\limits {0.5 + \frac{6}{(t+4)^{3} } } \, dt \\= \int\limits {0.5} \, dt + \int\limits\frac{6}{(t+4)^{3} } } \, dx } \, \\= 0.5t +\int\limits {6u^{-3} } \, du \ where \ u = t+4 \ and\ du = dt\\= 0.5t + 6*\frac{u^{-2} }{-2} + C\\= 0.5t-3u^{-2} +C\\= 0.5t-3(t+4)^{-2} + C$

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

$\int\limits^2_1 {0.5 + \frac{6}{(t+4)^{3} } } \, dt = [0.5t-3(t+4)^{-2}]^2_1\\= [0.5(2)-3(2+4)^{-2}] - [0.5(1)-3(1+4)^{-2}]\\= [1-3(6)^{-2}] - [0.5-3(5)^{-2}]\\ = [1-\frac{1}{12}] - [0.5-\frac{3}{25} ]\\= \frac{11}{12}-\frac{1}{2}+\frac{3}{25}\\ = 0.9167 - 0.5 + 0.12\\= 0.5367feet$

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

$\int\limits^3_2 {0.5 + \frac{6}{(t+4)^{3} } } \, dt = [0.5t-3(t+4)^{-2}]^3_2\\= [0.5(3)-3(3+4)^{-2}] - [0.5(2)-3(2+4)^{-2}]\\= [1.5-3(7)^{-2}] - [1-3(6)^{-2}]\\ = [1.5-\frac{3}{49}] - [1-\frac{1}{12} ]\\ = 1.439 - 0.9167\\= 0.5223feet$

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

$\int\limits^2_0 {0.5 + \frac{6}{(t+4)^{3} } } \, dt = [0.5t-3(t+4)^{-2}]^2_0\\= [0.5(2)-3(2+4)^{-2}] - [0.5(0)-3(0+4)^{-2}]\\= [1-3(6)^{-2}] - [0-3(4)^{-2}]\\ = [1-\frac{1}{12}] - [-\frac{3}{16} ]\\= \frac{11}{12}+\frac{3}{16}\\ = 0.9167 - 0.1875\\= 0.7292feet$

8 0

2 years ago

Netflix charges Geyon $15 per month for a membership, plus a $5 one-time fee for streaming on his phone. How many months will Ge

Nutka1998 [239]

Answer:

2 and a half months

Step-by-step explanation:

You need to divide 50 by 20 (because member ship+netflix)

8 0

3 years ago

Helppppppppppppppppppppppppppp

Dmitry_Shevchenko [17]

Answer:

126 $m^{2}$

Step-by-step explanation:

4 0

3 years ago

Kepler’s law states that if one object is in orbit around another, the square of the time it takes that object to complete a rev

Nitella [24]

Kepler's 3rd Law is t^2 = r^3
Let's say "r" is 2, then
t^2 = 8
t = <span> <span> <span> 2.8284271247 </span> </span> </span>
Basically, t = r^1.5

If you want to know more about Kepler's 3rd Law click here:
http://www.1728.org/kepler3a.htm

6 0

3 years ago

Factor completely. 5x2 - 45 A. 5(x + 3)(x - 3) B. 5(x2 - 45) C. 5(x - 9)(x + 9) D. (5x + 9)(x - 5)

zimovet [89]

Answer:

The correct answer is A. 5(x + 3)(x - 3)

Step-by-step explanation:

In order to solve this, we start by pulling out the greatest common factor.

5x^2 - 45

5(x^2 - 9)

Now we can use the difference of two squares to factor the rest of the equation.

5(x + 3)(x - 3)

4 0

2 years ago

Read 2 more answers

US Find the measure of 48. 48 97/83 97 48 = [?] Enter