What is the sum of 1.57 and 6.88?
Ok, so lets work this out together!
Sum means add.
6.88
+ 1.57
That would be:
= 8.45
Hope i helped!
<h3>Answer:</h3>
![f'(x)=\dfrac{8x^4-2x^2-\left(28x^4+83x^2-3\right)\ln{\left(x^2+3\right)}}{2x^2\left(x^2+3\right)\left(4x^2-1\right)^4}](https://tex.z-dn.net/?f=f%27%28x%29%3D%5Cdfrac%7B8x%5E4-2x%5E2-%5Cleft%2828x%5E4%2B83x%5E2-3%5Cright%29%5Cln%7B%5Cleft%28x%5E2%2B3%5Cright%29%7D%7D%7B2x%5E2%5Cleft%28x%5E2%2B3%5Cright%29%5Cleft%284x%5E2-1%5Cright%29%5E4%7D)
<h3>Explanation:</h3>
It can work well to consider the function in parts. Define the following:
... a(x) = (1/2)ln(x^2+3)
... b(x) = x(4x^2-1)^3
Then the derivatives of these are ...
... a'(x) = (1/2)·1/(x^2 +3)·2x = x/(x^2+3)
... b'(x) = (4x^2 -1)^3 + 3x(4x^2 -1)^2·8x = (4x^2 -1)^2·(4x^2 -1 +24x^2)
... = (4x^2 -1)^2·(28x^2 -1)
___
<em>Putting the parts together</em>
f(x) = a(x)/b(x)
f'(x) = (b(x)a'(x) -a(x)b'(x))/b(x)^2 . . . . . rule for quotient of functions
Substituting values, we have
... f'(x) = (x(4x^2 -1)^3·x/(x^2 +3) -(1/2)ln(x^2 +3)·(4x^2 -1)^2·(28x^2 -1)) / (x(4x^2 -1)^3)^2
We can cancel (4x^2 -1)^2 from numerator and denominator. We can also eliminate fractions (1/2, 1/(x^2+3)). Then we have ...
... f'(x) = 2x^2(4x^2 -1) -(x^2 +3)ln(x^2 +3)·(28x^2 -1)/(2x^2·(x^2 +3)(4x^2 -1)^4))
Simplifying a bit, this becomes ...
... f'(x) = (8x^4 -2x^2 -ln(x^2 +3)·(28x^4 +83x^2 -3))/(2x^2·(x^2 +3)(4x^2 -1)^4))
Answer:
The population that gives the maximum sustainable yield is 45000 swordfishes.
The maximum sustainable yield is 202500 swordfishes.
Step-by-step explanation:
Let be
, the maximum sustainable yield can be found by using first and second derivatives of the given function: (First and Second Derivative Tests)
First Derivative Test
![f'(p) = -0.02\cdot p +9](https://tex.z-dn.net/?f=f%27%28p%29%20%3D%20-0.02%5Ccdot%20p%20%2B9)
Let equalize the resulting expression to zero and solve afterwards:
![-0.02\cdot p + 9 = 0](https://tex.z-dn.net/?f=-0.02%5Ccdot%20p%20%2B%209%20%3D%200)
![p = 450](https://tex.z-dn.net/?f=p%20%3D%20450)
Second Derivative Test
![f''(p) = -0.02](https://tex.z-dn.net/?f=f%27%27%28p%29%20%3D%20-0.02)
This means that result on previous part leads to an absolute maximum.
The population that gives the maximum sustainable yield is 45000 swordfishes.
The maximum sustainable yield is:
![f(450) = -0.01\cdot (450)^{2}+9\cdot (450)](https://tex.z-dn.net/?f=f%28450%29%20%3D%20-0.01%5Ccdot%20%28450%29%5E%7B2%7D%2B9%5Ccdot%20%28450%29)
![f(450) =2025](https://tex.z-dn.net/?f=f%28450%29%20%3D2025)
The maximum sustainable yield is 202500 swordfishes.
<span>15b^2 + 20b
=5b(3b + 4)
......................</span>
Answer:
Ew... oatmeal cookies
Step-by-step explanation: