Answer: In the resulting equation: " a² - 12a + 32 = 0 " ;
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The "coefficient" of the "a" term is: " - 12" .
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The "constant" is: " 32 " .
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Explanation:
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Let: "a = x² + 4 " .
Given: (x² + 4)² + 32 = 12x² + 48 ;
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Factor: "12x² + 48" into " (x² + 4) " ;
"12x² + 48" = 12 (x² + 4) " ;
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Given: (x² + 4)² + 32 = 12x² + 48 ;
rewrite as; "a² + 32 = 12a " ;
Subtract "12a" from each side of the equation;
"a² + 32 - 12a = 12a - 12a ;
to get:
" a² - 12a + 32 = 0 " .
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The coefficient of the "a" term; that is:
The "coefficient" of " -12a" ; is: "- 12" .
The constant is: "32<span>" .
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Your answer is D,
3 + d -3<3 - d -3 , you minus three from both sides.
Results :d<-d
Then, d+d<-d+d.
Which is, 2d/2<0/2.
Answer : d<0
Answer:
Step-by-step explanation:
a. Draw a direction field for the given differential equation
b. Based on the inspection of the direction field, describe ow solutions behave for large t.
The solution appear oscillatory
All solutions seems to converge to the function y0(t)=4
All solutions seems to converge to the function y0(t)=0
All solutions seems to seems to eventually have negative slopes a and hence decrease without bound
All solutions seems to seems to eventually have positive slopes a and hence increase without bound
C
As t-infinity
All solutions seems to seems to eventually have positive slopes a and hence decrease without bound
All solutions seems to converge to the function y0(t)=0
All solutions seems to seems to eventually have negative slopes a and hence decrease without bound
All solutions seems to converge to the function y0(t)=4
The solution are oscillatory
Sin(theta) = O/H = 5/16 (this us the ratio)
If we go further for the problem:
sin(theta) = 5/16 becomes sin-1 (5/16) = 18.2°
Good luck!
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
Let equalize the resulting expression to zero and solve afterwards:
Second Derivative Test
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:
The maximum sustainable yield is 202500 swordfishes.