Find the point of intersection algebraically for the system of equations. Make sure to write your answer as an ordered pair.
1 answer:
Answer:
Step-by-step explanation:
hello :
1) the system is : y=5x+4
y = 2x+1
so :5x+4 =2x+1
5x-2x=1-4
3x= -3 so : x= -1 but y =2x+1 put x=-1 you have : y =-1
the solution : (x,y) =( -1, -1)
2) the system is : x + y = 4
4x -y = 1
means : y = - x+4 (line red)
y= 4x-1 (line blue)
graficly : intrsection is : (x,y) =(1 ,3 )
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Answer:
The water temperature that produces the maximum number of salmon swimming upstream is approximately 12.305 degrees Celsius.
Step-by-step explanation:
Let , for
.
represents the temperature of the water, measured in degrees Celsius, and
is the number of salmon swimming upstream to spawn, dimensionless.
We compute the first and second derivatives of the function:
(Eq. 1)
(Eq. 2)
Then we equalize (Eq. 1) to zero and solve for :
And all roots are found by Quadratic Formula:
,
Only the first root is inside the given interval of the function. Hence, the correct answer is:
Now we evaluate the second derivative at given result. That is:
According to the Second Derivative Test, a negative value means that critical value leads to a maximum. In consequence, the water temperature that produces the maximum number of salmon swimming upstream is approximately 12.305 degrees Celsius.
16 = c8
c =
c = 2
hope this helps!