<u>Answer:
</u>
The vertex of the function 
is (h,k) = (3 , -1)
<u>Solution:
</u>
The vertex form of quadratic equation is generally given as,
Where h,k is the vertex of the parabola.
From question, given that 
.
we have to find the vertex of the function.
Let us first convert the given quadratic equation to vertex form (eqn 1)
By adding “9” on both sides of equation, we get
By using the identity 
,the right hand side of above equation becomes,
Now,the equation is of the vertex form.
By comparing with 
we get the values of (h,k)
a = 1; h = 3; k = -1
hence the vertex of the function is (h,k) = (3 , -1)
We have the following function:
p (x) = - 2 (x-9) ^ 2 +200
We derive to find the maximum of the function:
p '(x) = - 4 (x-9)
Rewriting:
p '(x) = - 4x + 36
We match zero:
-4x + 36 = 0
We clear x
x = 36/4
x = 9 degrees
The maximum population occurs when x = 9.
We evaluate the function for this value:
p (9) = - 2 * (9-9) ^ 2 +200
p (9) = 200
Answer:
The maximum number of fish is:
p (9) = 200
Step by step:
Each day it takes a sample of 15 pies - on Monday he needed 4:
4/15 = x/450 (450 being the total for each day)
4 x 450 = 1800
1800 divided by 15 = 120
120 is the amount of pies that were made on Monday
Hope this helps
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The value of x from the diagram is 29 degrees.
<h3>SOH CAH TOA identity</h3>
From the given figure, we have the following parameters:
- Opposite = 12
- Hypotenuse = 25
<h3>According to the theorem:</h3>
Sin x = opposite/hypotenuse
Sin x = 12/25
Sin x = 0.48
x = arcsin(0.48)
x = 28.685
x = 29 degrees
Hence the value of x from the diagram is 29 degrees.
Learn more on SOH CAH TOA here: brainly.com/question/20734777
Answer:
A=4ft²
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Step-by-step explanation:
