Answer:
P=(3,3)
Step-by-step explanation:
We need to find a point P in the line
such that
where 
Observe that the coordinates of P are
because P is in the line.
Then,

We reeplace the value of x in the coordinates of P and obtain the point

A. Well she starts with 24 buns. She ate 1/2 half of a bun leaving 23 1/2 buns left. Then she gave her mother and father a bun each so you do 23 1/2 - 2 which gets you 21 1/2 buns. So the total number of buns that she has left is 21 and 1/2 buns.
Answer:
The dimensions are (7m-3) by (7m-3)
Step-by-step explanation:
We have the area of the rectangular field to be:

We need to factorize this expression.
Let us rewrite to obtain:

We can easily see that the expression is actually a perfect square trinomial.
This gives us:

Or

Answer:

Step-by-step explanation:
The domain is the set of all possible values for x.
The function does not cross the line x = 1.
The domain is all real numbers except 1.
The range is the set of all possible values for y.
The function does not cross the line y = 0.
The range is all real numbers except 0.
Refer to the diagram shown below.
The volume of the container is 10 m³, therefore
x*2x*h = 10
2x²h = 10
h = 5/x² (1)
The base area is 2x² m².
The cost is $10 per m², therefore the cost of the base is
(2x²)*($10) = 20x²
The area of the sides is
2hx + 2(2xh) = 6hx = 6x*(5/x²) = 30/x m²
The cost is $6 per m², therefore the cost of the sides is
(30/x)*($6) = 180/x
The total cost is
C = 20x² + 180/x
The minimum cost is determined by C' = 0.
That is,
40x - 180/x² = 0
x³ = 180/40 = 4.5
x = 1.651
The second derivative of C is
C'' = 40 + 360/x³
C''(1.651) = 120 >0, so x = 1.651 m yields the minimum cost.
The total cost is
C = 20(1.651)² + 180/1.651 = $163.54
Answer: $163.54