MODELING WITH MATHEMATICS A farmer plants a garden that contains corn and pumpkins. The total area (in square
1 answer:
Answer:
The equation in standard form that models area of pumpkins is:
and the area is:
Step-by-step explanation:
Given that the garden has corn and pumpkins
The expressions are:
Total area of garden:
Area of Corn:
Area of Pumpkins:
The sum of areas of corn and pumpkins is the total area of the garden.
It can be expressed mathematically as:
If we have to find the area of pumpkins,
Putting the values
The equation in standard form that models area of pumpkins is:
and the area is:
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Answer:
The dimensions of the box is 3 ft by 3 ft by 30.22 ft.
The length of one side of the base of the given box is 3 ft.
The height of the box is 30.22 ft.
Step-by-step explanation:
Given that, a rectangular box with volume of 272 cubic ft.
Assume height of the box be h and the length of one side of the square base of the box is x.
Area of the base is =
The volume of the box is = area of the base × height
Therefore,
The cost per square foot for bottom is 20 cent.
The cost to construct of the bottom of the box is
=area of the bottom ×20
cents
The cost per square foot for top is 10 cent.
The cost to construct of the top of the box is
=area of the top ×10
cents
The cost per square foot for side is 1.5 cent.
The cost to construct of the sides of the box is
=area of the side ×1.5
cents
cents
Total cost =
Let
C
Putting the value of h
Differentiating with respect to x
Again differentiating with respect to x
Now set C'=0
Now
Since at x=3 , C''>0. So at x=3, C has a minimum value.
The length of one side of the base of the box is 3 ft.
The height of the box is
=30.22 ft.
The dimensions of the box is 3 ft by 3 ft by 30.22 ft.