Find the sum of
1 answer:
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Answer:
He should plant 100 acres of corn and 400 acres of wheat.
Step-by-step explanation:
This problem can be solved by a siple system of equations.
]x denotes the number of acres of corn
y denotes the number of acres of wheat
Building the system:
The Johnson Farm has 500 acres of land allotted for cultivating corn and wheat. This means that:
The cost of cultivating corn and wheat (including seeds and labor) is $42 and $30 per acre, respectively. Jacob Johnson has $16,200 available for cultivating these crops. This means that:
So, we have the following system
If he wishes to use all the allotted land and his entire budget for cultivating these two crops, how many acres of each crop should he plant?
I am going to write y as a function of x in 1), and replace in 2). So:
means that
Now, going back to 1:
He should plant 100 acres of corn and 400 acres of wheat.
We know that:
is an equation of a circle.
When we substitute x and y (from the pairs we have), we'll get a system of equations:
and all we have to do is solve it for a, b and r.
There will be:
From equations (II) and (III) we have:
and from (I) and (II):
Now we can easly calculate a and b:
Finally we calculate
:
And the equation of the circle is:
is an equation of a circle.
When we substitute x and y (from the pairs we have), we'll get a system of equations:
and all we have to do is solve it for a, b and r.
There will be:
From equations (II) and (III) we have:
and from (I) and (II):
Now we can easly calculate a and b:
Finally we calculate
And the equation of the circle is: