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dmitriy555 [2]
3 years ago
7

When planning his crops, Farmer Joe knows that his 5 acres can support corn and strawberries. He wants to make $5,500 from his c

rops. He can make $1,000 per acre of corn (the variable c) and $1,500 per acre of strawberries (the variable s). Which equation below would be a constraint in his system of equations?
Mathematics
1 answer:
qaws [65]3 years ago
3 0
This can be solved using the system of equations:

5500 = 1000c + 1500s
5 = c + s

As the first equation can have different combinations, it is the second equation that defines just how much acres or corn or strawberries(or mathematically, it defines the values of c or s in the first equation) there are. Therefore, the equation " 5 = c + s" is the constraint.
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Step-by-step explanation:

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Given that the expression 2x^3 + mx^2 + nx + c leaves the same remainder when divided by x -2 or by x+1 I prove that m+n =-6
Alla [95]

Given:

The expression is:

2x^3+mx^2+nx+c

It leaves the same remainder when divided by x -2 or by x+1.

To prove:

m+n=-6

Solution:

Remainder theorem: If a polynomial P(x) is divided by (x-c), thent he remainder is P(c).

Let the given polynomial is:

P(x)=2x^3+mx^2+nx+c

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P(2)=2(8)+m(4)+2n+c

P(2)=16+4m+2n+c

Now, substitute the values of P(2) and P(-1) in (i), we get

16+4m+2n+c=-2+m-n+c

16+4m+2n+c+2-m+n-c=0

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3m+3n=-18

Divide both sides by 3.

\dfrac{3m+3n}{3}=\dfrac{-18}{3}

m+n=-6

Hence proved.

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