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dalvyx [7]
3 years ago
5

A person wants to create a vegetable garden and keeps the rabbits out by enclosing it with 100 feet of fencing. The area of the

garden is giving by the function A (w) = (50-w) where w is the width (in feet) of the garden. Can the garden have an area of 700 ft^2?
Mathematics
1 answer:
alekssr [168]3 years ago
4 0

Answer:

The garden can not have area of 700ft^2

Step-by-step explanation:

We are given equation for area as

A(w)=w\times (50-w)

where

w is the width (in feet) of the garden

now, we are given area =700 ft^2

so, we can set area =700

and then we can solve for w

w\times (50-w)=700

50w-w^2=700

-w^2+50w-700=0

now, we can use quadratic formula

ax^2+bx+c=0

w=\frac{-b\pm \sqrt{b^2-4ac}}{2a}

we can compare and find a,b, and c

a=-1 , b=50 , c=-700

now, we can plug values

w=\frac{-50\pm \sqrt{50^2-4\left(-1\right)\left(-700\right)}}{2\left(-1\right)}

w=25-5\sqrt{3}i,\:w=25+5\sqrt{3}i

We can see that values of w is not real

so, w does not exists when area =700

so, The garden can not have area of 700ft^2


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