SOLUTION: hello tutor i am having a problem with my algebra homework my tutoring got cancelled today :-( can you help me (pretend exponent is ^1) One more rectangular-shaped piece of meta

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Question 950440: hello tutor i am having a problem with my algebra homework my tutoring got cancelled today :-( can you help me
(pretend exponent is ^1)
One more rectangular-shaped piece of metal siding needs to be cut to cover
the exterior of a pole barn. The area of the piece is 30 ft^2. The length is 1 less
than 3 times the width. How wide should the metal piece be? Round to the nearest hundredth of a foot.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
One more rectangular-shaped piece of metal siding needs to be cut to cover
the exterior of a pole barn. The area of the piece is 30 ft^2. The length is 1 less
than 3 times the width. How wide should the metal piece be? Round to the nearest hundredth of a foot.
L=length=3W-1; W=width; Area=L*W=30 sq ft
L*W=30 sq ft Substitute for L
(3W-1)(W)=30 sq ft
3W%5E2-W=30+sq+ft
3W%5E2-W-30+sq+ft=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aW%5E2%2BbW%2Bc=0 (in our case 3W%5E2%2B-1W%2B-30+=+0) has the following solutons:

W%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-1%29%5E2-4%2A3%2A-30=361.

Discriminant d=361 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+361+%29%29%2F2%5Ca.

W%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+361+%29%29%2F2%5C3+=+3.33333333333333
W%5B2%5D+=+%28-%28-1%29-sqrt%28+361+%29%29%2F2%5C3+=+-3

Quadratic expression 3W%5E2%2B-1W%2B-30 can be factored:
3W%5E2%2B-1W%2B-30+=+3%28W-3.33333333333333%29%2A%28W--3%29
Again, the answer is: 3.33333333333333, -3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-1%2Ax%2B-30+%29

Answer W=3.33 ft ANSWER: The width should be 3.33 feet.
CHECK
L=3W-1=10-1=9
A=L*W
30 sq ft=9(3.33)
30 sq ft=30 sq ft