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Mathematics 24 Online
OpenStudy (anonymous):

Will medal attaching picture

OpenStudy (anonymous):

6,7,&8

OpenStudy (anonymous):

& 9

OpenStudy (michele_laino):

first part of your exercise can be modeled by this equation: \(L=30+W\) where \(L\) is the length, and \(W\) is the width of the soccer field

OpenStudy (michele_laino):

furthermore, from your data, we can write this condition: \(L \cdot W=8800\)

OpenStudy (michele_laino):

Substituting the first equation, into the second one, we get: \[\left( {30 + W} \right) \cdot W = 8800\] which is a quadratic equation. Please solve such equation

OpenStudy (anonymous):

I'm confused @Michele_Laino

OpenStudy (michele_laino):

If I apply the distributive property of multiplication over addition, we get: \[30W + {W^2} = 8800\] therefore I simplify, so I get: \[{W^2} + 30W - 8800 = 0\] please solve that equation for \(W\)

OpenStudy (anonymous):

how do i that? I don't know what W is and there arent any like terms?

OpenStudy (michele_laino):

please, do you know how to solve a quadratic equation?

OpenStudy (anonymous):

not really..

OpenStudy (anonymous):

i can look it up?

OpenStudy (anonymous):

w(w+30)=8800

OpenStudy (michele_laino):

I'm sorry, it is not the right procedure for solving a quadratic equation

OpenStudy (anonymous):

so how do i this problem??

OpenStudy (michele_laino):

I'm thinking...

OpenStudy (michele_laino):

sincerely speaking, I don't know how we can solve your problem without solving a quadratic equation

OpenStudy (michele_laino):

please try to ask to another helper

OpenStudy (michele_laino):

@dan815 please help

OpenStudy (michele_laino):

@ freckles please help

OpenStudy (anonymous):

@freckles

OpenStudy (anonymous):

i really need help :( thank you @Michele_Laino for trying!

OpenStudy (michele_laino):

:)

OpenStudy (anonymous):

i got 7 and 8

OpenStudy (anonymous):

i really need 6

OpenStudy (michele_laino):

I'm sorry, the solution is \(W=80\), so \(L=80+30=110\)

OpenStudy (anonymous):

i got 6!

OpenStudy (anonymous):

now 9 i have to find 9 lol

OpenStudy (michele_laino):

please, what is \(6\)?

OpenStudy (anonymous):

one second

OpenStudy (anonymous):

The quadratic formula for this solution: \[w=\frac{-b \pm \sqrt{b^2-4ac} }{ 2a }\] Subsitute the values a=1, b=30, and c=-8800 into the quadratic formula to solve x. \[w=\frac{ -30\pm \sqrt{(30)^2 -4(1)(-8800)} }{ 2(1) }\] Simplify the section inside the radical. \[w=\frac{ -30 \pm \sqrt{30^2-4 * 1 * -8800} }{ 2(1) }\] Raise 30 to the power of 2 to get 900. \[w=\frac{ -30 \pm \sqrt{900-4 * -8800} }{ 2 }\] Multiply -4 by -8800 to get 35200. \[w=\frac{ -30+\sqrt{900+35200} }{ 2 }\] Add 900 and 35200 to get 36100. \[w=\frac{ -30\pm \sqrt{36100} }{ 2 }\] Rewrite 36100 as 190^2. \[w=\frac{ -30\pm \sqrt{190^2} }{ 2 }\] Get rid of the terms from the radical. \[w=\frac{ -30\pm190 }{ 2 }\] Simplify it \[\frac{( -30+190) }{ (2) }\] \[w=-15\pm95\] w= -15+95= 80 w=-15-95=110 w=80,-110

OpenStudy (anonymous):

@angelmaxine @Michele_Laino

OpenStudy (anonymous):

whoa :o thank you!

OpenStudy (anonymous):

@Austin1617

OpenStudy (anonymous):

for #9 can i post what i got ? and can you look over it @Austin1617

OpenStudy (anonymous):

Let x = the width and x + 30 = the length. x(x + 3) = 8800 x^2 + 3x = 8800 x^2 + 3x - 8800 = 0 Using the Quadratic Formula, I get x ≈ 92.320 yd and x + 30 ≈ 122.320 yd. 2x + 2x + 60 = 600 4x + 60 = 600 4x = 540 x = 135 x + 30 = 165 The area would be 22275 yd^2.

OpenStudy (anonymous):

@Austin1617 @Michele_Laino

OpenStudy (michele_laino):

please, the right equation is: x(x+30)=8800

OpenStudy (anonymous):

@Michele_Laino sorry typo

OpenStudy (anonymous):

does everything else look ok

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