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Sholpan [36]
3 years ago
9

A swimming pool  20 m long and 10 m wide is surrounded by a deck of uniform width. The total area of the swimming pool and the d

eck is 704 m^2. Find the width of the deck.

Mathematics
2 answers:
Anna007 [38]3 years ago
8 0
S = 704 \ m^2 \\width \ of \ the \ deck - x \\ \\S=a \cdot b \\ \\ (10+2x)(20+2x) = 704 \\ \\ 200+20x +40x+4x^2-704 =0\\ \\4x^2 +60x -504=0\ \ /:4
 
x^2+15x -126=0\\ \\a=1, \ b=15 , \ c= - 126 \\ \\\Delta =b^2-4ac = 15^2 -4\cdot1\cdot (-126) = 225 +504=729 \\ \\x_{1}=\frac{-b-\sqrt{\Delta} }{2a}=\frac{-15-\sqrt{729}}{2 }=\frac{ -15-27}{2}=\frac{-42}{2}=-21 \ can \ not\ be \ negative \\ \\x_{2}=\frac{-b+\sqrt{\Delta} }{2a}=\frac{-15+\sqrt{729}}{2 }=\frac{ -15+27}{2}= 6 \ m \\ \\ Answer : \   waist \ width  \ is \ 6 \ m


Soloha48 [4]3 years ago
6 0
Let x = width of the deck.
Therefore total area of pool : 
(10+2x)m*(20+2x)m = 704 m^2
( 200 + 20x + 40x + 4x^2 ) m^2 = 704 m^2
(200 + 60x + 4x^2)   = 704
 4x^2 + 60x = 704-200
 4x^2 + 60x = 504
 4x^2 + 60x - 504 = 0
4(x^2 + 15x - 126) = 0
(x+21) * (x-6) = 0
Therefore x, the deck's width is 6m (it can't be -21 as width is measured as a positive value)
Kindly press the Thank You button and indicate this as best answer if it answers your question correctly. Thanks.
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Exercise 7.3.5 The following is a Markov (migration) matrix for three locations        1 5 1 5 2 5 2 5 2 5 1 5 2 5 2 5 2
fredd [130]

Answer:

Both get the same results that is,

\left[\begin{array}{ccc}140\\160\\200\end{array}\right]

Step-by-step explanation:

Given :

\bf M=\left[\begin{array}{ccc}\frac{1}{5}&\frac{1}{5}&\frac{2}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{1}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{2}{5}\end{array}\right]

and initial population,

\bf P=\left[\begin{array}{ccc}130\\300\\70\end{array}\right]

a) - After two times, we will find in each position.

P_2=[P].[M]^2=[P].[M].[M]

M^2=\left[\begin{array}{ccc}\frac{1}{5}&\frac{1}{5}&\frac{2}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{1}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{2}{5}\end{array}\right]\times \left[\begin{array}{ccc}\frac{1}{5}&\frac{1}{5}&\frac{2}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{1}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{2}{5}\end{array}\right]

     =\frac{1}{25} \left[\begin{array}{ccc}7&7&7\\8&8&8\\10&10&10\end{array}\right]

\therefore\;\;\;\;\;\;\;\;\;\;\;P_2=\left[\begin{array}{ccc}7&7&7\\8&8&8\\10&10&10\end{array}\right] \times\left[\begin{array}{ccc}130\\300\\70\end{array}\right] = \left[\begin{array}{ccc}140\\160\\200\end{array}\right]

b) - With in migration process, 500 people are numbered. There will be after a long time,

After\;inifinite\;period=[M]^n.[P]

Then,\;we\;get\;the\;same\;result\;if\;we\;measure [M]^n=\frac{1}{25} \left[\begin{array}{ccc}7&7&7\\8&8&8\\10&10&10\end{array}\right]

                                   =\left[\begin{array}{ccc}140\\160\\200\end{array}\right]

4 0
3 years ago
It's a little blurry sorry please help
Ghella [55]

<u>Answer:</u>

It's X=2

<u>Working out:</u>

<u>(left one):</u>

2(x+3)=10

2x+6=10

2x=10-6

2x=4

x=2

Working out:

(right one):

2(x+3) must be all divided by 2 so it will be x+3 and same for 10, it will be 5 so...

x+3=5

x=5-3

x=2

Hope it helps ^---^

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20% off means you are paying 80% of the original price ( 100% - 20% = 80%)

Multiply the price of the tv by 80% to find the sale price:

500 x 0.80 = 400

Now multiply the sales price by 1 plus the tax rate to find final cost:

400 x 1.06 = 424

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