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Dafna11 [192]
3 years ago
12

A circular pool of radius r m has a path 2 m wide around its perimeter. If the area of the pool is four-fifths of the total area

, prove that r²-16r-16=0. Hence calculate the radius of the pool in metres.
Mathematics
1 answer:
Rainbow [258]3 years ago
4 0

9514 1404 393

Answer:

  pool radius is 8+4√5 ≈ 16.94 meters

Step-by-step explanation:

Let r represent the radius of the pool. Then r+2 is the radius to the outside of the walkway. The ratio of areas is given as 4/5, so we have ...

  πr²/(π(r+2)²) = 4/5

  5r² = 4(r² +4r +4) . . . . cross-multiply

  r² -16r -16 = 0 . . . . . . . subtract the right-side expression from both sides

__

  r² -16r +64 = 80 . . . . . add 80 to complete the square

  (r -8)² = 80

  r -8 = √80 = 4√5 . . . . square root; use only the positive root

  r = 8 +4√5 ≈ 16.94 . . . meters

The radius of the pool is 8+4√5 ≈ 16.94 meters.

_____

The area of a circle of radius r is given by the formula ...

  A = πr²

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3 years ago
Divide 4 2/3 & 3 1/3. Simplify the answer and write it as a mixed number.
Leto [7]

Answer:

4 2/3 ÷ 3 1/3= 1 2/5

Step-by-step explanation:

First, you turn the mixed terms into an improper fraction like this

4 2/3 → 14/3 because when you multiply 4 times 3 equaling 12 then having 2 then adding that you get 14/3.

3 1/3 → 10/3 because when you multiply 3*3=9 then having 1 and adding that you get 10/3.

Then, you do KCF which stands for <u>Keep Change Flip</u> so for this you would do: 14/3 ÷ 10/3 → 14/3 × 3/10

14 × 3 = 42 and 3 × 10= 30

Now being 42/30 this is considered an improper fraction in which you have to transform it into a mixed number like this:

(For this you need to find the greatest common factor)

42/30 →  42 and 30 greatest common factor is 6 because they are divisible and factor of 6.

Now you divide both the denominator and the numerator y 6 like this:

42 ÷ 6= 7

30 ÷ 6= 5

Now we have 7/5, this is still an improper number so we see how many times 7 can go to 5 which is once. So we have 1 as whole number, now we put the reminder as the numenator of the mix fraction keeping 5 as being the denominator.

Overall, We have our answer 1 2/5

I hope this helps :D  

7 0
3 years ago
Add and subtract rational numbers without common denominators. Show work! 1. 7/4 - 3/2 - 2/5 = 2. - 5/16 + 3/4 + 1/8 = 3. 3/4 -
alukav5142 [94]
\dfrac{7}{4}  -  \dfrac{3}{2} -  \dfrac{2}{5}

= \dfrac{7 \times 5}{4 \times 5}  -  \dfrac{3 \times 10}{2 \times 10} -  \dfrac{2 \times 4}{5 \times 4}

= \dfrac{35}{20}  -  \dfrac{30}{20} -  \dfrac{8}{20}

= \dfrac{35-30-8}{20}

= \dfrac{3}{20}

---------------------------------------------------------------

-\dfrac{5}{16}  + \dfrac{3}{4} + \dfrac{1}{8}

= -\dfrac{5}{16}  + \dfrac{3 \times 4}{4 \times 4} + \dfrac{1 \times 2}{8 \times 2}

= -\dfrac{5}{16}  + \dfrac{12}{16} + \dfrac{2}{16}

= \dfrac{-5+ 12 + 2}{16}

= \dfrac{9}{16}

---------------------------------------------------------------

\dfrac{3}{4} -  \dfrac{1}{3} - \dfrac{7}{12}

= \dfrac{3 \times 3}{4 \times 3} -  \dfrac{1 \times 4}{3 \times 4} - \dfrac{7}{12}

= \dfrac{9}{12} -  \dfrac{4}{12} - \dfrac{7}{12}

= \dfrac{9 - 4 - 7}{12}

= -\dfrac{2}{12}

= -\dfrac{1}{6}

---------------------------------------------------------------

\dfrac{2}{9}  -  \dfrac{2}{12} -  \dfrac{2}{3}

= \dfrac{2}{9}  -  \dfrac{1}{6} -  \dfrac{2}{3}

= \dfrac{2 \times 2}{9 \times 2}  -  \dfrac{1 \times 3}{6 \times 3} -  \dfrac{2 \times 6}{3 \times 6}

= \dfrac{4}{18}  -  \dfrac{3}{18} -  \dfrac{12}{18}

= \dfrac{4 - 3 - 12}{18}

= - \dfrac{11}{18}
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