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lawyer [7]
3 years ago
12

The top 1/8 of the runners advance to the finals for the track and field competition. What is the decimal value of the number? S

how your work. plz help me ill mark brainliest
Mathematics
1 answer:
egoroff_w [7]3 years ago
8 0
To find the decimal form, you have to manually divide 1 by 8. Since 8 is greater than 1, the quotient would then start with 0., then you add a 0 next to 1, to make it 10. This time, divide 10 by 8. The nearest answer would be 1, because 1 *8 = 8. Subtracting this from 10, you get 2. Add another 0 to 2, to make it 20. Do the cycle all over again. The complete solution is as follows:
          0.125
       ---------------------------
   8 |   10
         - 8
        ------------------------
           20
         -16
          -------------
            40
          - 40
       -------------
            0

<em>Hence, the decimal form of 1/8 is 0.125.</em>
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Answer:

\sf a. \quad \dfrac{21}{10+x}+\dfrac{21}{10-x}=5

Step-by-step explanation:

<u>Formula</u> for calculating speed:

\boxed{\sf Speed=\dfrac{Distance}{Time}}

Therefore:

\boxed{\sf Time=\dfrac{Distance}{Speed}}

<u>Given values</u>:

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If the boat is traveling downstream, the current (x mph) will be pushing the boat <u>faster</u>, and so the boat's speed will increase by x mph.

Therefore, the expression for the time it takes for the boat to travel downstream is:

\sf Time\:(downstream)=\dfrac{21}{10+x}

If the boat is traveling upstream, the current (x mph) will be pushing <u>against</u> the boat and so the boat's speed will decrease by x mph.

Therefore, the expression for the time it takes for the boat to travel upstream is:

\sf Time\:(upstream)=\dfrac{21}{10-x}

Therefore, if the total time it takes to travel downstream <em>and</em> upstream is 5 hours:

\implies \sf \dfrac{21}{10+x}+\dfrac{21}{10-x}=5

<u />

<u>To solve for x</u>:

\implies \sf \dfrac{21}{10+x}+\dfrac{21}{10-x}=5

\implies \sf \dfrac{21(10-x)}{(10+x)(10-x)}+\dfrac{21(10+x)}{(10-x)(10+x)}=5

\implies \sf \dfrac{21(10-x)+21(10+x)}{(10+x)(10-x)}=5

\implies \sf21(10-x)+21(10+x)=5(10+x)(10-x)

\implies \sf 210-21x+210+21x=5(100-10x+10x-x^2)

\implies \sf 420=500-5x^2

\implies \sf 5x^2=80

\implies \sf x^2=16

\implies \sf x=\pm4

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