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miss Akunina [59]
3 years ago
15

Ella is 12.537 miles from her house which shows the value of 12.537 rounded to the nearest tenth and nearest hundredths F 12.6,

12.54 G 12.5, 12.54 H.13.0, 12.53 J 12.5, 12.53
Mathematics
1 answer:
ratelena [41]3 years ago
7 0

Answer:

12.5 is to the nearest tenth

12.54 is to the nearest hundredth

Step-by-step explanation:

12.537

The first number after the decimal is the tenths place

we look at the number after it to determine whether to round up or down

12.53  the 3 is less than 5 so we leave it alone

13.5 is rounded to the nearest tenth

The second number after the decimal is the hundrdeths place

we look at the number after it to determine whether to round up or down

12.537  the 7 is greather than or equal to 5 so we round up

13.537  is rounded becomes 13.54

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Find the solution (in explicit form) for the following initial value problem:    y 0 = xy3 (1 + x 2 ) − 1 2 y(0) = 1.
natta225 [31]

Complete Question

The  complete question is shown on the first uploaded image

Answer:

The solution is  y^2 = \frac{1}{ 3 - 2 (1 + x^2 ) ^{\frac{1}{2} }}    

Step-by-step explanation:

From the question we are told that

  The  function is  \left \{ {{y' =  xy^3 (1 + x^2)^{-\frac{1}{2} }} \atop {y(0) =  1}} \right.

Generally the above  equation can be represented as

      \frac{dy}{dx}  =  xy^3  (1+ x^2)^{- \frac{1}{2} }

      =>   \frac{dy}{y^3}  =  \frac{x}{ (1 + x^2)^{\frac{1}{2} }} dx

     \int\limits { \frac{dy }{y^3} } \,    =  \int\limits {\frac{x}{(1 + x^2) ^{\frac{1}{2} }} } \, dx

=>    - \frac{1}{2y^2}  =  (1 + x^2)^{\frac{1}{2} }+ C

From the question we are told that at y(0) =  1

     - \frac{ 1}{2 * (1) } =  (1 + (0)^2)^{\frac{1}{2} } + C

     C =  - \frac{3}{2}

So

       - \frac{1}{2y^2}  =  (1 + x^2)^{- \frac{1}{2}}  - \frac{3}{2}      

     \frac{1}{y^2}  =  3-2(1 + x^2)^{\frac{1}{2} }

     y^2 = \frac{1}{ 3 - 2 (1 + x^2 ) ^{\frac{1}{2} }}    

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3 years ago
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