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Softa [21]
3 years ago
7

-5 2/3- (-6 1/5)+ 1 7/12 Show how please

Mathematics
1 answer:
blagie [28]3 years ago
4 0

Answer:

2⁷/₆₀  

Step-by-step explanation:

-5⅔ - (-6⅕) + 1⁷/₁₂

1. Remove parentheses

-5⅔ - (-6⅕) + 1⁷/₁₂ = -5⅔ + 6⅕+ 1⁷/₁₂

2. Convert the fractions to their lowest common denominators.

The lowest common denominator of 3, 5,  and 12 is 60. Thus

-5⅔ + 6⅕+ 1⁷/₁₂ = -5⁴⁰/₆₀ + 6¹²/₆₀+ 1³⁵/₆₀

3. Add integers and fractions separately

\begin{array}{lr}-5 & -\dfrac{40}{60} \\\\+6 & \dfrac{12}{60} \\\\+1 & \dfrac{35}{60} \\\\\mathbf{2} & \mathbf{\dfrac{7}{60}} \\\end{array}

4. Add the integer and the fraction

2 + ⁷/₆₀ = 2⁷/₆₀

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Step-by-step explanation:

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Step-by-step explanation:

Any complex number is of the form: a + bi where a is real part and B is imaginary part.

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Hence, first two options are correct.

Last two options are incorrect because of the following reasons:

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Find the general solution of the given differential equation.y^(4)+18y"+81y=0
kotykmax [81]

Answer:

The general solution of the given differential equation

y =  ( c_{1} + c_{2} x ) cos3 x + (  c_{3} +c_{4} x) sin3 x

Step-by-step explanation:

Step(I):-

Given differential equation

                                   y⁴+18y"+81y=0

                         ⇒    (D⁴+18D²+81)y =0

The auxiliary equation

                               m^4+18m^2+81 =0

                              (m^2)^{2} + 2 (9) m^{2} +(9)^2 = 0

        we will use formula  ( a + b)² = a² + 2 a b + b²    

                  ⇒    ( m² + 9 ) ² = 0

                   ⇒    ( m² + 9 ) ( m² + 9 ) = 0

                      m^{2} =-9\\m= - 3i and m=3i

            m² + 9 = 0      

      m² = -9\\m= -3i and m=3i

The complex roots are   0± 3 i ,0 ± 3 i

<em>Step(ii)</em>:-

The complementary function  

              y = e^{\alpha x } ( c_{1} + c_{2} x ) cos\beta x + (  c_{3} +c_{4} x) sin\beta x

The general solution of the given differential equation

          y = e^{0 x } ( c_{1} + c_{2} x ) cos3 x + (  c_{3} +c_{4} x) sin3 x

The general solution of the given differential equation

   y =  ( c_{1} + c_{2} x ) cos3 x + (  c_{3} +c_{4} x) sin3 x    



             



3 0
3 years ago
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