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mr_godi [17]
3 years ago
5

PLEASE HELP ASAP!! :D

Mathematics
1 answer:
MaRussiya [10]3 years ago
4 0

Answer:

x+39°+93°=180°

x+132°=180°

x=180°-132°

x=148°

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478 divided 16 using partial quotients
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In partial quotients, it need several steps before it can  find the quotient.

Example : 
      16    |     478    |
                  - 320   |  20
                   158     |         
                   -144    | 9
                     12

Since 12 is less than 16, it now became a remainder

so the answer is 29 R 12

hope this helps

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3 years ago
Find a linear second-order differential equation f(x, y, y', y'') = 0 for which y = c1x + c2x3 is a two-parameter family of solu
Alisiya [41]
Let y=C_1x+C_2x^3=C_1y_1+C_2y_2. Then y_1 and y_2 are two fundamental, linearly independent solution that satisfy

f(x,y_1,{y_1}',{y_1}'')=0
f(x,y_2,{y_2}',{y_2}'')=0

Note that {y_1}'=1, so that x{y_1}'-y_1=0. Adding y'' doesn't change this, since {y_1}''=0.

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f(x,y,y',y'')=y''+xy'-y=0

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To make sure everything cancels out, multiply the second degree term by -\dfrac{x^2}3, so that

f(x,y,y',y'')=-\dfrac{x^2}3y''+xy'-y

Then if y=y_1+y_2, we get

-\dfrac{x^2}3(0+6x)+x(1+3x^2)-(x+x^3)=-2x^3+x+3x^3-x-x^3=0

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