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andre [41]
3 years ago
6

Solve the differential equation x^3y"'− 3x^2 y" 6xy'−6y = 0.

Mathematics
1 answer:
Anna [14]3 years ago
3 0
<span>Equation at the end of step  1  :</span><span> (((x3)•y)-(((3x2•y6)•x)•y))-6y = 0 </span><span>Step  2  :</span><span>Step  3  :</span>Pulling out like terms :

<span> 3.1 </span>    Pull out like factors :

  <span> -3x3y7 + x3y - 6y</span>  =  <span> -y • (3x3y6 - x3 + 6)</span> 

Trying to factor a multi variable polynomial :

<span> 3.2 </span>   Factoring   <span> 3x3y6 - x3 + 6</span> 

Try to factor this multi-variable trinomial using trial and error<span> 

 </span>Factorization fails

<span>Equation at the end of step  3  :</span><span> -y • (3x3y6 - x3 + 6) = 0 </span><span>Step  4  :</span>Theory - Roots of a product :

<span> 4.1 </span>   A product of several terms equals zero.<span> 

 </span>When a product of two or more terms equals zero, then at least one of the terms must be zero.<span> 

 </span>We shall now solve each term = 0 separately<span> 

 </span>In other words, we are going to solve as many equations as there are terms in the product<span> 

 </span>Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

<span> 4.2 </span>     Solve  :    -y = 0<span> 

 </span>Multiply both sides of the equation by (-1) :  y = 0 

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Answer:

a.) First check on the height of the bar that ranges between 20 and 24 which is 6. The 6 is the number of students who bought 20 books or more, so get the percentage of those students who bought 20 or more books; divide 6 which is the number of students who bought 20 books or more with the total number of students which is 40 then multiply with 100.

% of students who bought 20 or more books = 6/40 ×100

=15

Step-by-step explanation:

b.) Find the area of a trapezium

= 1/2 × {a+b} × h

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= 132

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4 0
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When solving a linear inequality, what is different compared to solving a linear equa- tion? For which steps do you have to hbe
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Answer:

See explanation below

Step-by-step explanation:

When solving a linear inequality, the main difference resides in the following:

When we change the signs of the terms (either from positive to negative or from negative to positive) we have to change the sign of the inequality (if the sign was ≥, we change it to ≤, if the sign was ≤, we change it to ≥). Therefore we have to be more careful while doing this.

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How long will it take for a sum of $800 attracting simple interest to become $830 if the rate is 9%? Compute the return on this
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Answer:

5 months

ROI = 3.75 %

Step-by-step explanation:

Since,

The simple interest formula,

I=P\times r\times t

Where,

P = Principal amount,

r = rate per period ( in decimal )

t = number of periods,

Here, P = 800, r = 9% = 0.09,

If A is the future amount,

We have, A = 830

I = A - P = 830 - 800 = 30

By substituting the values in the above formula,

30=800\times 0.09\times t

30=72t

\implies t =\frac{30}{72}=\frac{5}{12}

Hence, it will take 5 months.  ( 1 year = 12 months )

Now,

\text{Return on investment }=\frac{I}{P}\times 100

=\frac{30}{800}\times 100

=3.75\%

3 0
3 years ago
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