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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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The first two terms in an arithmetic progression are -2 and 5. The last term in the progression is the only number in the progre
Rudik [331]

Given:

The first two terms in an arithmetic progression are -2 and 5.

The last term in the progression is the only number in the progression that is greater than 200.

To find:

The sum of all the terms in the progression.

Solution:

We have,

First term : a=-2

Common difference : d = 5 - (-2)

                                      = 5 + 2

                                      = 7

nth term of an A.P. is

a_n=a+(n-1)d

where, a is first term and d is common difference.

a_n=-2+(n-1)(7)

According to the equation, a_n>200.

-2+(n-1)(7)>200

(n-1)(7)>200+2

(n-1)(7)>202

Divide both sides by 7.

(n-1)>28.857

Add 1 on both sides.

n>29.857

So, least possible integer value is 30. It means, A.P. has 30 term.

Sum of n terms of an A.P. is

S_n=\dfrac{n}{2}[2a+(n-1)d]

Substituting n=30, a=-2 and d=7, we get

S_{30}=\dfrac{30}{2}[2(-2)+(30-1)7]

S_{30}=15[-4+(29)7]

S_{30}=15[-4+203]

S_{30}=15(199)

S_{30}=2985

Therefore, the sum of all the terms in the progression is 2985.

6 0
3 years ago
What is 2x . 5x . 79x
murzikaleks [220]

Answer:

790x

may i am correct

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3 0
2 years ago
Orlando's sports-card collection features players from four teams, as shown in the table below
alukav5142 [94]

Answer:D

Step-by-step explanation:

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8 0
3 years ago
Can anyone help me I don’t understand plz
Citrus2011 [14]

There we have an information of two functions g(t)\,  and \, h(t)

Using this two functions g(t)\,  and \, h(t), we need to find the composition of functions (h\circ g)(t).

The composition of two functions h and g is the new function , by performing g first and then performing h.

(h\circ g)(t)=h(g(t))

g(t)=3(t+1)

h(t)=2t

Composition of h and g (t) = (h\circ g)(t)

=h(g(t))

First plugin the value of g(t)=3(t+1)

h(g(t))=h(3(t+1))

=h(3t+3)

We know that h(t)=2t, we need to find h(3t+3),

That is, to replace t by 3t+3,

=2(3t+3)

Now distribute 2 into 3t+3,

=6t+6

Now plug in t=-6,

h(g(-6))=6(-6)+6

=-36+6 \\ =-30

Thus the solution is (D). h(g(-6))=-30.

5 0
3 years ago
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A GRAPH THAT DOES NOT CROSS THE ORIGINS IS<br> CONSIDERED a what
Morgarella [4.7K]

Answer:

non linear graph

Step-by-step explanation:

3 0
2 years ago
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