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Pani-rosa [81]
3 years ago
15

List the numbers that have 30 as a multiple

Mathematics
1 answer:
olga2289 [7]3 years ago
3 0
First we list the multiples of each number.
multiples of 5 are 10,15,20,25,30,35,40,...
multiples of 6 are 12,18,24,30,36,42,48,...
multiples of 15 are 30,45,60,75,90,...
now, when you look at the list of multiples, you can see that 30 is the smallest number that appears in each list.
therefore, the least common multiple of...... 5,6 and 15 is 30.
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If 20 divided by 5 = 4 <br> Then 20 divided by 5.5=4.?
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Determine the singular points of the given differential equation. Classify each singular point as regular or irregular. (Enter y
Zina [86]

Answer:

Step-by-step explanation:

The given differential equation is:

x^3y'' + 2x^2y' + 4y

the main task here is to determine the singular points of the given differential equation and Classify each singular point as regular or irregular.

So, for a regular singular point ;  x=x_o is  located at the first power in the denominator of P(x) likewise at the Q(x) in the second power of the denominator. If that is not the case, then it is termed as an irregular singular point.

Let first convert it to standard form by dividing through with x³

y'' + \dfrac{2x^2y'}{x^3} + \dfrac{4y}{x^3} =0

y'' + \dfrac{2y'}{x} + \dfrac{4y}{x^3} =0

The standard form of the differential equation is :

\dfrac{d^2y}{dy} + P(x) \dfrac{dy}{dx}+Q(x)y =0

Thus;

P(x) = \dfrac{2}{x}

Q(x) = \dfrac{4}{x^3}

The zeros of x,x^3  is 0

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Classify each singular point as regular or irregular.

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p(x) = xP(x)

p(x) = x*\dfrac{2}{x}

p(x) = 2

q(x) = x²Q(x)

q(x) = x^2 * \dfrac{4}{x^3}

q(x) =\dfrac{4}{x}

The function (f) is analytic if at a given point a it is represented by power series in x-a either with a positive or infinite radius of convergence.

Thus ; from above; we can say that q(x) is not analytic  at x = 0

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Thus, the point x =0 is an irregular singular point

6 0
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