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3 years ago

StartFraction 2 Over n EndFraction = two-thirds

Mathematics

1 answer:

Vitek1552 [10]3 years ago

4 0

Answer:

n = 3

Step-by-step explanation:

Let's consider the following proportion.

2/n = 2/3

To solve a proportion, we can use the rule that states that <em>the product of the end-terms is equal to the products of the inner-terms</em>. That is,

end-term × end-term = inner-term × inner-term

2 × 3 = 2 × n

6 = 2 × n

We can solve for n, dividing both terms by 2.

6/2 = 2 × n/2

n = 3

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Answer:

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Step-by-step explanation:

The problem is very simple, since they give us the solution from the start. However I will show you how they came to that solution:

A differential equation of the form:

$a_n y^n +a_n_-_1y^{n-1}+...+a_1y'+a_oy=0$

Will have a characteristic equation of the form:

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Where solutions $r_1,r_2...,r_n$ are the roots from which the general solution can be found.

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For real repeated roots the solution is given by:

$y(t)=c_1e^{rt} +c_2te^{rt}$

For complex roots the solution is given by:

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Where:

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Let's find the solution for $x''+x=0$ using the previous information:

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Therefore, the solution is:

$x(t)=c_1cos(t)+c_2sin(t)$

As you can see, is the same solution provided by the problem.

Moving on, let's find the derivative of $x(t)$ in order to find the constants $c_1$ and $c_2$ :

$x'(t)=-c_1sin(t)+c_2cos(t)$

Evaluating the initial conditions:

$x(0)=-1\\\\-1=c_1cos(0)+c_2sin(0)\\\\-1=c_1$

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Now we have found the value of the constants, the solution of the second-order IVP is:

$x=-cos(t)+2sin(t)$

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Please help and show ur work:)

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3/4...there’s no work to show

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