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4 years ago

What's the solution to |1x-12| < 15

1 answer:

5 0

Start with |1x - 12| < 15. Add 12 to both sides. Then |1x - 12 + 12| < 15 + 12

Simplifying, |x| < 27. Then the two solutions are x < 27 and x > -27. In words, the solution set is the set of all x greater than -27 and less than +27.

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6/9 - 1/2 in simplest fraction form ppllleeeaasseee

Citrus2011 [14]

6/9 - 1/2 = 3/18 = 1/6

So, 9 and 2 is equivanlent to 19

and 6/9 x 2 = 12/18

1/2 x 9 = 9/18

so it's

12/18 - 9/18 = 3/18 = 1/6

I hope this helps

3 0

3 years ago

Using power series, solve the LDE: (2x^2 + 1) y" + 2xy' - 4x² y = 0 --- - -- -

sattari [20]

We're looking for a solution of the form

$y=\displaystyle\sum_{n\ge0}a_nx^n$

with derivatives

$y'=\displaystyle\sum_{n\ge0}(n+1)a_{n+1}x^n$

$y''=\displaystyle\sum_{n\ge0}(n+2)(n+1)a_{n+2}x^n$

Substituting these into the ODE gives

$\displaystyle\sum_{n\ge0}\left(\bigg(2(n+2)(n+1)a_{n+2}-4a_n\bigg)x^{n+2}+2(n+1)a_{n+1}x^{n+1}+(n+2)(n+1)a_{n+2}x^n\right)=0$

Shifting indices to get each term in the summand to start at the same power of $x$ and pulling the first few terms of the resulting shifted series as needed gives

$2a_2+(2a_1+6a_3)x+\displaystyle\sum_{n\ge2}\bigg((n+2)(n+1)a_{n+2}+2n^2a_n-4a_{n-2}\bigg)x^n=0$

Then the coefficients in the series solution are given according to the recurrence

$\begin{cases}a_0=y(0)\\\\a_1=y'(0)\\\\a_2=0\\\\2a_1+6a_3=0\implies a_3=-\dfrac{a_1}3\\\\a_n=\dfrac{-2(n-2)^2a_{n-2}+4a_{n-4}}{n(n-1)}&\text{for }n\ge4\end{cases}$

Given the complexity of this recursive definition, it's unlikely that you'll be able to find an exact solution to this recurrence. (You're welcome to try. I've learned this the hard way on scratch paper.) So instead of trying to do that, you can compute the first few coefficients to find an approximate solution. I got, assuming initial values of $y(0)=y'(0)=1$ , a degree-8 approximation of

$y(x)\approx1+x-\dfrac{x^3}3+\dfrac{x^4}3+\dfrac{x^5}2-\dfrac{16x^6}{45}-\dfrac{79x^7}{125}+\dfrac{101x^8}{210}$

Attached are plots of the exact (blue) and series (orange) solutions with increasing degree (3, 4, 5, and 65) and the aforementioned initial values to demonstrate that the series solution converges to the exact one (over whichever interval the series converges, that is).

5 0

3 years ago

Consider the sequence following a minus 8 pattern: 9, 1, −7, −15, ….

photoshop1234 [79]

Answer: -287

Step-by-step explanation:

The given pattern: 9, 1, -7, -15, ….

We observe that ,

First term : a=9

Common difference between the terms= 1-9=-8

For Arithmetic sequence , the formula to find the nth term is given by :-

$a_n=a+(n-1)d$

Then, 38th term will be :-

$a_{38}=9+(-8)(38-1)\\\\=9-8(37)=9-296=-287$

Hence, the 38th term of the sequence.= -287

3 0

3 years ago

what is the total number of unique triangles that can be made with the side lengths of 4cm, 5cm, and 10cm can be drawn? PLS HELP

Novay_Z [31]

Answer:

One

Step-by-step explanation:

First, we need to check a triangle with these sides is possible. Since 4 plus 5 is 9, and 9 is less than 10, we can make a triangle with these sides.

To answer the question, we can only make one unique triangle. Why? They give us three lengths and a triangle has three sides.

However, if they are counting a triangle in different positions the answer will be greater. Since it would just be the same triangle, I am going with the answer of only one.

7 0

2 years ago

6. True or False: Common logarithms are logarithms with a base of 10.

deff fn [24]

Answer:

true

Step-by-step explanation:

5 0

3 years ago