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3 years ago

The standard equation of a circle with center (h.k) and radius r is (% - hy * (y - Ky = p. Which

Mathematics

1 answer:

zlopas [31]3 years ago

3 0

Answer:

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Determine the singular points of the given differential equation. Classify each singular point as regular or irregular. (Enter y

ludmilkaskok [199]

Answer:

Step-by-step explanation:

Given that:

The differential equation; $(x^2-4)^2y'' + (x + 2)y' + 7y = 0$

The above equation can be better expressed as:

$y'' + \dfrac{(x+2)}{(x^2-4)^2} \ y'+ \dfrac{7}{(x^2- 4)^2} \ y=0$

The pattern of the normalized differential equation can be represented as:

y'' + p(x)y' + q(x) y = 0

This implies that:

$p(x) = \dfrac{(x+2)}{(x^2-4)^2} \$

$p(x) = \dfrac{(x+2)}{(x+2)^2 (x-2)^2} \$

$p(x) = \dfrac{1}{(x+2)(x-2)^2}$

Also;

$q(x) = \dfrac{7}{(x^2-4)^2}$

$q(x) = \dfrac{7}{(x+2)^2(x-2)^2}$

From p(x) and q(x); we will realize that the zeroes of (x+2)(x-2)² = ±2

When x = - 2

$\lim \limits_{x \to-2} (x+ 2) p(x) = \lim \limits_{x \to2} (x+ 2) \dfrac{1}{(x+2)(x-2)^2}$

$\implies \lim \limits_{x \to2} \dfrac{1}{(x-2)^2}$

$\implies \dfrac{1}{16}$

$\lim \limits_{x \to-2} (x+ 2)^2 q(x) = \lim \limits_{x \to2} (x+ 2)^2 \dfrac{7}{(x+2)^2(x-2)^2}$

$\implies \lim \limits_{x \to2} \dfrac{7}{(x-2)^2}$

$\implies \dfrac{7}{16}$

Hence, one (1) of them is non-analytical at x = 2.

Thus, x = 2 is an irregular singular point.

5 0

2 years ago

Select all the simplified expression <br>

sineoko [7]

Answer:

1 / 3^5

1/ 243

Step-by-step explanation:

3^4 ÷ 3^9

We know that a^b ÷ a^c = a^ ( b-c)

3 ^ ( 4-9)

3^ -5

We can rewrite this as a^-b = 1/ a^b

1 / 3^5

We know that 3^5 = 243

1/ 243

5 0

2 years ago

Read 2 more answers

X + y = -15, what is the answer?

kvv77 [185]

Answer:

10+5=15

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

I have no idea what the answers are

lara [203]

Hello from MrBillDoesMath!

Answer:

Top line: y = (2/3)x + 2

Bottom line: y = (2/3)x -1

Discussion:

The graph provided is hard to read but I did the best I could.

The top line appears to pass through the points (0,2) and (-3,0)

For this line

m = change y /change x = (0-2)/(-3-0) = -2/-3 = +2/3. So

y = mx + b => y = (2/3) x+ b. As the line passes through (0,2) set x = 0, y= 2 in y = (2/3)x + b =>

2 = (2/3) 0 + b => b = 2

Therefore y = (2/3)x + 2

The bottom line appears to pass through the points (0,-1) and (3,1)

For this line

m = change y /change x = (1-(-1)) /(3-0) = +2/-3. So

y = mx + b => y = (2/3) x+ b. As the line passes through (0,-1) set x = 0, y= -1 in y = (2/3)x + b =>

-1 = (2/3) 0 + b => b = -1

Therefore y = (2/3)x + -1

Thank you,

MrB

5 0

3 years ago

If you select a card at random, what is the probability of getting:A number smaller than 5 (counting the ace as a 1)?

garri49 [273]

4 Aces, 4 2's, 4 3's 4 4's

= 16 cards total out of 52 cards

so probability would be 16/52 which reduces to 4/13

4 0

3 years ago