Eric has 4 bags of marbles and 6 single marbles how many marbles does eric have

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

3 years ago

Find the measure of angle A

Ray Of Light [21]

In the fist you have to know: any angle opposite the head is equal in measurement.
so now we know one angle in the triangle it is 82
All corners of the triangle are equal 180
so we have to do this 180-82=98
so we have to collection (4x+8)+(8x-6)=98
12x+2=98
12x=96
x=8
4(8)+8=40
the answer is 40

8 0

2 years ago

What is 1/6x=4 in solving equations with rational coefficients

Debora [2.8K]

To solve an equation with a rational (fraction) coefficient you need to multiply both sides of the equation by the reciprocal (invert the fraction - flip it).

$\frac{1}{6}x =4$ The reciprocal of 1/6 is 6/1 or 6
$6( \frac{1}{6} x)= 6(4)$ The product of reciprocals equals 1
1x = 24
x = 24

7 0

3 years ago

A paddleboat can move at a speed of 4 km/h in still water. The boat is paddled 12 km downstream in a river in the same time it

Bas_tet [7]

Answer:

Speed of the river = $\frac{4}{3}$ km per hour

Step-by-step explanation:

Speed of the boat in still water = 4 km per hour

Let the speed of the river = v km per hour

Speed of the boat upstream = (4 - v) km per hour

Time taken to cover 6 km = $\frac{\text{Distance}}{\text{Speed}}$

= $\frac{6}{4-v}$ hours

Speed of the boat downstream = (4 + v) km per hour

Time taken to cover 12 km = $\frac{12}{4+v}$ hours

Since, time taken by the boat in both the cases is same,

$\frac{6}{4-v}= \frac{12}{4+v}$

6(4 + v) = 12(4 - v)

24 + 6v = 48 - 12v

12v + 6v = 48 - 24

18v = 24

v = $\frac{24}{18}$

v = $\frac{4}{3}$ km per hour

3 0

3 years ago

Find two numbers, if … b Their sum is −7 and their difference is 14

Delicious77 [7]

Answer:

x=0

y=-21/7

Step-by-step explanation:

Let the two unknown be x and y

x+y=-7...(1)

x-y=14...(2)

From (1) make x the subject of formula

x=-7-y...(3)

Substitute (3) into (2)

-7-y-y=14

-7-2y=14

Add 7 to both sides

-2y=21

Add both sides by-2

y=-21/2

Substitute the value of y into (3)

x=-7-(-21/2)

x=-7+21/3

Lcm

x=-21+21/3

x=0/3

x=0

4 0

3 years ago