14 3/5 in decimal form show the work

First change to standard form of first order linear differential equation and then by finding the appropriate integrating factor

Leokris [45]

Answer:

Step-by-step explanation:

Given is a Differential equation as

$xy' + y = lnx ; y(e)=1$

To bring it to linear form we can divide the full equation by x

$y'+\frac{y}{x} =\frac{ln x}{x}$

This is of the form

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

p(x) = 1/x

So find

$e^{\int\limits{\frac{1}{x} } \, dx } = e^{ln x} = x$

Solution is

$xy = \int {x*lnx /x } \, dx =xln x -x +C$

Use the initial value as y(e) =1

$e= eln e -e+C\\C=e$

So solution is

$xy =xln x -x+e$

5 0

3 years ago

Find all real solutions of the polynomial equation. (enter your answers as a comma-separated list.) z^4 + z^3 + z^2 + 3z − 6 = 0

viva [34]

I can't figure out a factor for this but graphing it shows x = -2 and +1 as real roots.

3 0

4 years ago

Consider the following system of equations:

IrinaK [193]

Answer:

x = 6 ; y = -9

Step-by-step explanation:

8 x + 2 y = 30 ..........equ No 1

7 x + 2 y = 24......... equ No 2

8 x = 30 - 2y

∴ x = $\frac{ 30 - 2 y}{8}$

substituting the value of x in equ No 2

7 $\frac{30 - 2 y}{8}$ + 2 y = 24

7 ( 30 -2 y) + 2 y × 8 = 24 × 8

7 × 30 - 14 y + 16 y = 192

210 + 2 y = 192

2 y = 192 - 210

2 y = - 18

∴ y = - 9

put y = -9 , 8 x = 30 - 2 y

8 x = 30 - 2 ( -9)

8 x = 30 - ( -18)

8 x = 48

∴ x = 6

x = 6 ; y = -9

3 0

3 years ago

Mitra created a mosaic design using square 2x2 cm white tiles and 2x3 cm rectangular centimeter black tiles. She used twice as m

zvonat [6]

Mitra used 156 white tiles of 2x2 cm and 76 black tiles of 2x3 cm to form a pattern with an area of 1092 cm²

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the number of white tiles and y represent the number of black tiles.

Area of white tiles = 2 cm * 2 cm = 4 cm²

Area of black tiles = 2 cm * 3 cm = 6 cm²

She used twice as many white tiles as black tiles. Hence:

x = 2y (1)

Also, the finished pattern was 1092 square centimeters in area. Hence:

4x + 6y = 1092 (2)

From both equations:

x = 156, y = 78

Mitra used 156 white tiles of 2x2 cm and 76 black tiles of 2x3 cm to form a pattern with an area of 1092 cm²

Find out more on equation at: brainly.com/question/2972832

#SPJ1

3 0

2 years ago

HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

andre [41]

Answer:

Option A is correct.

Step-by-step explanation:

If Δ YES ∼ Δ NOT, then it means that ΔYES and ΔNOT are similar triangles.

The similar triangles means that all the corresponding angles of the two triangles are same i.e. ∠ Y = ∠ N, ∠ E = ∠ O and ∠ S = ∠ T

Therefore, according to the property of similar triangles we can write that

$\frac{NO}{YE} = \frac{OT}{ES} = \frac{NT}{YS}$ .

Therefore, option A is correct.

8 0

3 years ago