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2 years ago

PLEASE HELP!!!

Mathematics

1 answer:

elena-s [515]2 years ago

7 0

Coordinates after 270 clockwise rotation is (-6,-2), (-3,-5) and (-8, -5).

<h3>What is graph?</h3>

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given coordinates are: (-2,6) , (-5, 3) and (-5, 8)

For 270° clockwise about the origin, we have the following rule:

(x, y)= (-y, x)

So,

coordinates (-2,6) change into (-6,-2)

coordinates (-5, 3) change into (-3,-5)

coordinates (-5, 8) change into (-8, -5).

Learn more about this concept here:

brainly.com/question/12673036

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Consider the following differential equation to be solved by undetermined coefficients. y(4) − 2y''' + y'' = ex + 1 Write the gi

kompoz [17]

Answer:

The general solution is

$y= (C_{1}+C_{1}x) e^0x+(C_{3}+C_{4}x) e^x +\frac{1}{2} (e^x(x^2-2x+2)-e^x(2(x-1)+e^x(2))$

+ $\frac{x^2}{2}$

Step-by-step explanation:

Step :1:-

Given differential equation y(4) − 2y''' + y'' = e^x + 1

The differential operator form of the given differential equation

$(D^4 -2D^3+D^2)y = e^x+1$

comparing f(D)y = e^ x+1

The auxiliary equation (A.E) f(m) = 0

$m^4 -2m^3+m^2 = 0$

$m^2(m^2 -2m+1) = 0$

$(m^2 -2m+1) this is the expansion of (a-b)^2$

$m^2 =0 and (m-1)^2 =0$

The roots are m=0,0 and m =1,1

complementary function is $y_{c} = (C_{1}+C_{1}x) e^0x+(C_{3}+C_{4}x) e^x$

<u>Step 2</u>:-

The particular equation is $\frac{1}{f(D)} Q$

P.I = $\frac{1}{D^2(D-1)^2} e^x+1$

P.I = $\frac{1}{D^2(D-1)^2} e^x+\frac{1}{D^2(D-1)^2}e^{0x}$

P.I = $I_{1} +I_{2}$

$\frac{1}{D^2} (\frac{x^2}{2!} )e^x + \frac{1}{D^{2} } e^{0x}$

$\frac{1}{D} means integration$

$\frac{1}{D^2} (\frac{x^2}{2!} )e^x = \frac{1}{2D} \int\limits {x^2e^x} \, dx$

applying in integration u v formula

$\int\limits {uv} \, dx = u\int\limits {v} \, dx - \int\limits ({u^{l}\int\limits{v} \, dx } )\, dx$

$I_{1}$ = $\frac{1}{D^2(D-1)^2} e^x$

$\frac{1}{2D} (e^x(x^2)-e^x(2x)+e^x(2))$

$\frac{1}{2} (e^x(x^2-2x+2)-e^x(2(x-1)+e^x(2))$

$I_{2}$ $= \frac{1}{D^2(D-1)^2}e^{0x}$

$\frac{1}{D} \int\limits {1} \, dx= \frac{1}{D} x$

again integration $\frac{1}{D} x = \frac{x^2}{2!}$

The general solution is $y = y_{C} +y_{P}$

$y= (C_{1}+C_{1}x) e^0x+(C_{3}+C_{4}x) e^x +\frac{1}{2} (e^x(x^2-2x+2)-e^x(2(x-1)+e^x(2))$

+ $\frac{x^2}{2!}$

3 0

3 years ago

Simplify the following expression (3x^2y)^3

kolezko [41]

Answer:

$\large\boxed{\left(3x^2y\right)^3=27x^6y^3}$

Step-by-step explanation:

$\text{Use}\ (ab)^n=a^nb^n\ \text{and}\ (a^n)^m=a^{nm}\\\\\left(3x^2y\right)^3=3^3(x^2)^3y^3=27x^6y^3$

6 0

3 years ago

Researchers randomly surveyed people at two amusement parks, Funland and Thrillville, to find out how many times they visit the

STALIN [3.7K]

On average, people visit Thrillville 2 more times per year than Funland.

<h3><u>Averages</u></h3>

To determine how many more times per year, on average, do people visit Thrillville than Funland, the following calculation must be performed:

Funland: 4,1,2,1,5,6,3,2,4,3,2,6,1,3,2 = 45
45 / 15 = 3
Thrillville: 8,6,5,7,2,5,4,2,1,9,3,8,3,7,5,2,9,4,2,8 = 100
100 / 20 = 5
5 - 3 = 2

Therefore, on average, people visit Thrillville 2 more times per year than Funland.

Learn more about averages in brainly.com/question/2426692

4 0

2 years ago

Solve for x:5x/2=330/4

bezimeni [28]

First we have to get x by itself, so we multiply two on each side,

then we get 5x=660/4, I like to simplify here, so I would change it to 5x=165, then we divide each side by 5

x=33

:)

5 0

3 years ago

Sven can type 30 words per minute.How many words would he type in 20 minutes?

saveliy_v [14]

30 x 20=600
your answer is that he would type 600 words in 20 minutes.

8 0

3 years ago