**NEED HELP ASAP WILL GIVE BRAINIEST TO FASTEST ANSWER IF CORRECT**

Use the substitution method to solve the system of equations. Choose the correct ordered pair.

andrezito [222]

2*4+3y=29
3y=21
y=7
x=4 choice c

7 0

3 years ago

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3y''-6y'+6y=e*x sexcx

Simora [160]

From the homogeneous part of the ODE, we can get two fundamental solutions. The characteristic equation is

$3r^2-6r+6=0\iff r^2-2r+2=0$

which has roots at $r=1\pm i$ . This admits the two fundamental solutions

$y_1=e^x\cos x$
$y_2=e^x\sin x$

The particular solution is easiest to obtain via variation of parameters. We're looking for a solution of the form

$y_p=u_1y_1+u_2y_2$

where

$u_1=-\displaystyle\frac13\int\frac{y_2e^x\sec x}{W(y_1,y_2)}\,\mathrm dx$
$u_2=\displaystyle\frac13\int\frac{y_1e^x\sec x}{W(y_1,y_2)}\,\mathrm dx$

and $W(y_1,y_2)$ is the Wronskian of the fundamental solutions. We have

$W(e^x\cos x,e^x\sin x)=\begin{vmatrix}e^x\cos x&e^x\sin x\\e^x(\cos x-\sin x)&e^x(\cos x+\sin x)\end{vmatrix}=e^{2x}$

and so

$u_1=-\displaystyle\frac13\int\frac{e^{2x}\sin x\sec x}{e^{2x}}\,\mathrm dx=-\int\tan x\,\mathrm dx$
$u_1=\dfrac13\ln|\cos x|$

$u_2=\displaystyle\frac13\int\frac{e^{2x}\cos x\sec x}{e^{2x}}\,\mathrm dx=\int\mathrm dx$
$u_2=\dfrac13x$

Therefore the particular solution is

$y_p=\dfrac13e^x\cos x\ln|\cos x|+\dfrac13xe^x\sin x$

so that the general solution to the ODE is

$y=C_1e^x\cos x+C_2e^x\sin x+\dfrac13e^x\cos x\ln|\cos x|+\dfrac13xe^x\sin x$

7 0

3 years ago

10 POINTS PLEASE HELP

Llana [10]

Answer:

A company sells tents in two styles, shown below.

The sides and floor of each tent made of nylon.

For tunnel tent:

In a composite figure of tunnel tent :

There are two semi circle, half cylindrical shape and its base is made of Square.

Area of semi-circle is given by:

where r is the radius the circle.

Here, Diameter(d) = 8 feet

We know that: Diameter(d) = 2 r

then;

8 = 2r

⇒ r= 4 ft.

Area of square =

then;

Area of square = square ft

Lateral surface area of cylinder = where r is the radius and h is the height

Here, h = 8 ft

Lateral surface area of half cylinder = square ft

Total Surface area of tunnel tent(S)=2(Area of semi-circle)+(Lateral surface area of half cylindrical)+(Area of square)

Substitute the given values we have;

square ft.

For Pup tent:

Each side of tent = 8 ft

In a figure of Pup tent:

There are 3 square shape and two triangle.

Area of square =

then;

Area of square = square ft

Area of a triangle is given by:

Each side of a triangle is same.

This is an equilateral triangle, and its height is given by:

then;

Area of triangle = square ft.

Substitute the given values we have;

Total surface area of Pup tent(S')

= square ft.

⇒S' > S

therefore, the tunnel tent require less nylon to manufacture.

<h2 /><h2>PLZ GIMME BRAINLIEST :)) !!!!!!</h2>

6 0

4 years ago

a box of crayons costs $1.75, including tax. mr. valentino wants to purchase boxes of crayons for his class and has a $25 budget

Murljashka [212]

The answer to this question is $1.75x ≤ $25

7 0

4 years ago

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Water is frozen at what degree

Jet001 [13]

Water can freeze at 32 degrees f

3 0

3 years ago

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