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Artyom0805 [142]

3 years ago

8

Mr. Standford’s greenhouse has the dimensions shown. The volume of the greenhouse is 90 cubic yards. Find the missing dimension

of the greenhouse.

1 answer:

salantis [7]3 years ago

3 0

Hey read the image I have attached. Ignore what I am typing here I need to type 20 characters.

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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

What is the growth rate for 3x-y=8x-7

nydimaria [60]

Answer:

you mean like this :))

-5x +7 = Y

Step-by-step explanation:

3x - y = 8x - 7

<=>3x - 8x = y - 7

<=>-5x = y - 7

<=>-5x + 7 = Y

8 0

3 years ago

How is a net useful when finding the surface area of prisms and pyramids?

Sladkaya [172]

I believe it is because with a net you simply find the area, and measuring 2D shapes is far easier than 3D shapes.
Hope this helped!
- Z

5 0

2 years ago

Latasha bought a concert ticket. She does not remember the price of the ticket, but she remembers that she had to pay $1 in tax.

docker41 [41]

Answer:

Original price of ticket = $12.5

Step-by-step explanation:

Given:

8% amount = $1

Find:

Original price of ticket

Computation:

Original price of ticket = 1(100/8)

Original price of ticket = $12.5

7 0

2 years ago

What does 144 =to for a squared

Dafna11 [192]

12 *12 = 144

Therefore 12^2 = 144

5 0

2 years ago

Read 2 more answers