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3 years ago

12

HELP HELP PLEASE!!! <3

2 answers:

zmey [24]3 years ago

4 0

12 x 12 = 144, 144 x 3 and then subtract 5 to get 427

ArbitrLikvidat [17]3 years ago

4 0

Answer:

427

Step-by-step explanation:

f(x)=3x^2-5

f(x)=3(-12)^2-5=427

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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 explicit formula for this geometric sequence?

victus00 [196]

Answer:

The explicit formula for this geometric sequence is 27.3(n-1)

4 0

3 years ago

-5x+1+2x+2=-2+2x<br> I’m super lost

DaniilM [7]

Are you trying to simplify the equation? if so, combine the like terms on each side first. -3x + 3 = -2 + 2x. Then simplify, -5x = -5. And solve, x = 1

3 0

3 years ago

An ice cream cone is filled with vanilla and chocolate ice cream at a ratio of 2:1. If the diameter of the cone is 2 inches and

Sophie [7]

Volume of cone=(1/3)hpir^2

d/2=r
d=2
d/2=2/2=1=r
h=6

V=(1/3)6pi1^2
V=2pi in^3 is volume

ratio of 2:1

2+1=3
2pi=3 units
divide both sides by 3
2/3pi=1 unit

vanila=2 units
times 2/3pi by 2
4/3pi
aprox pi=3.141592
4.188
round
4.2 in^3 of vanilla

3 0

3 years ago

Read 2 more answers

3/24 in simplest form

daser333 [38]

1/8

3 divide by 3=1

24 divide by 3= 8

which gives you 1/8

5 0

3 years ago

Read 2 more answers