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3 years ago

20 POINTS! Please help

Mathematics

1 answer:

Marysya12 [62]3 years ago

3 0

The complete square will be $(x-3)^{2}$ = 3

Step-by-step explanation:

Given,

$2x^{2} -12x+12=0$

or, $x^{2} -6x+6=0$ [ by eliminating 2 from both the sides]

To make it square

$x^{2} -6x+6=0$

or, $x^{2} -2xX3+9-9+6=0$ [ $(a+b)^{2}=a^{2} +2ab+b^{2}$

or, $(x-3)^{2}$ = 9-6

or, $(x-3)^{2}$ = 3

Hence the correct option is B

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Terminating decimals: these have a finite number of digits after the decimal point. Recurring/repeating decimals: these have one or more repeating numbers or sequences of numbers after the decimal point, which continue infinitely.

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3 years ago

I have to round an answer to the nearest tenth. My original answer is 15.98. Do I go to 16, or 15.9? Please answer soon.

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3 years ago

Find a particular solution to the nonhomogeneous differential equation y??+4y?+5y=?10x+e^(?x).

Firdavs [7]

Answer:

A) Particular solution:

$2x+\frac{1}{2}e^{-x}-\frac{8}{5}$

B) Homogeneous solution:

$y_{h}=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))$

C) The most general solution is

$y=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))+2x+\frac{1}{2}e^{-x}-\frac{8}{5}$

Step-by-step explanation:

Given non homogeneous ODE is

$y''+4y'+5y=10x+e^{-x}---(1)$

To find homogeneous solution:

$D^{2}+4D+5=0\\D^{2}+4D+4-4+5=0\\\\(D+2)^{2}=-1\\D+2=\pm iD=-2 \pm i\\y_{h}=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))---(2)$

To find particular solution:

$y_{p}=Ax+B+Ce^{-x}\\\\y'_{p}=A-Ce^{-x}\\y''_{p}=Ce^{-x}\\$

Substituting $y_{p},y'_{p},y''_{p}$ in (1)

$y''_{p}+4y'_{p}+5y_{p}=10x+e^{-x}\\Ce^{-x}+4(A-Ce^{-x})+5(Ax+B+Ce^{-x})=10x+e^{-x}\\$

Equating the coefficients

$5Ax+2Ce^{-x}+4A+5B=10x+e^{-x}\\5A=10\\A=2\\4A+5B=0\\B=-\frac{4A}{5}B=-\frac{8}{5}2C=1\\C=\frac{1}{2}\\So,\\y_{p}=2x+\frac{1}{2}e^{-x}-\frac{8}{5}---(3)\\$