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bixtya [17]
3 years ago
11

3(12x2+x+1)+12(12x2+x+1)=15(12x2+x+1)

Mathematics
2 answers:
Morgarella [4.7K]3 years ago
8 0

Answer:

infinite solutions

Step-by-step explanation:

3(12x2+x+1)+12(12x2+x+1)=15(12x2+x+1)

Combine like terms

3(12x2+x+1)+12(12x2+x+1)=15(12x2+x+1)

15(12x2+x+1) = 15(12x2+x+1)

Divide by 15

(12x2+x+1) = (12x2+x+1)

Since they are the same

x can be any real value

Vsevolod [243]3 years ago
6 0

Answer:

All real values of x

Step-by-step explanation:

3(12x²+x+1)+12(12x²+x+1)=15(12x²+x+1)

(12x² + x + 1)(3+12) = 15(12x²+x+1)

15(12x²+x+1) = 15(12x²+x+1)

Since both sides are identical, all real values of x will satisfy the equation

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Answer:

52= 8×(4+5)-20

so I guess it's correct

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3 years ago
I need help with this problem.<br>please help<br><br>Directions: Solve each system by substitution.​
artcher [175]

Answer:

(-1,-6)

Step-by-step explanation:

Plug 6x for y into the bottom equation:

2x+3(6x)= -20

2x+18x= -20

20= -20

x= -1

Substitute -1 for x in the equation for y:

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3 years ago
2) write a linear function that passes through point ( 3, 6) and is perpendicular to Y=2X-1.
SVETLANKA909090 [29]

Answer:

y=-1/2*+5

Step-by-step explanation:

3 0
2 years ago
Solve y ' ' + 4 y = 0 , y ( 0 ) = 2 , y ' ( 0 ) = 2 The resulting oscillation will have Amplitude: Period: If your solution is A
Vlad [161]

Answer:

y(x)=sin(2x)+2cos(2x)

Step-by-step explanation:

y''+4y=0

This is a homogeneous linear equation. So, assume a solution will be proportional to:

e^{\lambda x} \\\\for\hspace{3}some\hspace{3}constant\hspace{3}\lambda

Now, substitute y(x)=e^{\lambda x} into the differential equation:

\frac{d^2}{dx^2} (e^{\lambda x} ) +4e^{\lambda x} =0

Using the characteristic equation:

\lambda ^2 e^{\lambda x} + 4e^{\lambda x} =0

Factor out e^{\lambda x}

e^{\lambda x}(\lambda ^2 +4) =0

Where:

e^{\lambda x} \neq 0\\\\for\hspace{3}any\hspace{3}\lambda

Therefore the zeros must come from the polynomial:

\lambda^2+4 =0

Solving for \lambda:

\lambda =\pm2i

These roots give the next solutions:

y_1(x)=c_1 e^{2ix} \\\\and\\\\y_2(x)=c_2 e^{-2ix}

Where c_1 and c_2 are arbitrary constants. Now, the general solution is the sum of the previous solutions:

y(x)=c_1 e^{2ix} +c_2 e^{-2ix}

Using Euler's identity:

e^{\alpha +i\beta} =e^{\alpha} cos(\beta)+ie^{\alpha} sin(\beta)

y(x)=c_1 (cos(2x)+isin(2x))+c_2(cos(2x)-isin(2x))\\\\Regroup\\\\y(x)=(c_1+c_2)cos(2x) +i(c_1-c_2)sin(2x)\\

Redefine:

i(c_1-c_2)=c_1\\\\c_1+c_2=c_2

Since these are arbitrary constants

y(x)=c_1sin(2x)+c_2cos(2x)

Now, let's find its derivative in order to find c_1 and c_2

y'(x)=2c_1 cos(2x)-2c_2sin(2x)

Evaluating    y(0)=2 :

y(0)=2=c_1sin(0)+c_2cos(0)\\\\2=c_2

Evaluating     y'(0)=2 :

y'(0)=2=2c_1cos(0)-2c_2sin(0)\\\\2=2c_1\\\\c_1=1

Finally, the solution is given by:

y(x)=sin(2x)+2cos(2x)

5 0
3 years ago
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