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2 years ago

2x+3y=1, -x+2y=-4 solve using substitution method

Mathematics

1 answer:

ollegr [7]2 years ago

8 0

Step-by-step explanation:

1) 2x+3y-3y=1-3y. -x+2y= -4

2x/2=1-3y/2. -(1-3y/2)=-4

x=1-3y/2. -1+3y/2= -4

x=1-3(-2)/2 3y/2= -4+1

x=1+6/2 3y/2×2/3= -3×2/3

x=7/2 y= -2

S.s{ 7/3,-2}

2). -4x-6y+6y=7-6y. 4x+y= -2

-4x/-4=7-6y/-4. 4(-7-6y/4)+y= -2

x= -7-6y/4. -7-6y+y = -2

x= -7-6/4 -5y/5= 5/5

x=-13/4 y= 1

S.s { -13/4, 1 }

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2 years ago

Find a power series for the function, centered at c. g(x) = 4x x2 2x − 3 , c = 0

BartSMP [9]

The power series for given function $g(x)=\frac{4x}{(x-1)(x+3)}$ is $g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n)$

For given question,

We have been given a function g(x) = 4x / (x² + 2x - 3)

We need to find a power series for the function, centered at c, for c = 0.

First we factorize the denominator of function g(x), we have:

$\Rightarrow g(x)=\frac{4x}{(x-1)(x+3)}$

We can write g(x) as,

$\Rightarrow g(x)=\frac{1}{x-1}+\frac{3}{x+3}\\\\\Rightarrow g(x)=\frac{-1}{1-x}+\frac{1}{1+\frac{x}{3} }\\\\\Rightarrow g(x)=\frac{-1}{1-x}+\frac{1}{1-(-\frac{x}{3} )}\\$

We know that, $\frac{1}{1-x}=\sum{_{n=0}^\infty}~{x^n}$ if |x| < 1

and $\frac{1}{1-(-\frac{x}{3} )}=\sum{_{n=0}^\infty}~x^n(-\frac{x}{3} )^n$ if $|\frac{x}{6}| < 1$

$\Rightarrow g(x)=-\sum{_{n=0}^\infty}~x^n+\sum{_{n=0}^\infty}~x^n(-\frac{x}{3} )^n\\$ if |x| < 1 and if $|\frac{x}{6}| < 1$

$\Rightarrow g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n)$ if |x| < 1

Therefore, the power series for given function $g(x)=\frac{4x}{(x-1)(x+3)}$ is $g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n)$

Learn more about the power series here:

brainly.com/question/11606956

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1 year ago

480kg of concrete mix. sand and gravel in the ratio 1:3:4

Anestetic [448]

Answer:

Step-by-step explanation:

1+3+4 = 8

480 / 8 = 60

60 x 1 = 60 (concrete)

60 x 3 = 180 (sand)

60 x 4 = 240 (gravel)

60:180:240

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2 years ago

Solve for x 2x +3y = Q

Marianna [84]

Hello! :)

2x + 3y + −3y = q + −3y Add -3y to both sides

2x = q − 3y

2x/2 = q-3y/2 Divide both sides by 2

x = 1/2q + -3/2 y (ANSWER)

Hope this helped you

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3 years ago

What is the exact volume of the cylinder? Cylinder with height of 6 inches and radius of 3 inches. 324π in3 18π in3 36π in3 54π

Afina-wow [57]

Volume of a cylinder is pi*r^2*h where r = radius and h = height
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54 pi is the answer. mark me brainliest please!

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2 years ago

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