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Popular Trigonometry >

solvefor t,4r+12s+9t=e^3x-2y+xy+cos(2x+3y)

Solution

solvefor

Solution

t = \frac{e ^{3} x - 2 y + x y + cos ( 2 x + 3 y ) - 4 r - 12 s}{9}

Solution steps

4 r + 12 s + 9 t = e^{3} x - 2 y + x y + cos (2 x + 3 y)

Move

4 r

to the right side

4 r + 12 s + 9 t = e^{3} x - 2 y + x y + cos (2 x + 3 y)

Subtract

4 r

from both sides

4 r + 12 s + 9 t - 4 r = e^{3} x - 2 y + x y + cos (2 x + 3 y) - 4 r

Simplify

12 s + 9 t = e^{3} x - 2 y + x y + cos (2 x + 3 y) - 4 r

12 s + 9 t = e^{3} x - 2 y + x y + cos (2 x + 3 y) - 4 r

Move

12 s

to the right side

12 s + 9 t = e^{3} x - 2 y + x y + cos (2 x + 3 y) - 4 r

Subtract

12 s

from both sides

12 s + 9 t - 12 s = e^{3} x - 2 y + x y + cos (2 x + 3 y) - 4 r - 12 s

Simplify

9 t = e^{3} x - 2 y + x y + cos (2 x + 3 y) - 4 r - 12 s

9 t = e^{3} x - 2 y + x y + cos (2 x + 3 y) - 4 r - 12 s

Divide both sides by

9

9 t = e^{3} x - 2 y + x y + cos (2 x + 3 y) - 4 r - 12 s

Divide both sides by

9

\frac{9 t}{9} = \frac{e ^{3} x}{9} - \frac{2 y}{9} + \frac{x y}{9} + \frac{cos ( 2 x + 3 y )}{9} - \frac{4 r}{9} - \frac{12 s}{9}

Simplify

\frac{9 t}{9} = \frac{e ^{3} x}{9} - \frac{2 y}{9} + \frac{x y}{9} + \frac{cos ( 2 x + 3 y )}{9} - \frac{4 r}{9} - \frac{12 s}{9}

Simplify

\frac{9 t}{9} : t

\frac{9 t}{9}

Divide the numbers:

\frac{9}{9} = 1

= t

Simplify

\frac{e ^{3} x}{9} - \frac{2 y}{9} + \frac{x y}{9} + \frac{cos ( 2 x + 3 y )}{9} - \frac{4 r}{9} - \frac{12 s}{9} : \frac{e ^{3} x - 2 y + x y + cos ( 2 x + 3 y ) - 4 r - 12 s}{9}

\frac{e ^{3} x}{9} - \frac{2 y}{9} + \frac{x y}{9} + \frac{cos ( 2 x + 3 y )}{9} - \frac{4 r}{9} - \frac{12 s}{9}

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{e ^{3} x - 2 y + x y + cos ( 2 x + 3 y ) - 4 r - 12 s}{9}

t = \frac{e ^{3} x - 2 y + x y + cos ( 2 x + 3 y ) - 4 r - 12 s}{9}

t = \frac{e ^{3} x - 2 y + x y + cos ( 2 x + 3 y ) - 4 r - 12 s}{9}

t = \frac{e ^{3} x - 2 y + x y + cos ( 2 x + 3 y ) - 4 r - 12 s}{9}

Graph

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