Solve ( x - 2 ) 24 + ( y + 1 ) 29 = 1

Question

Function

Find the x -intercept/zero

Find the y-intercept

Find the slope

x = \frac{5}{6}

Evaluate

(x - 2) \times 24 + (y + 1) \times 29 = 1

To find the x -intercept,set y =0

(x - 2) \times 24 + (0 + 1) \times 29 = 1

Simplify

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Evaluate

(x - 2) \times 24 + (0 + 1) \times 29

Removing 0 doesn't change the value,so remove it from the expression

(x - 2) \times 24 + 1 \times 29

Multiply the terms

24 (x - 2) + 1 \times 29

Any expression multiplied by 1 remains the same

24 (x - 2) + 29

24 (x - 2) + 29 = 1

Move the expression to the left side

24 (x - 2) + 29 - 1 = 0

Subtract the numbers

24 (x - 2) + 28 = 0

Calculate

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Evaluate

24 (x - 2) + 28

Expand the expression

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Calculate

24 (x - 2)

Apply the distributive property

24 x - 24 \times 2

Multiply the numbers

24 x - 48

24 x - 48 + 28

Add the numbers

24 x - 20

24 x - 20 = 0

Move the constant to the right-hand side and change its sign

24 x = 0 + 20

Removing 0 doesn't change the value,so remove it from the expression

24 x = 20

Divide both sides

\frac{24 x}{24} = \frac{20}{24}

Divide the numbers

x = \frac{20}{24}

Solution

x = \frac{5}{6}

Show Solution

Solve the equation

Solve for x

Solve for y

x = \frac{20 - 29 y}{24}

Evaluate

(x - 2) \times 24 + (y + 1) \times 29 = 1

Simplify

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Evaluate

(x - 2) \times 24 + (y + 1) \times 29

Multiply the terms

24 (x - 2) + (y + 1) \times 29

Multiply the terms

24 (x - 2) + 29 (y + 1)

24 (x - 2) + 29 (y + 1) = 1

Rewrite the expression

24 (x - 2) + 29 y + 29 = 1

Move the expression to the left side

24 (x - 2) + 29 y + 29 - 1 = 0

Subtract the numbers

24 (x - 2) + 29 y + 28 = 0

Calculate

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Evaluate

24 (x - 2) + 29 y + 28

Expand the expression

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Calculate

24 (x - 2)

Apply the distributive property

24 x - 24 \times 2

Multiply the numbers

24 x - 48

24 x - 48 + 29 y + 28

Add the numbers

24 x - 20 + 29 y

24 x - 20 + 29 y = 0

Move the expression to the right-hand side and change its sign

24 x = 0 - (- 20 + 29 y)

Subtract the terms

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Evaluate

0 - (- 20 + 29 y)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

0 + 20 - 29 y

Removing 0 doesn't change the value,so remove it from the expression

20 - 29 y

24 x = 20 - 29 y

Divide both sides

\frac{24 x}{24} = \frac{20 - 29 y}{24}

Solution

x = \frac{20 - 29 y}{24}

Show Solution

Testing for symmetry

Testing for symmetry about the origin

Testing for symmetry about the x-axis

Testing for symmetry about the y-axis

Not symmetry with respect to the origin

Evaluate

(x - 2) 24 + (y + 1) 29 = 1

Simplify the expression

24 (x - 2) + 29 (y + 1) = 1

To test if the graph of 24 (x - 2) + 29 (y + 1) = 1 is symmetry with respect to the origin,substitute -x for x and -y for y

24 (- x - 2) + 29 (- y + 1) = 1

Solution

Not symmetry with respect to the origin

Show Solution

Rewrite the equation

Rewrite in polar form

Rewrite in standard form

Rewrite in slope-intercept form

r = \frac{20}{24 cos ( θ ) + 29 sin ( θ )}

Evaluate

(x - 2) \times 24 + (y + 1) \times 29 = 1

Evaluate

More Steps

Evaluate

(x - 2) \times 24 + (y + 1) \times 29

Multiply the terms

24 (x - 2) + (y + 1) \times 29

Multiply the terms

24 (x - 2) + 29 (y + 1)

Expand the expression

More Steps

Calculate

24 (x - 2)

Apply the distributive property

24 x - 24 \times 2

Multiply the numbers

24 x - 48

24 x - 48 + 29 (y + 1)

Expand the expression

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Calculate

29 (y + 1)

Apply the distributive property

29 y + 29 \times 1

Any expression multiplied by 1 remains the same

29 y + 29

24 x - 48 + 29 y + 29

Add the numbers

24 x - 19 + 29 y

24 x - 19 + 29 y = 1

To convert the equation to polar coordinates,substitute x for r cos (θ) and y for r sin (θ)

24 cos (θ) \times r - 19 + 29 sin (θ) \times r = 1

Factor the expression

(24 cos (θ) + 29 sin (θ)) r - 19 = 1

Subtract the terms

(24 cos (θ) + 29 sin (θ)) r - 19 - (- 19) = 1 - (- 19)

Evaluate

(24 cos (θ) + 29 sin (θ)) r = 20

Solution

r = \frac{20}{24 cos ( θ ) + 29 sin ( θ )}

Show Solution

Find the first derivative

Find the derivative with respect to x

Find the derivative with respect to y

\frac{d y}{d x} = - \frac{24}{29}

Calculate

(x - 2) 24 + (y + 1) 29 = 1

Simplify the expression

24 x - 19 + 29 y = 1

Take the derivative of both sides

\frac{d}{d x} (24 x - 19 + 29 y) = \frac{d}{d x} (1)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (24 x - 19 + 29 y)

Use differentiation rules

\frac{d}{d x} (24 x) + \frac{d}{d x} (- 19) + \frac{d}{d x} (29 y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (24 x)

Use differentiation rule \frac{d}{d x} (c f (x)) = c \times \frac{d}{d x} (f (x))

24 \times \frac{d}{d x} (x)

Use \frac{d}{d x} x^{n} = n x^{n - 1} to find derivative

24 \times 1

Any expression multiplied by 1 remains the same

24

24 + \frac{d}{d x} (- 19) + \frac{d}{d x} (29 y)

Use \frac{d}{d x} (c) = 0 to find derivative

24 + 0 + \frac{d}{d x} (29 y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (29 y)

Use differentiation rules

\frac{d}{d y} (29 y) \times \frac{d y}{d x}

Evaluate the derivative

29 \frac{d y}{d x}

24 + 0 + 29 \frac{d y}{d x}

Evaluate

24 + 29 \frac{d y}{d x}

24 + 29 \frac{d y}{d x} = \frac{d}{d x} (1)

Calculate the derivative

24 + 29 \frac{d y}{d x} = 0

Move the constant to the right-hand side and change its sign

29 \frac{d y}{d x} = 0 - 24

Removing 0 doesn't change the value,so remove it from the expression

29 \frac{d y}{d x} = - 24

Divide both sides

\frac{29 \frac{d y}{d x}}{29} = \frac{- 24}{29}

Divide the numbers

\frac{d y}{d x} = \frac{- 24}{29}

Solution

\frac{d y}{d x} = - \frac{24}{29}

Show Solution

Find the second derivative

Find the second derivative with respect to x

Find the second derivative with respect to y

\frac{d ^{2} y}{d x ^{2}} = 0

Calculate

(x - 2) 24 + (y + 1) 29 = 1

Simplify the expression

24 x - 19 + 29 y = 1

Take the derivative of both sides

\frac{d}{d x} (24 x - 19 + 29 y) = \frac{d}{d x} (1)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (24 x - 19 + 29 y)

Use differentiation rules

\frac{d}{d x} (24 x) + \frac{d}{d x} (- 19) + \frac{d}{d x} (29 y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (24 x)

Use differentiation rule \frac{d}{d x} (c f (x)) = c \times \frac{d}{d x} (f (x))

24 \times \frac{d}{d x} (x)

Use \frac{d}{d x} x^{n} = n x^{n - 1} to find derivative

24 \times 1

Any expression multiplied by 1 remains the same

24

24 + \frac{d}{d x} (- 19) + \frac{d}{d x} (29 y)

Use \frac{d}{d x} (c) = 0 to find derivative

24 + 0 + \frac{d}{d x} (29 y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (29 y)

Use differentiation rules

\frac{d}{d y} (29 y) \times \frac{d y}{d x}

Evaluate the derivative

29 \frac{d y}{d x}

24 + 0 + 29 \frac{d y}{d x}

Evaluate

24 + 29 \frac{d y}{d x}

24 + 29 \frac{d y}{d x} = \frac{d}{d x} (1)

Calculate the derivative

24 + 29 \frac{d y}{d x} = 0

Move the constant to the right-hand side and change its sign

29 \frac{d y}{d x} = 0 - 24

Removing 0 doesn't change the value,so remove it from the expression

29 \frac{d y}{d x} = - 24

Divide both sides

\frac{29 \frac{d y}{d x}}{29} = \frac{- 24}{29}

Divide the numbers

\frac{d y}{d x} = \frac{- 24}{29}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

\frac{d y}{d x} = - \frac{24}{29}

Take the derivative of both sides

\frac{d}{d x} (\frac{d y}{d x}) = \frac{d}{d x} (- \frac{24}{29})

Calculate the derivative

\frac{d ^{2} y}{d x ^{2}} = \frac{d}{d x} (- \frac{24}{29})

Solution

\frac{d ^{2} y}{d x ^{2}} = 0

Show Solution

Function

Solve the equation

Testing for symmetry

Rewrite the equation

Find the first derivative

Find the second derivative

Graph