Solve 36x - 36y - 90 = 0 - Socratic AI (ScanMath)

Question

Function

Find the x -intercept/zero

Find the y-intercept

Find the slope

x = \frac{5}{2}

Evaluate

36 x - 36 y - 90 = 0

To find the x -intercept,set y =0

36 x - 36 \times 0 - 90 = 0

Any expression multiplied by 0 equals 0

36 x - 0 - 90 = 0

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

36 x - 90 = 0

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

36 x = 0 + 90

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

36 x = 90

Divide both sides

\frac{36 x}{36} = \frac{90}{36}

Divide the numbers

x = \frac{90}{36}

Solution

x = \frac{5}{2}

Show Solution

Solve the equation

Solve for x

Solve for y

x = \frac{2 y + 5}{2}

Evaluate

36 x - 36 y - 90 = 0

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

36 x = 0 + 36 y + 90

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

36 x = 36 y + 90

Divide both sides

\frac{36 x}{36} = \frac{36 y + 90}{36}

Divide the numbers

x = \frac{36 y + 90}{36}

Solution

More Steps

Evaluate

\frac{36 y + 90}{36}

Rewrite the expression

\frac{18 ( 2 y + 5 )}{36}

Cancel out the common factor 18

\frac{2 y + 5}{2}

x = \frac{2 y + 5}{2}

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

36 x - 36 y - 90 = 0

To test if the graph of 36 x - 36 y - 90 = 0 is symmetry with respect to the origin,substitute -x for x and -y for y

36 (- x) - 36 (- y) - 90 = 0

Evaluate

More Steps

Evaluate

36 (- x) - 36 (- y) - 90

Multiply the numbers

- 36 x - 36 (- y) - 90

Multiply the numbers

- 36 x + 36 y - 90

- 36 x + 36 y - 90 = 0

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{5}{2 cos ( θ ) - 2 sin ( θ )}

Evaluate

36 x - 36 y - 90 = 0

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

36 cos (θ) \times r - 36 sin (θ) \times r - 90 = 0

Factor the expression

(36 cos (θ) - 36 sin (θ)) r - 90 = 0

Subtract the terms

(36 cos (θ) - 36 sin (θ)) r - 90 - (- 90) = 0 - (- 90)

Evaluate

(36 cos (θ) - 36 sin (θ)) r = 90

Solution

r = \frac{5}{2 cos ( θ ) - 2 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} = 1

Calculate

36 x - 36 y - 90 = 0

Take the derivative of both sides

\frac{d}{d x} (36 x - 36 y - 90) = \frac{d}{d x} (0)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (36 x - 36 y - 90)

Use differentiation rules

\frac{d}{d x} (36 x) + \frac{d}{d x} (- 36 y) + \frac{d}{d x} (- 90)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (36 x)

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

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

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

36 \times 1

Any expression multiplied by 1 remains the same

36

36 + \frac{d}{d x} (- 36 y) + \frac{d}{d x} (- 90)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 36 y)

Use differentiation rules

\frac{d}{d y} (- 36 y) \times \frac{d y}{d x}

Evaluate the derivative

- 36 \frac{d y}{d x}

36 - 36 \frac{d y}{d x} + \frac{d}{d x} (- 90)

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

36 - 36 \frac{d y}{d x} + 0

Evaluate

36 - 36 \frac{d y}{d x}

36 - 36 \frac{d y}{d x} = \frac{d}{d x} (0)

Calculate the derivative

36 - 36 \frac{d y}{d x} = 0

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

- 36 \frac{d y}{d x} = 0 - 36

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

- 36 \frac{d y}{d x} = - 36

Change the signs on both sides of the equation

36 \frac{d y}{d x} = 36

Divide both sides

\frac{36 \frac{d y}{d x}}{36} = \frac{36}{36}

Divide the numbers

\frac{d y}{d x} = \frac{36}{36}

Solution

More Steps

Evaluate

\frac{36}{36}

Reduce the numbers

\frac{1}{1}

Calculate

1

\frac{d y}{d x} = 1

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

36 x - 36 y - 90 = 0

Take the derivative of both sides

\frac{d}{d x} (36 x - 36 y - 90) = \frac{d}{d x} (0)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (36 x - 36 y - 90)

Use differentiation rules

\frac{d}{d x} (36 x) + \frac{d}{d x} (- 36 y) + \frac{d}{d x} (- 90)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (36 x)

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

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

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

36 \times 1

Any expression multiplied by 1 remains the same

36

36 + \frac{d}{d x} (- 36 y) + \frac{d}{d x} (- 90)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 36 y)

Use differentiation rules

\frac{d}{d y} (- 36 y) \times \frac{d y}{d x}

Evaluate the derivative

- 36 \frac{d y}{d x}

36 - 36 \frac{d y}{d x} + \frac{d}{d x} (- 90)

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

36 - 36 \frac{d y}{d x} + 0

Evaluate

36 - 36 \frac{d y}{d x}

36 - 36 \frac{d y}{d x} = \frac{d}{d x} (0)

Calculate the derivative

36 - 36 \frac{d y}{d x} = 0

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

- 36 \frac{d y}{d x} = 0 - 36

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

- 36 \frac{d y}{d x} = - 36

Change the signs on both sides of the equation

36 \frac{d y}{d x} = 36

Divide both sides

\frac{36 \frac{d y}{d x}}{36} = \frac{36}{36}

Divide the numbers

\frac{d y}{d x} = \frac{36}{36}

Divide the numbers

More Steps

Evaluate

\frac{36}{36}

Reduce the numbers

\frac{1}{1}

Calculate

1

\frac{d y}{d x} = 1

Take the derivative of both sides

\frac{d}{d x} (\frac{d y}{d x}) = \frac{d}{d x} (1)

Calculate the derivative

\frac{d ^{2} y}{d x ^{2}} = \frac{d}{d x} (1)

Solution

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

Show Solution

36x 36y 90 = 0

Function

Solve the equation

Testing for symmetry

Rewrite the equation

Find the first derivative

Find the second derivative

Graph