Question
Function
Find the x-intercept/zero
Find the y-intercept
Find the slope
x=0
Evaluate
5x=3y(10×7)
To find the x-intercept,set y=0
5x=3×0×(10×7)
Any expression multiplied by 0 equals 0
5x=0
Solution
x=0
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Solve the equation
Solve for x
Solve for y
x=42y
Evaluate
5x=3y(10×7)
Remove the parentheses
5x=3y×10×7
Multiply the terms
More Steps

Evaluate
3×10×7
Multiply the terms
30×7
Multiply the numbers
210
5x=210y
Divide both sides
55x=5210y
Divide the numbers
x=5210y
Solution
More Steps

Evaluate
5210y
Reduce the numbers
142y
Calculate
42y
x=42y
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Testing for symmetry
Testing for symmetry about the origin
Testing for symmetry about the x-axis
Testing for symmetry about the y-axis
Symmetry with respect to the origin
Evaluate
5x=3y(10⋅7)
Simplify the expression
5x=210y
To test if the graph of 5x=210y is symmetry with respect to the origin,substitute -x for x and -y for y
5(−x)=210(−y)
Evaluate
−5x=210(−y)
Evaluate
−5x=−210y
Solution
Symmetry with respect to the origin
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Rewrite the equation
Rewrite in polar form
Rewrite in standard form
Rewrite in slope-intercept form
r=0θ=arctan(421)+kπ,k∈Z
Evaluate
5x=3y(10×7)
Evaluate
More Steps

Evaluate
3y(10×7)
Remove the parentheses
3y×10×7
Multiply the terms
More Steps

Evaluate
3×10×7
Multiply the terms
30×7
Multiply the numbers
210
210y
5x=210y
Move the expression to the left side
5x−210y=0
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
5cos(θ)×r−210sin(θ)×r=0
Factor the expression
(5cos(θ)−210sin(θ))r=0
Separate into possible cases
r=05cos(θ)−210sin(θ)=0
Solution
More Steps

Evaluate
5cos(θ)−210sin(θ)=0
Move the expression to the right side
−210sin(θ)=0−5cos(θ)
Subtract the terms
−210sin(θ)=−5cos(θ)
Divide both sides
cos(θ)−210sin(θ)=−5
Divide the terms
More Steps

Evaluate
cos(θ)−210sin(θ)
Use b−a=−ba=−ba to rewrite the fraction
−cos(θ)210sin(θ)
Rewrite the expression
−210cos−1(θ)sin(θ)
Rewrite the expression
−210tan(θ)
−210tan(θ)=−5
Multiply both sides of the equation by −2101
−210tan(θ)(−2101)=−5(−2101)
Calculate
tan(θ)=−5(−2101)
Calculate
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Evaluate
−5(−2101)
Multiplying or dividing an even number of negative terms equals a positive
5×2101
Reduce the numbers
1×421
Multiply the numbers
421
tan(θ)=421
Use the inverse trigonometric function
θ=arctan(421)
Add the period of kπ,k∈Z to find all solutions
θ=arctan(421)+kπ,k∈Z
r=0θ=arctan(421)+kπ,k∈Z
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Find the first derivative
Find the derivative with respect to x
Find the derivative with respect to y
dxdy=421
Calculate
5x=3y(10⋅7)
Simplify the expression
5x=210y
Take the derivative of both sides
dxd(5x)=dxd(210y)
Calculate the derivative
More Steps

Evaluate
dxd(5x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
5×dxd(x)
Use dxdxn=nxn−1 to find derivative
5×1
Any expression multiplied by 1 remains the same
5
5=dxd(210y)
Calculate the derivative
More Steps

Evaluate
dxd(210y)
Use differentiation rules
dyd(210y)×dxdy
Evaluate the derivative
More Steps

Evaluate
dyd(210y)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
210×dyd(y)
Use dxdxn=nxn−1 to find derivative
210×1
Any expression multiplied by 1 remains the same
210
210dxdy
5=210dxdy
Swap the sides of the equation
210dxdy=5
Divide both sides
210210dxdy=2105
Divide the numbers
dxdy=2105
Solution
dxdy=421
Show Solution

Find the second derivative
Find the second derivative with respect to x
Find the second derivative with respect to y
dx2d2y=0
Calculate
5x=3y(10⋅7)
Simplify the expression
5x=210y
Take the derivative of both sides
dxd(5x)=dxd(210y)
Calculate the derivative
More Steps

Evaluate
dxd(5x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
5×dxd(x)
Use dxdxn=nxn−1 to find derivative
5×1
Any expression multiplied by 1 remains the same
5
5=dxd(210y)
Calculate the derivative
More Steps

Evaluate
dxd(210y)
Use differentiation rules
dyd(210y)×dxdy
Evaluate the derivative
More Steps

Evaluate
dyd(210y)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
210×dyd(y)
Use dxdxn=nxn−1 to find derivative
210×1
Any expression multiplied by 1 remains the same
210
210dxdy
5=210dxdy
Swap the sides of the equation
210dxdy=5
Divide both sides
210210dxdy=2105
Divide the numbers
dxdy=2105
Cancel out the common factor 5
dxdy=421
Take the derivative of both sides
dxd(dxdy)=dxd(421)
Calculate the derivative
dx2d2y=dxd(421)
Solution
dx2d2y=0
Show Solution
