Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the x-intercept/zero
Find the y-intercept
Find the slope
x=0
Evaluate
y%=20x
To find the x-intercept,set y=0
0%=20x
Swap the sides of the equation
20x=0%
Calculate
20x=0
Solution
x=0
Show Solution
Solve the equation
Solve for x
Solve for y
x=20001y
Evaluate
y%=20x
Calculate
More Steps
Evaluate
y%
By definition p%=p×0.01
y×0.01
Use the commutative property to reorder the terms
0.01y
0.01y=20x
Swap the sides of the equation
20x=0.01y
Divide both sides
2020x=200.01y
Divide the numbers
x=200.01y
Solution
More Steps
Evaluate
200.01y
Convert the decimal into a fraction
201001y
Calculate
20001y
x=20001y
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
Symmetry with respect to the origin
Evaluate
y%=20x
Simplify the expression
0.01y=20x
To test if the graph of 0.01y=20x is symmetry with respect to the origin,substitute -x for x and -y for y
0.01(−y)=20(−x)
Evaluate
−0.01y=20(−x)
Evaluate
−0.01y=−20x
Solution
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=0θ=arccot(20001)+kπ,k∈Z
Evaluate
y%=20x
Evaluate
More Steps
Evaluate
y%
By definition p%=p×0.01
y×0.01
Use the commutative property to reorder the terms
0.01y
0.01y=20x
Multiply both sides of the equation by LCD
0.01y×100=20x×100
Simplify the equation
y=20x×100
Simplify the equation
y=2000x
Move the expression to the left side
y−2000x=0
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
sin(θ)×r−2000cos(θ)×r=0
Factor the expression
(sin(θ)−2000cos(θ))r=0
Separate into possible cases
r=0sin(θ)−2000cos(θ)=0
Solution
More Steps
Evaluate
sin(θ)−2000cos(θ)=0
Move the expression to the right side
−2000cos(θ)=0−sin(θ)
Subtract the terms
−2000cos(θ)=−sin(θ)
Divide both sides
sin(θ)−2000cos(θ)=−1
Divide the terms
More Steps
Evaluate
sin(θ)−2000cos(θ)
Use b−a=−ba=−ba to rewrite the fraction
−sin(θ)2000cos(θ)
Rewrite the expression
−2000sin−1(θ)cos(θ)
Rewrite the expression
−2000cot(θ)
−2000cot(θ)=−1
Multiply both sides of the equation by −20001
−2000cot(θ)(−20001)=−(−20001)
Calculate
cot(θ)=−(−20001)
Multiplying or dividing an even number of negative terms equals a positive
cot(θ)=20001
Use the inverse trigonometric function
θ=arccot(20001)
Add the period of kπ,k∈Z to find all solutions
θ=arccot(20001)+kπ,k∈Z
r=0θ=arccot(20001)+kπ,k∈Z
Show Solution
Find the first derivative
Find the derivative with respect to x
Find the derivative with respect to y
dxdy=2000
Calculate
y%=20x
Simplify the expression
0.01y=20x
Take the derivative of both sides
dxd(0.01y)=dxd(20x)
Calculate the derivative
More Steps
Evaluate
dxd(0.01y)
Use differentiation rules
dyd(0.01y)×dxdy
Evaluate the derivative
More Steps
Evaluate
dyd(0.01y)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
0.01×dyd(y)
Use dxdxn=nxn−1 to find derivative
0.01×1
Any expression multiplied by 1 remains the same
0.01
0.01dxdy
0.01dxdy=dxd(20x)
Calculate the derivative
More Steps
Evaluate
dxd(20x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
20×dxd(x)
Use dxdxn=nxn−1 to find derivative
20×1
Any expression multiplied by 1 remains the same
20
0.01dxdy=20
Divide both sides
0.010.01dxdy=0.0120
Divide the numbers
dxdy=0.0120
Solution
More Steps
Evaluate
0.0120
Convert the decimal into a fraction
100120
Multiply by the reciprocal
20×100
Multiply the numbers
2000
dxdy=2000
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
y%=20x
Simplify the expression
0.01y=20x
Take the derivative of both sides
dxd(0.01y)=dxd(20x)
Calculate the derivative
More Steps
Evaluate
dxd(0.01y)
Use differentiation rules
dyd(0.01y)×dxdy
Evaluate the derivative
More Steps
Evaluate
dyd(0.01y)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
0.01×dyd(y)
Use dxdxn=nxn−1 to find derivative
0.01×1
Any expression multiplied by 1 remains the same
0.01
0.01dxdy
0.01dxdy=dxd(20x)
Calculate the derivative
More Steps
Evaluate
dxd(20x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
20×dxd(x)
Use dxdxn=nxn−1 to find derivative
20×1
Any expression multiplied by 1 remains the same
20
0.01dxdy=20
Divide both sides
0.010.01dxdy=0.0120
Divide the numbers
dxdy=0.0120
Divide the numbers
More Steps
Evaluate
0.0120
Convert the decimal into a fraction
100120
Multiply by the reciprocal
20×100
Multiply the numbers
2000
dxdy=2000
Take the derivative of both sides
dxd(dxdy)=dxd(2000)
Calculate the derivative
dx2d2y=dxd(2000)
Solution
dx2d2y=0
Show Solution
Graph
