Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
Solve for x
Solve for y
x=8−5y
Evaluate
(x)2×1+(y)2×5=8
Simplify
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Evaluate
(x)2×1+(y)2×5
Multiply the terms
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Evaluate
(x)2×1
Any expression multiplied by 1 remains the same
(x)2
Calculate
x
x+(y)2×5
Multiply the terms
More Steps
Evaluate
(y)2×5
Rewrite the expression
y×5
Use the commutative property to reorder the terms
5y
x+5y
x+5y=8
Solution
x=8−5y
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)2×1+(y)2×5=8
Simplify
More Steps
Evaluate
(x)2×1+(y)2×5
Multiply the terms
More Steps
Evaluate
(x)2×1
Any expression multiplied by 1 remains the same
(x)2
Calculate
x
x+(y)2×5
Multiply the terms
More Steps
Evaluate
(y)2×5
Rewrite the expression
y×5
Use the commutative property to reorder the terms
5y
x+5y
x+5y=8
To test if the graph of x+5y=8 is symmetry with respect to the origin,substitute -x for x and -y for y
−x+5(−y)=8
Evaluate
−x−5y=8
Solution
Not symmetry with respect to the origin
Show Solution
Rewrite the equation
r=cos(θ)+5sin(θ)8
Evaluate
(x)2×1+(y)2×5=8
Evaluate
More Steps
Evaluate
(x)2×1+(y)2×5
Multiply the terms
More Steps
Evaluate
(x)2×1
Any expression multiplied by 1 remains the same
(x)2
Calculate
x
x+(y)2×5
Multiply the terms
More Steps
Evaluate
(y)2×5
Rewrite the expression
y×5
Use the commutative property to reorder the terms
5y
x+5y
x+5y=8
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
cos(θ)×r+5sin(θ)×r=8
Factor the expression
(cos(θ)+5sin(θ))r=8
Solution
r=cos(θ)+5sin(θ)8
Show Solution
Find the first derivative
Find the derivative with respect to x
Find the derivative with respect to y
dxdy=−51
Calculate
x21+y25=8
Simplify the expression
x+5y=8
Take the derivative of both sides
dxd(x+5y)=dxd(8)
Calculate the derivative
More Steps
Evaluate
dxd(x+5y)
Use differentiation rules
dxd(x)+dxd(5y)
Use dxdxn=nxn−1 to find derivative
1+dxd(5y)
Evaluate the derivative
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Evaluate
dxd(5y)
Use differentiation rules
dyd(5y)×dxdy
Evaluate the derivative
5dxdy
1+5dxdy
1+5dxdy=dxd(8)
Calculate the derivative
1+5dxdy=0
Move the constant to the right-hand side and change its sign
5dxdy=0−1
Removing 0 doesn't change the value,so remove it from the expression
5dxdy=−1
Divide both sides
55dxdy=5−1
Divide the numbers
dxdy=5−1
Solution
dxdy=−51
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
x21+y25=8
Simplify the expression
x+5y=8
Take the derivative of both sides
dxd(x+5y)=dxd(8)
Calculate the derivative
More Steps
Evaluate
dxd(x+5y)
Use differentiation rules
dxd(x)+dxd(5y)
Use dxdxn=nxn−1 to find derivative
1+dxd(5y)
Evaluate the derivative
More Steps
Evaluate
dxd(5y)
Use differentiation rules
dyd(5y)×dxdy
Evaluate the derivative
5dxdy
1+5dxdy
1+5dxdy=dxd(8)
Calculate the derivative
1+5dxdy=0
Move the constant to the right-hand side and change its sign
5dxdy=0−1
Removing 0 doesn't change the value,so remove it from the expression
5dxdy=−1
Divide both sides
55dxdy=5−1
Divide the numbers
dxdy=5−1
Use b−a=−ba=−ba to rewrite the fraction
dxdy=−51
Take the derivative of both sides
dxd(dxdy)=dxd(−51)
Calculate the derivative
dx2d2y=dxd(−51)
Solution
dx2d2y=0
Show Solution