Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 7*x=0
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Equation 3x-2=x+4
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Equation tan(x)=7
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Equation (x-3)(x^2-2x+1)=3(x-1)
- Express {x} in terms of y where:
- 18*x-10*y=-9
- 18*x-12*y=-9
- 12*x+11*y=20
- 19*x-12*y=-9
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Identical expressions
- z=atan(x^ two +y)+ one /(x*y^ two)
- z equally arc tangent of gent of (x squared plus y) plus 1 divide by (x multiply by y squared )
- z equally arc tangent of gent of (x to the power of two plus y) plus one divide by (x multiply by y to the power of two)
- z=atan(x2+y)+1/(x*y2)
- z=atanx2+y+1/x*y2
- z=atan(x²+y)+1/(x*y²)
- z=atan(x to the power of 2+y)+1/(x*y to the power of 2)
- z=atan(x^2+y)+1/(xy^2)
- z=atan(x2+y)+1/(xy2)
- z=atanx2+y+1/xy2
- z=atanx^2+y+1/xy^2
- z=atan(x^2+y)+1 divide by (x*y^2)
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Similar expressions
- z=atan(x^2+y)-1/(x*y^2)
- z=atan(x^2-y)+1/(x*y^2)
- z=arctan(x^2+y)+1/(x*y^2)
z=atan(x^2+y)+1/(x*y^2) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/ 2 \ 1
z = atan\x + y/ + ----
2
x*y
$$z = \operatorname{atan}{\left(x^{2} + y \right)} + \frac{1}{x y^{2}}$$
Detail solution
Given the equation:
$$z = \operatorname{atan}{\left(x^{2} + y \right)} + \frac{1}{x y^{2}}$$
transform:
$$z = \operatorname{atan}{\left(x^{2} + y \right)} + \frac{1}{x y^{2}}$$
Expand brackets in the right part
Looking for similar summands in the right part:
We get the answer: z = 1/(x*y^2) + atan(y + x^2)
$$z = \operatorname{atan}{\left(x^{2} + y \right)} + \frac{1}{x y^{2}}$$
transform:
$$z = \operatorname{atan}{\left(x^{2} + y \right)} + \frac{1}{x y^{2}}$$
Expand brackets in the right part
z = 1/x*y+1/2 + atany+x+2
Looking for similar summands in the right part:
z = 1/(x*y^2) + atan(y + x^2)
We get the answer: z = 1/(x*y^2) + atan(y + x^2)
The graph
Rapid solution
[src]
/ / 1 \ / / 2\\\ / 1 \ / / 2\\
z1 = I*|im|----| + im\atan\y + x //| + re|----| + re\atan\y + x //
| | 2| | | 2|
\ \x*y / / \x*y /
$$z_{1} = i \left(\operatorname{im}{\left(\frac{1}{x y^{2}}\right)} + \operatorname{im}{\left(\operatorname{atan}{\left(x^{2} + y \right)}\right)}\right) + \operatorname{re}{\left(\frac{1}{x y^{2}}\right)} + \operatorname{re}{\left(\operatorname{atan}{\left(x^{2} + y \right)}\right)}$$
z1 = i*(im(1/(x*y^2)) + im(atan(x^2 + y))) + re(1/(x*y^2)) + re(atan(x^2 + y))
Sum and product of roots
[src]
sum
/ / 1 \ / / 2\\\ / 1 \ / / 2\\ I*|im|----| + im\atan\y + x //| + re|----| + re\atan\y + x // | | 2| | | 2| \ \x*y / / \x*y /
$$i \left(\operatorname{im}{\left(\frac{1}{x y^{2}}\right)} + \operatorname{im}{\left(\operatorname{atan}{\left(x^{2} + y \right)}\right)}\right) + \operatorname{re}{\left(\frac{1}{x y^{2}}\right)} + \operatorname{re}{\left(\operatorname{atan}{\left(x^{2} + y \right)}\right)}$$
=
/ / 1 \ / / 2\\\ / 1 \ / / 2\\ I*|im|----| + im\atan\y + x //| + re|----| + re\atan\y + x // | | 2| | | 2| \ \x*y / / \x*y /
$$i \left(\operatorname{im}{\left(\frac{1}{x y^{2}}\right)} + \operatorname{im}{\left(\operatorname{atan}{\left(x^{2} + y \right)}\right)}\right) + \operatorname{re}{\left(\frac{1}{x y^{2}}\right)} + \operatorname{re}{\left(\operatorname{atan}{\left(x^{2} + y \right)}\right)}$$
product
/ / 1 \ / / 2\\\ / 1 \ / / 2\\ I*|im|----| + im\atan\y + x //| + re|----| + re\atan\y + x // | | 2| | | 2| \ \x*y / / \x*y /
$$i \left(\operatorname{im}{\left(\frac{1}{x y^{2}}\right)} + \operatorname{im}{\left(\operatorname{atan}{\left(x^{2} + y \right)}\right)}\right) + \operatorname{re}{\left(\frac{1}{x y^{2}}\right)} + \operatorname{re}{\left(\operatorname{atan}{\left(x^{2} + y \right)}\right)}$$
=
/ / 1 \ / / 2\\\ / 1 \ / / 2\\ I*|im|----| + im\atan\y + x //| + re|----| + re\atan\y + x // | | 2| | | 2| \ \x*y / / \x*y /
$$i \left(\operatorname{im}{\left(\frac{1}{x y^{2}}\right)} + \operatorname{im}{\left(\operatorname{atan}{\left(x^{2} + y \right)}\right)}\right) + \operatorname{re}{\left(\frac{1}{x y^{2}}\right)} + \operatorname{re}{\left(\operatorname{atan}{\left(x^{2} + y \right)}\right)}$$
i*(im(1/(x*y^2)) + im(atan(y + x^2))) + re(1/(x*y^2)) + re(atan(y + x^2))