Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x+12=5
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Equation x^3=4
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Equation 0,144:(3,4-x)=2,4
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Equation x^4=(x-56)^2
- Express {x} in terms of y where:
- 15*x-5*y=-5
- 18*x+20*y=-2
- -5*x-6*y=-1
- -17*x-15*y=-17
- Graphing y =:
- x.diff(x)
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Identical expressions
- x.diff(x)= three *x- three *x^(four / three)*cos(y)
- x.diff(x) equally 3 multiply by x minus 3 multiply by x to the power of (4 divide by 3) multiply by co sinus of e of (y)
- x.diff(x) equally three multiply by x minus three multiply by x to the power of (four divide by three) multiply by co sinus of e of (y)
- x.diff(x)=3*x-3*x(4/3)*cos(y)
- x.diffx=3*x-3*x4/3*cosy
- x.diff(x)=3x-3x^(4/3)cos(y)
- x.diff(x)=3x-3x(4/3)cos(y)
- x.diffx=3x-3x4/3cosy
- x.diffx=3x-3x^4/3cosy
- x.diff(x)=3*x-3*x^(4 divide by 3)*cos(y)
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Similar expressions
- x.diff(x)=3*x+3*x^(4/3)*cos(y)
x.diff(x)=3*x-3*x^(4/3)*cos(y) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
4/3 1 = 3*x - 3*x *cos(y)
$$1 = - 3 x^{\frac{4}{3}} \cos{\left(y \right)} + 3 x$$
Detail solution
Given the equation
$$1 = - 3 x^{\frac{4}{3}} \cos{\left(y \right)} + 3 x$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\cos{\left(y \right)} = \frac{3 x - 1}{3 x^{\frac{4}{3}}}$$
This equation is transformed to
$$y = \pi n + \operatorname{acos}{\left(\frac{3 x - 1}{3 x^{\frac{4}{3}}} \right)}$$
$$y = \pi n + \operatorname{acos}{\left(\frac{3 x - 1}{3 x^{\frac{4}{3}}} \right)} - \pi$$
Or
$$y = \pi n + \operatorname{acos}{\left(\frac{3 x - 1}{3 x^{\frac{4}{3}}} \right)}$$
$$y = \pi n + \operatorname{acos}{\left(\frac{3 x - 1}{3 x^{\frac{4}{3}}} \right)} - \pi$$
, where n - is a integer
$$1 = - 3 x^{\frac{4}{3}} \cos{\left(y \right)} + 3 x$$
- this is the simplest trigonometric equation
Divide both parts of the equation by 3*x^(4/3)
The equation is transformed to
$$\cos{\left(y \right)} = \frac{3 x - 1}{3 x^{\frac{4}{3}}}$$
This equation is transformed to
$$y = \pi n + \operatorname{acos}{\left(\frac{3 x - 1}{3 x^{\frac{4}{3}}} \right)}$$
$$y = \pi n + \operatorname{acos}{\left(\frac{3 x - 1}{3 x^{\frac{4}{3}}} \right)} - \pi$$
Or
$$y = \pi n + \operatorname{acos}{\left(\frac{3 x - 1}{3 x^{\frac{4}{3}}} \right)}$$
$$y = \pi n + \operatorname{acos}{\left(\frac{3 x - 1}{3 x^{\frac{4}{3}}} \right)} - \pi$$
, where n - is a integer
The graph
Rapid solution
[src]
/-1 + 3*x\
y1 = - acos|--------| + 2*pi
| 4/3 |
\ 3*x /
$$y_{1} = - \operatorname{acos}{\left(\frac{3 x - 1}{3 x^{\frac{4}{3}}} \right)} + 2 \pi$$
/-1/3 + x\
y2 = acos|--------|
| 4/3 |
\ x /
$$y_{2} = \operatorname{acos}{\left(\frac{x - \frac{1}{3}}{x^{\frac{4}{3}}} \right)}$$
Sum and product of roots
[src]
sum
/-1 + 3*x\ /-1/3 + x\
0 + - acos|--------| + 2*pi + acos|--------|
| 4/3 | | 4/3 |
\ 3*x / \ x /
$$\left(\left(- \operatorname{acos}{\left(\frac{3 x - 1}{3 x^{\frac{4}{3}}} \right)} + 2 \pi\right) + 0\right) + \operatorname{acos}{\left(\frac{x - \frac{1}{3}}{x^{\frac{4}{3}}} \right)}$$
=
/-1 + 3*x\ /-1/3 + x\
- acos|--------| + 2*pi + acos|--------|
| 4/3 | | 4/3 |
\ 3*x / \ x /
$$\operatorname{acos}{\left(\frac{x - \frac{1}{3}}{x^{\frac{4}{3}}} \right)} - \operatorname{acos}{\left(\frac{3 x - 1}{3 x^{\frac{4}{3}}} \right)} + 2 \pi$$
product
/ /-1 + 3*x\ \ /-1/3 + x\ 1*|- acos|--------| + 2*pi|*acos|--------| | | 4/3 | | | 4/3 | \ \ 3*x / / \ x /
$$1 \left(- \operatorname{acos}{\left(\frac{3 x - 1}{3 x^{\frac{4}{3}}} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{x - \frac{1}{3}}{x^{\frac{4}{3}}} \right)}$$
=
/ /-1 + 3*x\ \ /-1 + 3*x\ |- acos|--------| + 2*pi|*acos|--------| | | 4/3 | | | 4/3 | \ \ 3*x / / \ 3*x /
$$\left(- \operatorname{acos}{\left(\frac{3 x - 1}{3 x^{\frac{4}{3}}} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{3 x - 1}{3 x^{\frac{4}{3}}} \right)}$$
(-acos((-1 + 3*x)/(3*x^(4/3))) + 2*pi)*acos((-1 + 3*x)/(3*x^(4/3)))