Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^2+9=(x+9)^2
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Equation 2*x^2-x-1=x^2-5*x-(-1-x^2)
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Equation 9x-26=30-5x
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Equation 13x+10=6x-4
- Express {x} in terms of y where:
- -16*x-14*y=-18
- 9*x+8*y=-20
- -11*x+15*y=7
- 1*x-17*y=-12
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Identical expressions
- y=2cos0.5xy=xlnx
- y equally 2 co sinus of e of 0.5xy equally xlnx
y=2cos0.5xy=xlnx equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$y = y 2 \cos{\left(0.5 x \right)}$$
transform
$$- 2 y \cos{\left(0.5 x \right)} + y - 1 = 0$$
$$- y 2 \cos{\left(0.5 x \right)} + y - 1 = 0$$
Do replacement
$$w = \cos{\left(0.5 x \right)}$$
Move free summands (without w)
from left part to right part, we given:
$$- 2 w y + y = 1$$
Divide both parts of the equation by (y - 2*w*y)/w
We get the answer: w = (-1 + y)/(2*y)
do backward replacement
$$\cos{\left(0.5 x \right)} = w$$
substitute w:
$$y = y 2 \cos{\left(0.5 x \right)}$$
transform
$$- 2 y \cos{\left(0.5 x \right)} + y - 1 = 0$$
$$- y 2 \cos{\left(0.5 x \right)} + y - 1 = 0$$
Do replacement
$$w = \cos{\left(0.5 x \right)}$$
Move free summands (without w)
from left part to right part, we given:
$$- 2 w y + y = 1$$
Divide both parts of the equation by (y - 2*w*y)/w
w = 1 / ((y - 2*w*y)/w)
We get the answer: w = (-1 + y)/(2*y)
do backward replacement
$$\cos{\left(0.5 x \right)} = w$$
substitute w:
The graph