I have to find the critical points of this function of two variables
4%2By%5E4-16%28x%2By%29%5E2%5C%5C" id="TexFormula1" title="\\f(x,y)=x^4+y^4-16(x+y)^2\\" alt="\\f(x,y)=x^4+y^4-16(x+y)^2\\" align="absmiddle" class="latex-formula">, for this we use the gradient method which equals to ZERO the first partial derivatives. After clearing both equations we should find the following points: P (__, 0), Q (4, __), R (4, __) My problem is that I cannot clear the following equations:
Is there any way to deal with these equations of degree n?
Is there any way to deal with these equations of degree n?
1 answer:
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Explanation:
Temperature range → 0 to 80'c
respective voltage output → 0.2v to 0.5v
required temperature range 20'c to 40'c
Where T = 20'c respective voltage
Therefore, Sensor output changes from 0.275v to 0.35volts for the ADC the required i/p should cover the dynamic range of ADC (ie - 0v to 3v)
so we have to design a circuit which transfers input voltage 0.275volts - 0.35v to 0 - 3v
Therefore, the formula for the circuit will be
The simplest circuit will be a op-amp
NOTE: Refer the figure attached
Vs is sensor output
Vr is the reference volt, Vr = 0.275v
choose R2, R1 such that it will maintain required ratio
The output Vo can be connected to voltage buffer if you required better isolation.
Answer:
The angular velocity is 7.56 rad/s
the maximum water height is 2 ft
Explanation:
The z-position as a function of r is equal to
(eq. 1)
where
h0 = initial height = 1 ft
w = angular velocity
R = radius of the cylinder = 1.5 ft
zs(r) = 0 when the free surface is lowest at the centre
Replacing and clearing w
if you consider the equation 1 for the free surface at the edge is equal to