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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Answer:
a = 40
b = 29
Explanation:
Give a place holder for the numbers that we don't know.
Lets call the two numbers a and b.
From the given info, we can write an expression and solve it:
"one number is 11 more than another number"
a = 11 + b
from this, we know that a > b.
''three times the larger number exceeds four times the smaller number by 4"
3a = 4b + 4
Now we have 2 equations, we can use them to solve using whatever method you want.
a = 11 + b
3a = 4b + 4
I will be using matrices RREF to solve for this.
a - b = 11
3a - 4b = 4
a = 40
b = 29
Answer:
Explanation:
speed of motor (N)=1500 rpm
power=4 hp = =2.9828 KW
service factor(k)= 2.75
now,
torque rating
Answer:
Pressure = 115.6 psia
Explanation:
Given:
v=800ft/s
Air temperature = 10 psia
Air pressure = 20F
Compression pressure ratio = 8
temperature at turbine inlet = 2200F
Conversion:
1 Btu =775.5 ft lbf, = 32.2 lbm.ft/lbf.s², 1Btu/lbm=25037ft²/s²
Air standard assumptions:
= 0.0240Btu/lbm.°R, R = 53.34ft.lbf/lbm.°R = 1717.5ft²/s².°R 0.0686Btu/lbm.°R
k= 1.4
Energy balance:
As enthalpy exerts more influence than the kinetic energy inside the engine, kinetic energy of the fluid inside the engine is negligible
hence
= 20+460 = 480°R
= 533.25°R
Pressure at the inlet of compressor at isentropic condition
=
= 14.45 psia
Answer:
2074.2 KW
Explanation:
<u>Determine power developed at steady state </u>
First step : Determine mass flow rate ( m )
m / Mmax = ( AV )₁ P₁ / RT₁ -------------------- ( 1 )
<em> where : ( AV )₁ = 8.2 kg/s, P₁ = 0.35 * 10^6 N/m^2, R = 8.314 N.M / kmol , </em>
<em> T₁ = 720 K . </em>
insert values into equation 1
m = 0.1871 kmol/s ( mix )
Next : calculate power developed at steady state ( using ideal gas tables to get the h values of the gases )
W( power developed at steady state )
W = m [ Yco2 ( h1 - h2 )co2
Attached below is the remaining part of the detailed solution
