Engineering
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Consider two cases involving parallel flow of dry air at v = 1 m/s, t[infinity]

Consider two cases involving parallel flow of dry air at v = 1 m/s, t[infinity] = 45°c, and atmospheric pressure over an isothermal plate at ts = 20°c. in the first case, rex,c = 5 × 105, while in the second case the flow is tripped to a turbulent state at x = 0 m. at what x-location are the thermal boundary layer thicknesses of the two cases equal? what are the local heat fluxes at this location for the two cases?
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ayowazzzgood
ayowazzzgood
4,5(85 marks)

The break-even points are:  x = 500, and x = 70

Step-by-step explanation:

The break even points are those x-values for which the Revenue equals the Cost, so there is no money lost.

Since the formulas for both Revenue and Cost are given, we find the breaking  points by setting the functions equal to each other:

C(x)=R(x)\\35,000 + 45\,x +0.2 \,x^2=\,615\,x-\,0.8\,x^2\\35,000 + 45\,x +0.2 \,x^2-\,615\,x+\,0.8\,x^2=0\\x^2-570\,x+35,000= 0

where we have gathered all terms on one side of the equation and written the equation in standard form.

We can use the quadratic formula to solve for "x":

ax^2+bx+c=0  has solutions given by: x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}

In our case,  a=1,\,\,b=-570,\,\,and\,\,c=35000

So the solutions are:

x=\frac{570+/-\sqrt{570^2-4*35000} }{2}\\x=\frac{570+/-\sqrt{184900} }{2}\\x=\frac{570+/-430 }{2}

This leads to two solutions:

x_1=\frac{570+430}{2} = 500\\x_2=\frac{570-430}{2} = 70\\

These are the break-even points.

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