In precalculus, you learned a formula for the position of the maximum or minimum of a quadratic equation y = a x 2 + b x + c , which was m = − b ( 2 a ) . Prove this formula using calculus.
In precalculus, you learned a formula for the position of the maximum or minimum of a quadratic equation y = a x 2 + b x + c , which was m = − b ( 2 a ) . Prove this formula using calculus.
In precalculus, you learned a formula for the position of the maximum or minimum of a quadratic equation
y
=
a
x
2
+
b
x
+
c
, which was
m
=
−
b
(
2
a
)
. Prove this formula using calculus.
Formula Formula A polynomial with degree 2 is called a quadratic polynomial. A quadratic equation can be simplified to the standard form: ax² + bx + c = 0 Where, a ≠ 0. A, b, c are coefficients. c is also called "constant". 'x' is the unknown quantity
Can you prove that P(a,b) >= P(a',b) for a >= a' >= b >= 0
Figure 1 Simulation structure diagram for a turbine cold-end system.
approximated by the two fourth degree polynomial equations as follows:
The turbine "cold-and" system generally consists of turbine exhaust and condenser, and cooling tower
(Fig. 1). For a 250 MW unit, the turbine performance data with the maximum steam throttle flow can be
NHR
NEW
NHR
Turbine
and
NHR = −45.19(CP)* + 420(CP)® – 1442(CP)2 + 2248(CP) +6666 (a)
NKW = 4,883(CP)* – 44,890(CP)3 + 152,600(CP)2 – 231,500(CP) + 383,400. (b)
The condenser and mechanical-draft cooling tower have the performance equations, respectively,
CP 1.6302-0.50095 x 10-1 (CWT)
OP
Coupling 1
Condenser
CR
WFR
CWT
Coupling 2
WST
Cooling Tower
CR
System Boundary
2
(The circulating water flow is assumed to flow at the rate of 145,000 gpm.)
In addition to the given performance equations give above, we also need two coupling equations to
complete the mathematical model for this cooling system. The first equation is the coupling between the…
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