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The Value of Quadratic Equation is defined as the value of the given expression when a particular value of x is inserted.

f (x) = (a \cdot x^{2}) + (b \cdot x) + (c)

First Root of Quadratic Equation

First Root of Quadratic Equation formula is defined as the value of one of the variables satisfying the given Quadratic Equation f(x), such that f(x1) = 0.

x 1 = \frac{- (b) + \sqrt{b^{2} - 4 \cdot a \cdot c}}{2 \cdot a}

Second Root of Quadratic Equation

Second Root of Quadratic Equation formula is defined as the value of one of the variables satisfying the given Quadratic Equation f(x), such that f(x2) = 0.

x 2 = \frac{- (b) - \sqrt{b^{2} - 4 \cdot a \cdot c}}{2 \cdot a}

Discriminant of Quadratic Equation

Discriminant of Quadratic Equation formula is defined as the expression that shows the nature of roots of the Quadratic Equation.

D = (b^{2}) - (4 \cdot a \cdot c)

Sum of Roots of Quadratic Equation

The Sum of Roots of Quadratic Equation formula is defined as the sum of the value of variables, x1 and x2, satisfying the given Quadratic Equation f(x).

S (x1+x2) = - \frac{b}{a}

Product of Roots of Quadratic Equation

The Product of Roots of Quadratic Equation formula is defined as the product of the value of variables, x1 and x2, satisfying the given Quadratic Equation f(x).

P (x1×x2) = \frac{c}{a}

Difference of Roots of Quadratic Equation

The Difference of Roots of Quadratic Equation formula is defined as the difference of the value of variables, x1 and x2, satisfying the given Quadratic Equation f(x).

D' (x1-x2) = \frac{\sqrt{D}}{a}

Sum of Roots of Quadratic Equation given Roots

The Sum of Roots of Quadratic Equation given Roots formula is defined as the sum of the value of variables, x1 and x2, satisfying the given Quadratic Equation f(x).

S (x1+x2) = (x 1) + (x 2)

Maximum or Minimum Value of Quadratic Equation

The Maximum or Minimum Value of Quadratic Equation formula is defined as the highest or lowest point on the graph of the Quadratic Equation depending on whether the coefficient 'a' is negative or positive respectively.

f (x)Max/Min = \frac{(4 \cdot a \cdot c) - (b^{2})}{4 \cdot a}

Numerical Coefficient 'a' of Quadratic Equation

The Numerical Coefficient 'a' of Quadratic Equation formula is defined as the coefficient of the term containing the variable raised to the second power in the Quadratic Equation a*x^2+b*x+c=0.

a = \frac{b^{2} - D}{4 \cdot c}

Numerical Coefficient 'b' of Quadratic Equation

The Numerical Coefficient 'b' of Quadratic Equation formula is defined as the coefficient of the term containing the variable raised to the first power in the Quadratic Equation a*x^2+b*x+c=0.

b = \sqrt{D + (4 \cdot a \cdot c)}

Numerical Coefficient 'c' of Quadratic Equation

The Numerical Coefficient 'c' of Quadratic Equation formula is defined is the coefficient of the term that does not contain the variable x, or the term with no x attached in the Quadratic Equation a*x^2+b*x+c=0.

c = \frac{b^{2} - D}{4 \cdot a}

Product of Roots of Quadratic Equation given Roots

The Product of Roots of Quadratic Equation given Roots formula is defined as the product of the value of variables, x1 and x2, satisfying the given Quadratic Equation f(x).

P (x1×x2) = x 1 \cdot x 2

First Root of Quadratic Equation given Discriminant

The First Root of Quadratic Equation given Discriminant is defined as one of the solutions (or roots) obtained when solving the Quadratic Equation.

x 1 = \frac{- b + \sqrt{D}}{2 \cdot a}

Second Root of Quadratic Equation given Discriminant

The Second Root of Quadratic Equation given Discriminant formula is defined as one of the solutions (or roots) obtained when solving the Quadratic Equation.

x 2 = \frac{- b - \sqrt{D}}{2 \cdot a}

Value of X for Maximum or Minimum Value of Quadratic Equation

The Value of X for Maximum or Minimum Value of Quadratic Equation formula is defined as the location of the highest or lowest point on the graph of the Quadratic Equation depending on whether the coefficient 'a' is negative or positive respectively.

x Max/Min = - \frac{b}{2 \cdot a}

Maximum or Minimum Value of Quadratic Equation using Discriminant

The Maximum or Minimum Value of Quadratic Equation using Discriminant formula is defined as the highest or lowest point on the graph of the Quadratic Equation depending on whether the coefficient 'a' is negative or positive respectively and calculated using the discriminant of the Quadratic Equation.

f (x)Max/Min = - \frac{D}{4 \cdot a}

Arrhenius Equation for Backward Equation

The Arrhenius Equation for backward Equation represents the fraction of collisions that have enough energy to overcome the activation barrier (i.e., have energy greater than or equal to the activation energy Ea) at temperature T for a backward reaction.

K b = A b \cdot \exp (- (\frac{E ab}{[R] \cdot T abs}))

Equation for Inflow from Continuity Equation

The Equation for Inflow from Continuity Equation formula is defined as the source of water within the body of water. It can also refer to the average volume of incoming water in unit time.

I = K \cdot R dq/dt + Q

Static Density Equation using Aerodynamic Equation

Static Density Equation using Aerodynamic Equation formula is defined as a measure of the effective air density in a flat plate for viscous flow case, which is a critical parameter in aerodynamics and fluid mechanics, used to analyze the behavior of air and its interaction with solid objects.

ρ e = \frac{q w}{u e \cdot St \cdot (h aw - h w)}

Equation for varying dimensionless group in Theis Equation

The Equation for varying dimensionless group in Theis Equation where a data plot of drawdown versus time (or drawdown versus t/rz) is matched to the type curve of W(u) versus 1/u to solve the Graphical Method.

u = \frac{r^{2} \cdot S}{4 \cdot T \cdot t}

Static Velocity Equation using Aerodynamic Heating Equation

Static Velocity Equation using Aerodynamic Heating Equation formula is defined as a measure of the velocity of a fluid in a flat plate for viscous flow case, taking into account the heat transfer and frictional forces, which is crucial in understanding the aerodynamic characteristics of an object.

u e = \frac{q w}{ρ e \cdot St \cdot (h aw - h w)}

Equation for Constant depending upon Latitude in Net Radiation of Evaporable Water Equation

The Equation for Constant depending upon Latitude in Net Radiation of Evaporable Water Equation formula is defined as the balance between incoming and outgoing energy at the top of the atmosphere.

a = 0.29 \cdot \cos (Φ)

Brus Equation

The Brus Equation formula is defined as the emission energy of quantum dot semiconductor nanocrystals (such as CdSe nanocrystals). This is useful for calculating the radius of a quantum dot from experimentally determined parameters.

E emission = E gap + (\frac{{[hP]}^{2}}{8 \cdot (a^{2})}) \cdot ((\frac{1}{[Mass-e] \cdot m e}) + (\frac{1}{[Mass-e] \cdot m h}))

Hamada Equation

The Hamada Equation formula is defined as a formula used in financial economics to estimate the leveraged beta of a leveraged firm. The leveraged beta reflects the risk of a firm's equity when it uses financial leverage (debt) to finance its operations.

β L = β UL \cdot (1 + (1 - T %) \cdot R D/E)

Avrami Equation

Avrami Equation is used to model the solid state phase tranformations.

y = 1 - \exp (- k \cdot t^{n})

Kirpich Equation

The Kirpich Equation formula is defined as it is popularly used for relating the time of concentration of the length or travel and slope of the catchment deduced by the Kirpich Equation (1940).

t c = 0.01947 \cdot L^{0.77} \cdot S^{- 0.385}

Blasius Equation

The Blasius Equation formula is defined as the steady two-dimensional laminar boundary layer that forms on a semi-infinite plate that is held parallel to a constant unidirectional flow.

f = \frac{0.316}{{Re}^{\frac{1}{4}}}

Penman's Equation

The Penman's Equation formula is defined as the evaporation (E) from an open water surface and was developed by Howard Penman in 1948.

PET = \frac{A \cdot H n + E a \cdot γ}{A + γ}

Philip's Equation

The Philip's Equation for Cumulative infiltration is the total volume of water infiltrated per unit area of soil surface during a specified time period.

F p = s \cdot t^{\frac{1}{2}} + k \cdot t

Snyder's Equation

The Snyder's Equation formula is defined as the elapsed time between the occurrences of the centroids of the effective rainfall.

t p = C r \cdot {(L b \cdot L ca)}^{0.3}

Equation for Risk

The Equation for Risk formula is defined as the probability of occurrence of an event at least once throughout 'n' successive years.

R = 1 - {(1 - p)}^{n}

Muskingum Equation

The Muskingum Equation formula is defined as the hydrological flow routing model with lumped parameters, which describes the transformation of discharge waves in a riverbed using two Equations.

ΔSv = K \cdot (x \cdot I + (1 - x) \cdot Q)

Kostiakov Equation

The Kostiakov Equation formula is defined as an Equation proposed by Kostiakov to calculate Cumulative Infiltration Capacity using the parameters in the Kostiakov model determined from the log (F) versus log (t) plot.

F p = a \cdot t^{b}

Manning's Equation

The Manning's Equation formula is defined as the computation of the flow of water in open non-full channels and pipes without the need for a flume, weir, or other structure.

v = (\frac{1}{n}) \cdot {(r H)}^{\frac{2}{3}} \cdot {(S̄)}^{\frac{1}{2}}

Rydberg's Equation

The Rydberg's Equation is used to determine the wavelength of light emitted by an electron moving between the energy levels of an atom.

ν' HA = [Rydberg] \cdot (Z^{2}) \cdot (\frac{1}{{n initial}^{2}} - (\frac{1}{{n final}^{2}}))

Arrhenius Equation

The Arrhenius Equation formula represents the fraction of collisions that have enough energy to overcome the activation barrier (i.e., have energy greater than or equal to the activation energy Ea) at temperature T.

K h = A \cdot (\exp (- (\frac{E a}{[R] \cdot T abs})))

Water Flow Equation

The Water flow Equation is defined as the product of the flow velocity and the cross sectional area of the pipe.

Q w = A cs \cdot V f

Green Ampt Equation

The Green Ampt Equation formula is defined as a simplified representation of the infiltration process. It assumes a homogeneous soil profile and a uniform distribution of initial soil water content.

f p = K \cdot (1 + \frac{η \cdot S c}{F p})

Equation for Runoff

The Equation for Runoff formula is defined as the flow of water occurring on the ground surface when excess rainwater, stormwater, meltwater, or other sources, can no longer sufficiently rapidly infiltrate in the soil.

Q V = S r + I

Ideal Diode Equation

Ideal Diode Equation Equation describes the behavior of an ideal diode in an electronic circuit under forward bias conditions. An ideal diode is a theoretical concept that serves as a simplified model of a real diode. It assumes that the diode has zero resistance when conducting in the forward direction and infinite resistance when reverse-biased, among other simplifications.

I d = I o \cdot (e^{\frac{[Charge-e] \cdot V d}{[BoltZ] \cdot T}} - 1)

Lens Makers Equation

Lens Makers Equation formula is defined as a mathematical relationship that describes the focal length of a thin lens in terms of the refractive indices of the lens material and the surrounding medium, and the radii of curvature of the lens surfaces, allowing for the calculation of the lens's focal length.

f thinlens = \frac{1}{(μ l - 1) \cdot (\frac{1}{R 1} - \frac{1}{R 2})}

Modern Lift Equation

The Modern Lift Equation is a measure of the upward force exerted on an object, such as an airplane wing, as it moves through the air, resulting from the interaction between the air and the wing's surface. It is an essential concept in aerodynamics, allowing engineers to design and optimize wing shapes for efficient flight.

L = \frac{C L \cdot ρ air \cdot S \cdot {u f}^{2}}{2}

Dalton-Type Equation

The Dalton-Type Equation formula is defined as the product of the wind speed correction factor and a coefficient to the difference between saturated vapour pressure and actual vapour pressure.

E lake = K \cdot f u \cdot (e s - e a)

Van der Waals Equation

Van der Waals Equation formula is defined as a relationship that describes the behavior of real gases by accounting for intermolecular forces and molecular volume, providing a more accurate representation than the ideal gas law under various conditions.

p = [R] \cdot \frac{T}{V m - b} - \frac{R a}{{V m}^{2}}

Equation for Well Loss

The Equation for Well Loss formula is defined as the drawdown caused by flow through well screen and axial movement within the well.

CQ n = C 2 \cdot Q^{2}

Darcy-Weisbach Equation

Darcy-Weisbach Equation formula is defined as a measure of the head loss due to friction in a pipe, which is a critical parameter in the design and operation of piping systems, particularly in reciprocating pumps, where accurate prediction of pressure drop is essential for efficient performance.

h f = \frac{4 \cdot μ f \cdot L 1 \cdot {v liquid}^{2}}{D d \cdot 2 \cdot [g]}

Entropy Balance Equation

Entropy Balance Equation formula is defined as a principle that quantifies the change in entropy within a system, accounting for the entropy generated and exchanged with the surroundings, thereby illustrating the second law of thermodynamics in practical applications.

δs = Gsys - Gsurr + TEG

Non-Ideal Diode Equation

Non-Ideal Diode Equation Equation gives an expression for the current through a non-ideal diode as a function of voltage.

I 0 = I o \cdot (e^{\frac{[Charge-e] \cdot V d}{Π \cdot [BoltZ] \cdot T}} - 1)

Scheibe-Lomakin Equation

The Scheibe-Lomakin Equation formula is defined as basis of quantitative spectrochemical analysis, which is a simple, empirical relationship between the content G of an element in the sample and the intensity I of a spectral line in the source of excitation.

I = k \cdot (G^{m})

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