They're the same. They're the same.
Manipulated variables are also known as independent variables. These are the variable which you change in an investigation. Plotted on the x axis.
The difference is that commercial sterilization takes place in irradiation chambers and regular sterilization does not. A irradiation chamber can hold up to 50 tons and is sealed up before the high energy x-rays kills off anything living.
Usually means the difference, called "Delta".Using /\ for triangle:/\ x means difference in xor is sometimes used to mean a small amount, eg x + /\ means x plus a very small (infinitesimal) amount
1 yard = 3 feet 1 foot = 0.3048 meter 500 yards = 500 x 3 x 0.3048 meters = 500 x 0.9148 meters =457.4000 meters Difference between 400 meters and 500 yards = 57.4 meters 400 meters is less than 500 yards by 57.4 meters
Greek letters such as delta are often used in different contexts. One use that is often given to delta is to indicate the difference between two values. Thus, delta-x can be the same as x2 - x1, where "x2" and "x1" are the values of "x" at different points in time, for example.
The integral of arcsin(x) dx is x arcsin(x) + (1-x2)1/2 + C.
The inverse sin function I write as arcsin x. Make use of the trignometric relationships: cos2θ + sin2θ = 1 ⇒ cosθ = √(1 - sin2θ) cotθ = cosθ/sinθ = √(1 - (sinθ)2)/sinθ sin(arcsin x) = x Then: cot(arcsin(x)) = √(1 - (sin(arcsin(x))2)/sin(arcsin(x)) = √(1 - x2)/x ⇒ cot(arcsin(4/7)) = √(1 - (4/7)2)/(4/7) = √(49/72 - 16/72) ÷ 4/7 = √(49 - 16) x 1/7 x 7/4 = 1/4 x √33
I presume that sin-1x is being used to represent the inverse sin function (I prefer arcsin x to avoid possible confusion). Make use of the trignometirc relationships: cos2θ + sin2θ = 1 ⇒ cosθ = √(1 - sin2θ) cotθ = cosθ/sinθ = √(1 - sin2θ)/sinθ sin(arcsin x) = x Then: cot(arcsin(x)) = √(1 - sin2(arcsin(x))/sin(arcsin(x)) = √(1 - x2)/x ⇒ cot(arcsin(2/3)) = √(1 - (2/3)2)/(2/3) = √(9/32 - 4/32) ÷ 2/3 = √(9 - 4) x 1/3 x 3/2 = 1/2 x √5
NO FALSE
yes y=sinx is x=arcsiny
If I read that correctly, you have: cot(sin-1(2/3)) which I understand to mean cot(arcsin(2/3)) which has the value 1/2 x √5 sin(arcsin(x)) = x cos2θ + sin2θ = 1 ⇒ cosθ = √(1 - sin2θ) cotθ = cosθ ÷ sinθ ⇒ cot(arcsin(2/3)) = cos(arcsin(2/3)) ÷ sin(arcsin(2/3) = √(1 - sin2(arcsin(2/3))) ÷ sin(arcsin(2/3) = √(1 - (2/3)2) ÷ (2/3) = 1/3 x √(9 - 4) x 3/2 = 1/2 x √5 As the reciprocal trignometric functions have separate names, eg 1/tan x = cot x, the use of the -1 "power" to indicate the inverse function is possible. However, to avoid any possible confusion, I prefer to use the arc- prefix to indicate the inverse function.
2 sin(x)2 - sin(x) - 1 = 0 Let Y=sin(x) then the equation is 2*Y2 - Y - 1 =0 Delta = (-1 * -1) - 4 * 2 * -1 = 9 Y = (1 + sqrt(9)) / 4 or Y = (1 - sqrt(9)) / 4 Y = 1 or Y = -1/2 Then x = Arcsin(Y) and (in radians) x = Arcsin(1) = Pi/2 +2*k*Pi or x=Arcsin(-1/2) = -Pi/6 + 2*k*Pi where k is an integer
2.5
0
This is solved by using substitution: Let x = sin θ → dx = cos θ dθ and √(1 - x²) = √(1 - sin² θ) = cos θ and θ = arcsin x → ∫ (x + 1)/√(1 - x²) dx = ∫ ((sin θ + 1)/ cos θ) cos θ dθ = ∫ sin θ + 1 dθ = -cos θ + θ + b = θ - cos θ + b = arcsin x - √(1 - x²) + c
If the length is L, the rise is R and the angle is x degrees, then sin(x) = R/L so that x = arcsin(R/L) or sin-1(R/L)
∫ f'(x)/√(a2 - f(x)2) dx = arcsin(f(x)/a) + C C is the constant of integration.