Answer:
The greatest prime factor of 38 is 19
Given function is a direct variation
Step-by-step explanation:
The direct proportion is defined as the increase in one quantity causes increase in other quantity.
If y is directly proportional to x, then it is given as:
y = kx
where k is the constant of proportionality
Given
y = 3x
Comparing the general form and given equation we see that both are same where k =3
So,
Given function is a direct variation
Keywords: Variation, functions
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x and y are the packs of organic and inorganic fertilizer, respectively.
pounds of nitrogen added = 2x + 6y = 120
pounds of potassium added = 3x + 2y = 54
eliminate the y terms. subtract the first equation from 3 times the second equation.
9x + 6y = 162
-2x - 6y = -120
------------------
7x = 42
x = 6
y = 18
If each letter is 1, abc would be equal to 3.
The axis of symmetry can be found by finding the average of the zeros, a derivation from the conservation of energy :P, or by finding the point when the velocity is equal to zero.
df/dx=-6x+12 so df/dx, velocity, equals zero when:
-6x+12=0
6x=12
x=2 so the axis of symmetry is the vertical line x=2
....
average of zeros...
3x^2-12x+6=0
x^2-4x+2=0
x^2-4x=-2
x^2-4x+4=2
(x-2)^2=2
x-2=±√2
x=2±√2 so the average of the zeros is obviously 2.
....
conservation of energy
vf-vi=at When vf=0, this is the maximum value for f(x)...
-vi=at, vi=b and a(acceleration)=2a(from quadratic) and t=x
-b=2ax
x=-b/(2a) in this case
x=-12/(2(-3))
x=-12/-6
x=2
