Z= a/m, for a It a literal equation
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Answer:
The exact work required to pump all the gasoline to the surface of the ground is π × 5.094 × 10⁶ j
Step-by-step explanation:
Here, we note that volume of a slice is given by
Length × Width × Height
Length of slice = Length of cylinder = 15 ft
Since the slice height is Δy ft thick and located y ft above the center of the cylinder, then
Width of slice = 2 × √(r² - y²)
Where:
r = Radius of the cylinder =5 ft
∴ Width of slice = 2 × √(25 - y²)
∴Volume of slice = 15 ×2 × √(25 - y²)×Δy
Mass of slice then = 42 × 15 ×2 × √(25 - y²)×Δy = 1260 × √(25 - y²)×Δy
The force required to lift the slice is the weight of the slice, which is given by
32.2 × 1260 × √(25 - y²)×Δy = 40572 × √(25 - y²)×Δy N (Newtons)
The work done by the force is the product of the force and the distsnce through which the force acts.
Work done = 40752×(10-y) × √(25 - y²)×Δy
Therefore total work done is given by
= 5094000·π J = π × 5.094 × 10⁶ j
The exact work required to pump all the gasoline to the surface of the ground = π × 5.094 × 10⁶ j
as you notice, the first term from the binomial, starts off with a highest exponent of 10, and then gradually goes down by 1 on every element.
the second term of the binomial, starts off with an exponent of 0, and goes up by 1 on every element.
now, to get the coefficient
the first coefficient is 1 and the second is the same as the binomial's exponent... those two are simple.... now, to get any subsequent one, we simply "get the product of the current coefficient and the exponent of the first term, and divide it by the exponent of the second term on the next element".
for example... how do we get 10 for the second element, basically 1 * 10/1
that one is simple
now how do we get say, 45 for the 3rd element?
10 * 9 / 2
how do we get 252 for the 6th element?
210 * 6 / 5
and so on, and from there, you can expand each element.