Answer:
(32/15, -2/5)
Step-by-step explanation:
(1) ³/₂x - 2y = 4
(2) x + ⅓y = 2
(3) 3x - 4y = 8 Multiplied (1) by 2
(4) 3x + y = 6 Multiplied (2) by 3
5y = -2 Subtracted (3) from (4)
(5) y = -⅖ Divided each side by 5
x + ⅓(-⅖) = 2 Substituted (5) into (2)
x - ²/₁₅ = 2
x = 2 + ²/₁₅ Added ²/₁₅ to each side
x = 32/15
The system of equations has only one solution: (32/15, -2/5).
Answer:
<em>work done is equal to 384279168 lb-ft</em>
<em></em>
Step-by-step explanation:
The cylinder has a circular base of 7 ft.
The height of the cylinder is 200 ft
The weight density of water in the cylinder is 62.4 lb/ft^3
First, we find the volume of the water in the cylinder by finding the volume of this cylinder occupied by the water.
The volume of a cylinder is given as
where, r is the radius,
and h is the height of the cylinder.
the volume of the cylinder = = <em>30791.6 ft^3</em>
Since the weight density of water is 62.4 lb/ft^3, then, the weight of the water within the cylinder will be...
weight of water = 62.4 x 30791.6 = <em>1921395.84 lb</em>
We know that the whole weight of the water will have to be pumped out over the height of cylindrical container. Also, we know that the work that will be done in moving this weight of water over this height will be the product of the weight of water, and the height over which it is pumped. Therefore...
The work done in pumping the water out of the container will be
==> (weight of water) x (height of cylinder) = 1921395.84 x 200
==> <em>work done is equal to 384279168 lb-ft</em>
Answer:
It would take 24 minutes for the element to decay to 50 grams
Step-by-step explanation:
The equation for the amount of the element present, after t minutes, is:
In which Q(X) decays radioactively with a half life of 12 minutes.(0) is the initial amount and r is the rate it decreases.
Half life of 12 minutes
This means that
So
If there are 200 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 50 grams?
This is t when Q(t) = 50. Q(0) = 200.
It would take 24 minutes for the element to decay to 50 grams