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aleksley [76]
2 years ago
8

Since there are 5,280 feet in one mile and 3.3 feet in one meter how many meters per second are equivalent to 144 miles per hour

Mathematics
1 answer:
chubhunter [2.5K]2 years ago
8 0
He would be going at a rate of
51 meters per second
Could you mark the Brainliest?
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Water is leaking out of an inverted conical tank at a rate of 6800 cubic centimeters per min at the same time that water is bein
ivanzaharov [21]

Answer:

1508527.582 cm³/min

Step-by-step explanation:

The net rate of flow dV/dt = flow rate in - flow rate out

Let flow rate in = k. Since flow rate out = 6800 cm³/min,

dV/dt = k - 6800

Now, the volume of a cone V = πr²h/3 where r = radius of cone and h = height of cone

dV/dt = d(πr²h/3)/dt = (πr²dh/dt)/3 + 2πrhdr/dt (since dr/dt is not given we assume it is zero)

So, dV/dt = (πr²dh/dt)/3

Let h = height of tank = 12 m, r = radius of tank = diameter/2 = 3/2 = 1.5 m, h' = height when water level is rising at a rate of 21 cm/min = 3.5 m and r' = radius when water level is rising at a rate of 21 cm/min

Now, by similar triangles, h/r = h'/r'

r' = h'r/h = 3.5 m × 1.5 m/12 m = 5.25 m²/12 m = 2.625 m = 262.5 cm

Since the rate at which the water level is rising is dh/dt = 21 cm/min, and the radius at that point is r' = 262.5 cm.

The net rate of increase of water is dV/dt = (πr'²dh/dt)/3

dV/dt = (π(262.5 cm)² × 21 cm/min)/3

dV/dt = (π(68906.25 cm²) × 21 cm/min)/3

dV/dt = 1447031.25π/3 cm³

dV/dt = 4545982.745/3 cm³

dV/dt = 1515327.582 cm³/min

Since dV/dt = k - 6800 cm³/min

k = dV/dt - 6800 cm³/min

k = 1515327.582 cm³/min - 6800 cm³/min

k = 1508527.582 cm³/min

So, the rate at which water is pumped in is 1508527.582 cm³/min

5 0
3 years ago
For f(x) = 3x +1 and g(x) = x2 – 6, find (f- g)(x).
Fiesta28 [93]

Answer:

\boxed{\sf (f-g)(x) = -{x}^{2}  + 3x + 7}

Given:

\sf f(x) = 3x + 1 \\ \sf g(x) =  {x}^{2}  - 6

To find:

\sf (f - g)(x) = f(x) - g(x)

Step-by-step explanation:

\sf \implies(f - g)x = f(x) - g(x) \\  \\ \sf \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:    = (3x + 1) - ( {x}^{2}  - 6) \\  \\ \sf \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:    = (3x + 1)  + (-  {x}^{2}  + 6) \\  \\ \sf \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:    = 3x + 1 -  {x}^{2}  + 6 \\  \\ \sf \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:    = - {x}^{2}  + 3x + 1 + 6 \\  \\ \sf \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:    =  -{x}^{2}  + 3x + 7

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Add4 Then Add 39 ok you got this
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on monday the bookstore sold 75 books. on tuesday the bookstore sold 125 books. the bookstore must sell 500 book by friday how m
Serhud [2]
There were 200 books sold. so, they need to sell 300 more to have 500 total books sold.
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Step-by-step explanation:

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