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abruzzese [7]
3 years ago
11

144

Mathematics
1 answer:
ahrayia [7]3 years ago
8 0

Answer:

a³b < 0

Step-by-step explanation:

If a > 0 then a³ > 0

and b < 0

then

a³b → + × - → -

that is a³b < 0

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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
Find the quotient of 2.632 · 104 and 2 · 10-7.
faust18 [17]
<span> 2.632 x 10^4  ÷  2 x 10-7 =

1.316 x 10^11


</span>
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3 years ago
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If 3 cups of rice serves 5 people, how many cups do you need to serve 13 people
elena-14-01-66 [18.8K]
First let's find out how many cups serve one person.

3 ÷ 5 = 1.6

1.6 of a cup serves one person.

1.6 × 13 = 20.8

It takes 20.8 (21 rounded) to serve 13 people.
3 0
3 years ago
On a coordinate plane, two parabolas open up. The solid-line parabola goes through (1, 3), has a vertex at (3, negative 1), and
anastassius [24]

Answer:

c.right 3 units, down 1 unit

Step-by-step explanation:

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if a 25 ft rope is cut into two sections with one section four times as long as the other section, how long is the shorter piece
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3.125 ft long or 3.13 ft long
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