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-BARSIC- [3]
3 years ago
12

A cup has the shape of a right circular cone. The height of the cup is 12 cm, and the radius of the opening is 3 cm. Water is po

ured into the cup at a constant rate of 32 cm /sec. What is the rate at which the water level is rising when the depth of water in the cup is 5cm?
Mathematics
1 answer:
torisob [31]3 years ago
3 0

Answer:

  about 6.52 cm/s

Step-by-step explanation:

The radius of the cone is 3/12 = 1/4 of its height, so the radius of the water surface at the time of interest is (5 cm)/4 = 1.25 cm.

The area of the water's surface is ...

  A = πr² = π(5/4 cm)² = 25π/16 cm²

The rate of change of depth multiplied by this area will give the rate of change of volume.

  dV/dt = (25π/16 cm²)(dh/dt)

  dh/dt = (32 cm³/s)/(25π/16 cm²) = 512/(25π) cm/s ≈ 6.52 cm/s

The water is rising at the rate of about 6.52 cm/s.

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aliya0001 [1]

Answer:

the guinea pig is 21 cm longer

Step-by-step explanation:

fish = 40 mm

guinea pig 25 cm

convert the fish to cm

1 cm = 10 mm

40 mm * 1 cm/10 mm =  4 cm


guinea  pig - fish

25 cm - 4 cm

21 cm

the guinea pig is 21 cm longer

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What is the simplest form of 8/40?
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1/5 is the Simples Form
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The angles of a triangle add up to 180 degrees.
Alex_Xolod [135]

Answer:

33°

Step-by-step explanation:

We were given that:

1- The angles of a triangle add up to 180 degrees

2- The second angle is 15 degrees larger than the smallest angle

3- The third angle is 3 times as big as the smallest angle

So, first of all, let's call the smallest angle x.

the second angle will be (x + 15°) since it is 15 degrees greater than the smallest angle

and the third will be 3x, since it is 3 times bigger than the smallest angle.

With the information we have, we can form an equation!

180° = x + (x+ 15°) + 3x

180° = 5x + 15°

180° - 15° = 5x + 15° - 15°

165° = 5x

165°/5 = 5x/5

33° = x

therefore, the smallest angle measures 33° degrees, the second angle measures 48° and the third angle measures 99°.

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so it is safe to say this answer is correct!

8 0
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What number is missing from the table of equivalent ratios
denpristay [2]

8 is missing for the table

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Answer:

Third option

Step-by-step explanation:

We can't factor this so we need to use the quadratic formula which states that when ax² + bx + c = 0, x = (-b ± √(b² - 4ac)) / 2a. However, we notice that b (which is 6) is even, so we can use the special quadratic formula which states that when ax² + bx + c = 0 and b is even, x = (-b' ± √(b'² - ac)) / a where b' = b / 2. In this case, a = 1, b' = 3 and c = 7 so:

x = (-3 ± √(3² - 1 * 7)) / 1 = -3 ± √2

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