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Kamila [148]
2 years ago
15

A cylindrical tank with radius 5 m is being filled with water at a rate of 3 cubic meters per minute. How fast is the height of

the water increasing
Mathematics
1 answer:
sasho [114]2 years ago
4 0

Answer:

Step-by-step explanation:

Let's calculate the volume of the tank per each meter in height.

The volume of a cylinder is πr²h, where h is the height.  

A height of 1 meter in a tank with a radius of 5 meters would hold a volume of:

Vol = (3.14)*(5 meters)^2 *(1 meter)

Vol (m^3) = 78.54 m^3 per 1 meter height.

If the tank were filled at a rate of 3 m^3/min, it would rise at at a rate of:

(78.54 m^3/meter)/(3 m^3/min) = 0.0382 meters/minute [38.2 cm/min

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Answer:

Step-by-step explanation:

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B)

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6 0
3 years ago
34
Vadim26 [7]

Answer:

They are similar by the definition of similarity in terms of a dilation

Step-by-step explanation:

The given vertices of triangle ΔABC are;

A(1, 5), B(3, 9), and C(5, 3)

The vertices of triangle ΔDEF are;

D(-3, 3), E(-2, 5), and F(-1, 2)

Therefore, we get;

The length of segment, \overline{AB} = √((9 - 5)² + (3 - 1)²) = 2·√5

The length of segment, \overline{BC} = √((9 - 3)² + (3 - 5)²) = 2·√10

The length of segment, \overline{AC} = √((5 - 3)² + (1 - 5)²) = 2·√5

The length of segment, \overline{DE} = √((5 - 3)² + (-2 - (-3))²) = √5

The length of segment, \overline{EF} = √((2 - 5)² + (-1 - (-2))²) = √10

The length of segment, \overline{DF} = √((2 - 3)² + (-1 - (-3))²) = √5

∴ \overline{AB}/\overline{DE} = 2·√5/(√5) = 2

\overline{BC}/\overline{EF} = 2·√10/(√10) = 2

\overline{AC}/\overline{DF} = 2·√5/(√5) = 2

The ratio of their corresponding sides are equal and therefore;

ΔABC and ΔDEF are similar by the definition of similarity in terms of dilation.

4 0
3 years ago
A science class helped to estimate the population of various species in their local woods. Initially they tagged various numbers
Morgarella [4.7K]

Answer:

67

Step-by-step explanation:

8 0
2 years ago
Calculate the mean, median, and mode of the following set of data. Round to the nearest tenth. 3, 15, 3, 3, 1, 11, 2, 8, 3, 7, 1
zubka84 [21]
The mode is 3. The median is 3. The mean is 6.45 and rounded to the nearest tenth is 6.5. So the mean is 6.5.
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3 years ago
Center ( 9,-8 ), passes through ( 19,22 )
katovenus [111]
Center at (h,k) and radius r is
(x-h)²+(y-k)²=r²

so given
center at (9,-8)

(x-9)²+(y-(-8))²=r²
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input the point (19,22) to find r²
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(19-9)²+(22+8)²=r²
10²+30²=r²
100+900=r²
1000=r²
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well, the equation is
(x-9)²+(y+8)²=1000
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