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lakkis [162]
3 years ago
8

R leaks out of a barrel so that the rate of change in the water level is proportional to the square root of the depth of the wat

er at that time. if the water level starts at 30 inches and drops to 29 inches in 1 hour, how many hours will it take for all of the water to leak out of the
Mathematics
1 answer:
Irina-Kira [14]3 years ago
5 0
Let y(t) represent the level of water in inches at time t in hours. Then we are given ...
  y'(t) = k√(y(t)) . . . . for some proportionality constant k
  y(0) = 30
  y(1) = 29

We observe that a function of the form
  y(t) = a(t - b)²
will have a derivative that is proportional to y:
  y'(t) = 2a(t -b)

We can find the constants "a" and "b" from the given boundary conditions.
At t=0
  30 = a(0 -b)²
  a = 30/b²
At t=1
  29 = a(1 - b)² . . . . . . . . . substitute for t
  29 = 30(1 - b)²/b² . . . . . substitute for a
  29/30 = (1/b -1)² . . . . . . divide by 30
  1 -√(29/30) = 1/b . . . . . . square root, then add 1 (positive root yields extraneous solution)
  b = 30 +√870 . . . . . . . . simplify

The value of b is the time it takes for the height of water in the tank to become 0. It is 30+√870 hours ≈ 59 hours 29 minutes 45 seconds
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A tennis ball in the shape or a sphere has a diameter of 6.7 centimeters which is closest to the volume
Lynna [10]
In your question it seems like there should be choices too! Either way, how does one find the volume of a sphere?
8 0
2 years ago
Order the numbers from least to greatest.<br><br> 1/2, 0.55, 5/7
nata0808 [166]

1/2 = .5

5/7 =.714...........

least to greatest

1/2, .55, 5/7

5 0
3 years ago
Need math helpppppp pls:)
Arisa [49]

Answer:

Similar AA

Step-by-step explanation:

To find the third angle of a right triangle you add 90 to the angle and subtract from 180

so angle E is 180-(55+90)=35 so the triangles have 2 angles are the same so

Similar AA

7 0
2 years ago
Julie bought $8.64 worth of 57-cent stamps and 30-cent stamps. The number of 30-cent stamps was 6 less than the number of 57-cen
Yuri [45]

Answer:

The number of 57-cent stamps that Julie bought is 12

Step-by-step explanation:

Given equation

0.57 s + 0.3 ( s − 6 ) = 8.64

Open bracket

0.57s + 0.3s - 1.8 = 8.64

Collect like terms

0.87s = 8.64 + 1.8

0.87s = 10.44

Divide both sides by 0.87

s = 12

The number of 57-cent stamps that Julie bought is 12

3 0
3 years ago
The length of the hypotenuse of a right triangle is 24. If the length of one leg is 8, what is approximate length of the other l
Verdich [7]

Something that a right triangle is characterised by is the fact that we may use Pythagoras' theorem to find the length of any one of its sides, given that we know the length of the other two sides. Here, we know the length of the hypotenuse and one other side, therefor we can easily use the theorem to solve for the remaining side.

Now, Pythagoras' Theorem is defined as follows:

c^2 = a^2 + b^2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

Given that we know that c = 24 and a = 8, we can find b by substituting c and a into the formula we defined above:

c^2 = a^2 + b^2

24^2 = 8^2 + b^2 (Substitute c = 24 and a = 8)

b^2 = 24^2 - 8^2 (Subtract 8^2 from both sides)

b = √(24^2 - 8^2) (Take the square root of both sides)

b = √512 (Evaluate 24^2 - 8^2)

b = 16√2 (Simplify √512)

= 22.627 (to three decimal places)

I wasn't sure about whether by 'approximate length' you meant for the length to be rounded to a certain number of decimal places or whether you were meant to do more of an estimate based on your knowledge of surds and powers. If you need any more clarification however don't hesitate to comment below.

4 0
3 years ago
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