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2 years ago

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A water tank is box shaped with a square base of side length 5 ft. The tank is fed by a pipe above and drains from its base. In

order to have a well mixed solution, both the feeder pipe and the drain must be opened. The tank is being filled at a rate of 25 ft3/s when the height of the liquid in the tank is 10 ft. If the drains are pulling 30 ft3/s, what is the rate of change in the depth of the solution in the tank

1 answer:

adell [148]2 years ago

6 0

Answer:

dy/dt = - (1/5) ft/s = - 0.2 ft/s

Step-by-step explanation:

Given

L = 5 ft

Qin = 25 ft³/s

Qout = 30 ft³/s

h = 10 ft

dy/dt = ?

We can apply the relation

ΔQ = Qint - Qout = 25 ft³/s - 30 ft³/s

⇒ ΔQ = - 5 ft³/s

Then we use the formula

Q = v*A

where Q = ΔQ, A = L² is the area of square base and v = dy/dt is the rate of change in the depth of the solution in the tank

⇒ ΔQ = (dy/dt)*L²

⇒ dy/dt = ΔQ/L²

⇒ dy/dt = (- 5 ft³/s)/(5 ft)²

⇒ dy/dt = - (1/5) ft/s = - 0.2 ft/s

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The values of 60, 62, and 84 were common to both samples. The three values are identified as outliers with respect to the age-gr

postnew [5]

Answer:

Only 60 is an identified outlier

Step-by-step explanation:

Given

<u>Age group: 40 to 50</u>

$Min = 60$ $Q_1 = 70$ $Median= 73$

$Q_3 = 76$ $Max = 85$

<u>Conditions for outlier</u>

$Value > Q_3 + 1.5 * IQR$

$Value < Q_1 - 1.5 * IQR$

<em>See attachment for complete question</em>

<u>Required</u>

Which of 60, 62 and 84 is an outlier of age grout 40 to 50 years

First, calculate the IQR of group 40 to 50.

This is calculated as:

$IQR = Q_3 - Q_1$

Where:

$Q_3 = 76$ and $Q_1 = 70$

So:

$IQR = 76 - 70$

$IQR = 6$

<em>Next, is to test the outlier conditions on each value (i.e. 60, 62 and 84)</em>

<u></u>

<u>Testing 60</u>

<u>Condition 1</u>

$Value > Q_3 + 1.5 * IQR$

$60 > 76 + 1.5 * 6$

$60 > 76 + 9$

$60 > 85$ --- False

<u>Condition 2</u>

$Value < Q_1 - 1.5 * IQR$

$60 < 70 - 1.5 * 6$

$60 < 70 - 9$

$60 < 61$ --- True

<em>Because one of the conditions is true, then 60 is an outlier of group 40 - 50 years</em>

<em></em>

<u>Testing 62</u>

<u>Condition 1</u>

$Value > Q_3 + 1.5 * IQR$

$62> 76 + 1.5 * 6$

$62 > 76 + 9$

$62 > 85$ --- False

<u>Condition 2</u>

$Value < Q_1 - 1.5 * IQR$

$62 < 70 - 1.5 * 6$

$62 < 70 - 9$

$62 < 61$ --- False

<em>Because both conditions are false, then 62 is not an outlier of group 40 - 50 years</em>

<em></em>

<u>Testing 84</u>

<u>Condition 1</u>

$Value > Q_3 + 1.5 * IQR$

$84> 76 + 1.5 * 6$

$84 > 76 + 9$

$84 > 85$ --- False

<u>Condition 2</u>

$Value < Q_1 - 1.5 * IQR$

$84 < 70 - 1.5 * 6$

$84 < 70 - 9$

$84 < 61$ --- False

<em>Because both conditions are false, then 84 is not an outlier of group 40 - 50 years</em>

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Step-by-step explanation:

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