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vlada-n [284]
3 years ago
14

A water tank has a square base of area 5 square meters. Initially the tank contains 70 cubic meters. Water leaves the tank, star

ting at t=0, at the rate of 2 + 4 t cubic meters per hour. Here t is the time in hours. What is the depth of water remaining in the tank after 3 hours
Mathematics
1 answer:
ANEK [815]3 years ago
3 0

Answer:

9.2\ \text{m}

Step-by-step explanation:

b = Surface area of base = 5 square meters

Volume of water in tank = 70 cubic meters

The rate at which the volume is reducing is

\dfrac{dV}{dt}=2+4t\\\Rightarrow dV=2+4tdt

Integrating from t=0 to t=3

V=\int^3_0(2+4t)dt\\\Rightarrow V=2t+2t^2|_0^3\\\Rightarrow V=2\times 3+2\times 3^2-0\\\Rightarrow V=24

Volume of water remaining in the tank is 70-24=46\ \text{m}^3

Suface area of base \times depth = Volume

5\times d=46\\\Rightarrow d=\dfrac{46}{5}\\\Rightarrow d=9.2\ \text{m}

The depth of the water remaining in the tank is 9.2\ \text{m}.

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Jobisdone [24]

Answer:

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<em>Or, equivalently: y=9</em>

<em>This represents a horizontal line</em>

Step-by-step explanation:

<em>Equation of the line</em>

The point-slope form of the equation of a line is:

y-k=m(x-h)

Where m is the slope and (h,k) is a point through which the line passes.

Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:

\displaystyle m=\frac{y_2-y_1}{x_2-x_1}

The points are (6,9) and (7,9). These points dfine a horizontal line, as we'll see later.

The slope is:

\displaystyle m=\frac{9-9}{7-6}=0

m=0

Now compute the equation in point-slope form:

y-9=0(x-6)

Solving for y:

y=9

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7 0
3 years ago
Simplify 8 over the quantity of 2 plus 2i.
dexar [7]

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5 0
3 years ago
What’s the distance between (4,-9) and (5,3)
laila [671]

Answer: Distance = √145

Concept:

Here, we need to know the concept of the distance formula.    

The distance formula is the formula, which is used to find the distance between any two points.

If you are still confused, please refer to the attachment below for a clear version of the formula.

Solve:

<u>Given information</u>

(x₁, y₁) = (4, -9)

(x₂, y₂) = (5, 3)

<u>Given formula</u>

Distance = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

<u>Substitute values into the formula</u>

Distance = \sqrt{(5-4)^2+(3+9)^2}

<u>Simplify values in the parentheses</u>

Distance = \sqrt{(1)^2+(12)^2}

<u>Simplify exponents</u>

Distance = \sqrt{1+144}

<u>Simplify by addition</u>

Distance = \sqrt{145}

Hope this helps!! :)

Please let me know if you have any questions

7 0
2 years ago
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Given:

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Leno4ka [110]

Answer:

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Step-by-step explanation:

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