Please help! Homework DUE TOMORROW!!!

A large fish tank at an aquarium needs to be emptied so that it can be cleaned. When its

VikaD [51]

Answer:

The draining time when only the big drain is opened is 2.303 hours.

The draining time when only the small drain is opened is 5.303 hours.

Step-by-step explanation:

From Physics, we know that volume flow rate ( $\dot V$ ), measured in liters per hour, is directly proportional to draining time ( $t$ ), measured in hours. That is:

$\dot V \propto \frac{1}{t}$

$\dot V = \frac{k}{t}$ (Eq. 1)

Where $k$ is the proportionality constant, measured in liters.

From statement, we have the following three expressions:

(i) Large and small drains are opened

$\dot V_{s}+\dot V_{l} = \frac{k}{2}$ (Eq. 2)

$\frac{\dot V_{s}+\dot V_{l}}{k} = \frac{1}{2}$

(ii) Only the small drain is opened

$\dot V_{s} = \frac{k}{t_{l}+3}$ (Eq. 3)

$\frac{\dot V_{s}}{k} = \frac{1}{t_{l}+3}$

(iii) Only the big drain is opened

$\dot V_{l} = \frac{k}{t_{l}}$ (Eq. 4)

$\frac{\dot V_{l}}{k} = \frac{1}{t_{l}}$

By applying (Eqs. 3, 4) in (Eq. 2) and making some algebraic handling, we find that:

$\frac{1}{t_{l}+3}+\frac{1}{t_{l}} = \frac{1}{2}$

$\frac{t_{l}+t_{l}+3}{t_{l}\cdot (t_{l}+3)} = \frac{1}{2}$

$2\cdot t_{l}+3 = t_{l}^{2}+3\cdot t_{l}$

$t_{l}^{2}-t_{l}-3 = 0$ (Eq. 5)

Whose roots are determined by the Quadratic Formula:

$t_{l,1}\approx 2.303\,h$ and $t_{l,2} \approx -1.302\,h$

Only the first roots offers a solution that is physically reasonable. Hence, the draining time when only the big drain is opened is 2.303 hours. And the time needed for the small drain is calculated by the following formula:

$t_{s} = 2.303\,h+3\,h$

$t_{s} = 5.303\,h$

The draining time when only the small drain is opened is 5.303 hours.

7 0

3 years ago

I am having some problem can anyone please help me out to do this math. (x + 3)(x + 4)

Lorico [155]

Answer:

x^2 + 7x + 12

Step-by-step explanation:

This is a product of two binomials. There's a formula:

(a + b)(c + d) = ac + ad + bc + bd.

Therefore, (x + 3)(x + 4) = x^2 + 3x + 4x + 12 = x^2 + 7x + 12

6 0

2 years ago

Is -33 irrational or rational?

vladimir2022 [97]

-33 is a rational number. It is an integer with a definitive stopping point (by this I mean it is not a decimal number with endless repeating digits).

4 0

3 years ago

Please help!!!!! 8g^2+6g-9

Paraphin [41]

Your answer is
2(4g^2+3g-3)

3 0

3 years ago

Read 2 more answers

An advertiser goes to a printer and is charged $73 for 100 copies of one flyer and $82 for 400 copies of a similar flyer. Assumi

USPshnik [31]

Answer:

y = 0.03x + 70

Slope here represents the variation in the charges with the change in the number of flyers

Positive slope means that the cost is increasing with increase in number of flyers

Step-by-step explanation:

Given:

for 100 copies advertiser is charged = $73

For 400 copies advertiser is charged = $82

Now,

here the charge is a function of number of flyers

we have the general line equation for a linear relationship as:

y = mx + c

here m is the slope

c is the constant

for the first case we have

y = $73

x = 100

thus,

73 = 100m + c ...........(1)

for the second case, we have

y = $82

x = 400

thus,

82 = 400m + c ...........(2)

subtracting (1) from (2)

82 = 400m + c

- ( 73 = 100m + c )

==================

9 = 300m + 0

or

m = 0.03

substituting the value of slope in equation (1)

73 = 100 × 0.03 + c

73 = 3 + c

or

c = 70

Hence,

the equation is y = 0.03x + 70

here y is amount charged and x are the number of flyers.

Slope here represents the variation in the charges with the change in the number of flyers

Positive slope means that the cost is increasing with increase in number of flyers

3 0

3 years ago