Which rational function has zeros at x = 1 and x = 3?

Can someone please give this answer and plz give me the right answers

Alenkinab [10]

girl come.................

8 0

2 years ago

Problem 10: A tank initially contains a solution of 10 pounds of salt in 60 gallons of water. Water with 1/2 pound of salt per g

AysviL [449]

Answer:

The quantity of salt at time t is $m_{salt} = (60)\cdot (30 - 29.833\cdot e^{-\frac{t}{10} })$ , where t is measured in minutes.

Step-by-step explanation:

The law of mass conservation for control volume indicates that:

$\dot m_{in} - \dot m_{out} = \left(\frac{dm}{dt} \right)_{CV}$

Where mass flow is the product of salt concentration and water volume flow.

The model of the tank according to the statement is:

$(0.5\,\frac{pd}{gal} )\cdot \left(6\,\frac{gal}{min} \right) - c\cdot \left(6\,\frac{gal}{min} \right) = V\cdot \frac{dc}{dt}$

Where:

$c$ - The salt concentration in the tank, as well at the exit of the tank, measured in $\frac{pd}{gal}$ .

$\frac{dc}{dt}$ - Concentration rate of change in the tank, measured in $\frac{pd}{min}$ .

$V$ - Volume of the tank, measured in gallons.

The following first-order linear non-homogeneous differential equation is found:

$V \cdot \frac{dc}{dt} + 6\cdot c = 3$

$60\cdot \frac{dc}{dt} + 6\cdot c = 3$

$\frac{dc}{dt} + \frac{1}{10}\cdot c = 3$

This equation is solved as follows:

$e^{\frac{t}{10} }\cdot \left(\frac{dc}{dt} +\frac{1}{10} \cdot c \right) = 3 \cdot e^{\frac{t}{10} }$

$\frac{d}{dt}\left(e^{\frac{t}{10}}\cdot c\right) = 3\cdot e^{\frac{t}{10} }$

$e^{\frac{t}{10} }\cdot c = 3 \cdot \int {e^{\frac{t}{10} }} \, dt$

$e^{\frac{t}{10} }\cdot c = 30\cdot e^{\frac{t}{10} } + C$

$c = 30 + C\cdot e^{-\frac{t}{10} }$

The initial concentration in the tank is:

$c_{o} = \frac{10\,pd}{60\,gal}$

$c_{o} = 0.167\,\frac{pd}{gal}$

Now, the integration constant is:

$0.167 = 30 + C$

$C = -29.833$

The solution of the differential equation is:

$c(t) = 30 - 29.833\cdot e^{-\frac{t}{10} }$

Now, the quantity of salt at time t is:

$m_{salt} = V_{tank}\cdot c(t)$

$m_{salt} = (60)\cdot (30 - 29.833\cdot e^{-\frac{t}{10} })$

Where t is measured in minutes.

7 0

3 years ago

Which is the graph of f(x) = -(x + 3)(x + 1)?

Bas_tet [7]

Answer:

See attachment

Step-by-step explanation:

A function is given to us and we need to tell which graph represents the given function. The function given to us is,

$\tt: \implies f(x) = -( x + 3 )( x + 1 )$

Let's find out at which points do the graph Intersects x axis / finding the roots. For that substitute f(x) = 0 , we have ,

$\tt: \implies -(x +3)( x + 1 ) = 0$

Equate each factor by 0 ,

$\tt: \implies \boxed{\blue{ \tt x = -1,-3 }}$

Therefore the graph will intersect x axis at x is equal to -1 and x is equal to -3 .

On looking at the given graphs in the options the second graph intersects x axis at -1 and -3 .

Hence the second option is correct . 

{ See attachment }

4 0

3 years ago

PLZZZZZZZZZZZZZ HELP MEE

user100 [1]

Answer:

it's B

Step-by-step explanation:

2/8 = 1/4 = 0.25

1/2=0.5

0.5>0.25

so (1/2)>(1/4)

7 0

3 years ago

The composite figure is made up of three simpler shapes. What is the area of the figure?

Flauer [41]

4 × 3
−−−− = 6cm²
2

6 × 3 = 18cm²

10 × 5 = 50cm²

50 + 18 + 6 = 72cm²

7 0

1 year ago

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