Given the domain {-1,1,3} and the function f(x)=x2+7. Find the Range of the above function Range=

A 500-gallon tank initially contains 220 gallons of pure distilled water. Brine containing 5 pounds of salt per gallon flows int

Wittaler [7]

Answer: The amount of salt in the tank after 8 minutes is 36.52 pounds.

Step-by-step explanation:

Salt in the tank is modelled by the Principle of Mass Conservation, which states:

(Salt mass rate per unit time to the tank) - (Salt mass per unit time from the tank) = (Salt accumulation rate of the tank)

Flow is measured as the product of salt concentration and flow. A well stirred mixture means that salt concentrations within tank and in the output mass flow are the same. Inflow salt concentration remains constant. Hence:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = \frac{d(V_{tank}(t) \cdot c(t))}{dt}$

By expanding the previous equation:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt} + \frac{dV_{tank}(t)}{dt} \cdot c(t)$

The tank capacity and capacity rate of change given in gallons and gallons per minute are, respectivelly:

$V_{tank} = 220\\\frac{dV_{tank}(t)}{dt} = 0$

Since there is no accumulation within the tank, expression is simplified to this:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt}$

By rearranging the expression, it is noticed the presence of a First-Order Non-Homogeneous Linear Ordinary Differential Equation:

$V_{tank} \cdot \frac{dc(t)}{dt} + f_{out} \cdot c(t) = c_0 \cdot f_{in}$ , where $c(0) = 0 \frac{pounds}{gallon}$ .

$\frac{dc(t)}{dt} + \frac{f_{out}}{V_{tank}} \cdot c(t) = \frac{c_0}{V_{tank}} \cdot f_{in}$

The solution of this equation is:

$c(t) = \frac{c_{0}}{f_{out}} \cdot ({1-e^{-\frac{f_{out}}{V_{tank}}\cdot t }})$

The salt concentration after 8 minutes is:

$c(8) = 0.166 \frac{pounds}{gallon}$

The instantaneous amount of salt in the tank is:

$m_{salt} = (0.166 \frac{pounds}{gallon}) \cdot (220 gallons)\\m_{salt} = 36.52 pounds$

3 0

2 years ago

Which polynomial is a quadratic trinomial?

il63 [147K]

<h3>Answer: Choice C</h3>

The largest exponent here is 4, so that makes it a quartic.

There are 3 terms, so we have a trinomial. Each term is separated by either a plus or a minus.

Choice A shows a quartic polynomial. Choice B is a cubic polynomial. Choice d is a quadratic trinomial.

5 0

2 years ago

Identify all factors of the expression 12x^2-14x-6

Evgen [1.6K]

Let's solve this by using the quadratic formula:

$\frac{-b+-\sqrt{b^2-4ac} }{2a}$

Note that we only use the coefficients so a=12, b=-14, and c=-6.

Plug values in the quadratic equation:

$\frac{ - ( - 14)± \sqrt{ {( - 14)}^{2} - 4(12)( - 6) } }{2(12)}$

And so by evaluating those values we obtain:

$\frac{14+-\sqrt{484} }{24}=\frac{14+-22}{24} \\\\$

Now we have two answers which are our factors one where we add another where we subtract and so:

First factor:

$\frac{14+22}{24}=\frac{36}{24}=\frac{3}{2}$

Second Factor:

$\frac{14-22}{24}=\frac{-8}{24}=-\frac{1}{3}$

And so your factors are

$\frac{3}{2},-\frac{1}{3}$

meaning that those are your roots/x-intercepts.

6 0

2 years ago

Sarah starts a Jewelry making business. She borrows the money for the supplies to start. She borrows $1,500.00 for 2 years at a

LuckyWell [14K]

O would be the answer, but I’m not sure why you have 3
(360.00 to be exact)

3 0

2 years ago

A car travels 30 miles in ½ hour. What is the average speed at which the car is traveling in miles per hour?

DochEvi [55]

The answer is 1 mile per hour

7 0

2 years ago