The price of a ticket to a play is $50 per person. On Monday afternoons, the theater reduces the ticket price to $35 per

in a regular polygon each interior angle is 140 greater than each exterior angle calculate the number of sides of each polygon .

Elodia [21]

Answer:

9

Step-by-step explanation:

Exterior sides = 180 - 140 = 40

number of sides = 360 / 40 = 9 sides

6 0

3 years ago

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

3 years ago

after this 120-second period , how much time,in seconds will it take for the scientist to travel back to sea level at the submar

love history [14]

Unanswerable. How bout you give us the appropriate info before asking a question?

4 0

3 years ago

Read 2 more answers

For 6 consecutive days, Alejandro studied for 5 minutes more each day than he did the previous day. Which best represents the ch

kap26 [50]

Answer:

I believe its 30

Step-by-step explanation:

because he studied for five minutes the first day and then added five minutes per day for 6 days so i think its 30

8 0

2 years ago

Read 2 more answers

Help me for the love of god

Colt1911 [192]

Answer:

(x, y) --> (x + 4, y - 3)

Step-by-step explanation:

The x value concerns left and right, while the y value concerns up and down. Adding to x makes it move right, and adding to y makes it move up.

3 0

3 years ago