(2x to the 5th power) 3x to the 3/5th power

3 litres of water is how many cups? 3 litres of water is how many cups? 1 following 5 answers 5 Report Abuse Are you sure you wa

Valentin [98]

If a cup is a regular sized cup that is 2 deciliters, and 1 liter equals 10 deciliters, that means that 1 liter = 5 cups, which means that 3 liters = 15 cups. If it is a cup that has 0.33 dl, then the correct number would be 9 cups.

8 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

Find the diameter of a dinner plate whose circumference is about 19 inches

vodka [1.7K]

The answer is 4.6
the equation is 19 * 4.13

8 0

3 years ago

Lapsed time 2:45-5:15

Arturiano [62]

The answer is 2 1/2hours

5 0

3 years ago

At the mall, buying a pair of shoes and buying a book are independent events.The probability that a shopper buys shoes is 0.20.

Goryan [66]

Answer: Probability that a shopper buys shoes and a book is 0.02.

Step-by-step explanation:

Since we have given that

Event A : Buying a pair of shoes

Event B: Buying a book

Since A and B are independent events.

Probability that a shopper buys shoes i.e.

P(A) = 0.20

Probability that a shopper buys a book i.e.

P(B)=0.10

So, we need to find the probability that a shopper buys shoes and a book is given by

$P(A\ and\ B)=P(A\cap B)=P(A).P(B)\\\\P(A\cap B)=0.20\times 0.10\\\\P(A\cap B)=0.02$

Hence, Probability that a shopper buys shoes and a book is 0.02.

3 0

3 years ago