If it costs $1.40 per square foot to install the garden, what is the cost for plan A?

Good Treads and Speed Tracks manufacture tires. Good Treads claims that their tires last longer than Speed Tracks tires. A car c

Crazy boy [7]

The answer is B... good treads claim is false therefore it can be concluded that speed tracks tires last longer than good treads tires

3 0

3 years ago

Read 2 more answers

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

Anwser true or false

m_a_m_a [10]

False because doing the math doesn’t match

6 0

2 years ago

Read 2 more answers

3y-x=3 and x is four times the value of y what is the value of x-y?

Aleonysh [2.5K]

Answer:

x - y = -9

Step-by-step explanation:

from the equation

3y - x = 3

and x is four times the value of y

i.e x = 4y

put x = 4y into the first equation

we have;

3y - 4Y = 3

-Y = 3

Divide both sides by -1

we have

y = -3

so put y = -3 in the 2nd equation

i.e x = 4y

x = 4 × -3

x = -12

therefore x = -12 and y = -3

so tho find x - y

we have

-12 - (-3)

= -9

therefore x - y = -9

7 0

3 years ago

Geometry it's about relations within triangles. need help solving for variables

elena-14-01-66 [18.8K]

Answer:

`18. x=9

19. x=4

20. x=25,5

21. x=3

22. x=3,5

23. x=10

Step-by-step explanation:

5 0

2 years ago