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3 years ago

I’ll give brainlist and all 5 stars!

Mathematics

2 answers:

malfutka [58]3 years ago

6 0

The answer is C, A, & C

blsea [12.9K]3 years ago

3 0

Answer:

Step-by-step explanation:

6) Slope = 5

(5 , 40) ; m =5

y - y1 = m(x -x1)

y - 40 = 5 (x - 5)

y -40 = 5x - 25

y = 5x - 25 + 40

y = 5x + 15

7) slope = 2

m =2 ; (-2 , 0)

y - y1 = m(x -x1)

y - 0 = 2(x -[-2])

y = 2(x +2)

y = 2x +4

8) D) It takes 6 miles to travel a mile

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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

Anyone know the answer to this?

Kaylis [27]

I think its a

because the line segments connect each other.

3 0

3 years ago

The sum of the quotient of a number and and 3 and 8 is 16 what is the number

zhuklara [117]

After having done this on paper:

$\frac{n}{3} + 8 = 16$

We want to isolate the variable, and the first step is to subtract the 8.

$\frac{n}{3} = 8$

Since the n is being multiplied by 3, and that = 8, we can multiply both sides by 3.

n = 24

Let me know if this helped you understand better.

Also, you can check this by substituting in 24 for n.

5 0

3 years ago

Qfind the product. Write the product in simplest form 1 2/3 x 4 2/5

Elan Coil [88]

1 2/3 = 5/3
4 2/5 = 22/5
5/3•22/5= 110/15
= 22/3

7 0

3 years ago

A restaurant bill comes to $28.35. Determine the total cost if the tax is 6.25% and a 20% tip is left on the amount before tax

Soloha48 [4]

In the given problem there are several known and important facts to take note of. Firstly the restaurant bill without tax and tips is $28.35. Then the tax of 6.25% needs to be added with the bill. Also a tip of 20% on the original bill needs to be added to find the total cost.
Then tax on the restaurant bill = (6.25/100) * 28.35
   = 1.77
So the tax on the restaurant bill is $1.77
Amount of tips given = 28.35 * (20/100)
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Amount of tips paid is $5.67
Total cost paid in the restaurant = ( 28.35 + 1.77 + 5.67) dollars
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8 0

3 years ago