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3 years ago

Find the value of x . A: 13/5 B: 5 C: 19/5 D: 3

Mathematics

2 answers:

LenaWriter [7]3 years ago

8 0

The correct answer is B, x=5 :)

Alisiya [41]3 years ago

3 0

For getting to the actual value of "x", we have to solve an equation.
(5x - 1/2 = 12
5x -1 = 12 * 2
5x - 1 = 24
5x = 24 + 1
5x = 25
x = 25/5
= 5
From the above deduction we can easily conclude that the value of "x" is 5 and the correct option among all the options that are given in the question is the second option or option "B". I hope the procedure is clear enough for you to understand.

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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

X is less than or equal to 2 Write in interval notation.

Talja [164]

X is less than -2, so -2 is our largest value of the interval, so it goes on the right. Since there is no lower endpoint (it is ALL values less than -2), we put the negative infinity symbol on the left side. The curved end on -2 indicates an open interval

3 0

3 years ago

What is the value of y in the solution to the system of equations?

Yuliya22 [10]

Answer: y = 8

Step-by-step explanation:

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Problem page a delivery truck is transporting boxes of two sizes: large and small. the large boxes weigh 45 pounds each, and the

marta [7]

S= number of small boxes
l= number of large boxes

equation 1: s+l=120
equation 2: 15s+45l=3300

solve by elimination, multiply equation 1 by -15.

-15(s+l=120) = -15s-15l=-1800 add to equation 2.

-15s+15s-15l+45l=-1800+3300 = 30l=1500

30l=1500 , l=50

s+l=120, s+50=120 --> s=70

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3 years ago

On a scale drawing, the scale factor is 1/12. A plum tree is 7 inches tall on the scale drawing. What is the actual height of th

Sedbober [7]

B. 84

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3 years ago

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