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4 years ago

Solve the following equation by factoring: x^2 - 2x - 48 = 0

Mathematics

1 answer:

Vlada [557]4 years ago

4 0

Answer:

B. x=-6 or x=8

Step-by-step explanation:

To solve this, factor the equation x^2-2x-48. Since -48 is negative, one of the factors has to be negative and one has to be positive. Since the coefficient of x is -2, the factors have to sum to -2. Trying factors, we realize that (x-8)(x+6)=0 works. Solving, x-8=0 and x+6=0, or x=8 or x=-6.

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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

Question 3 < > In a particular class of 33 students, 18 are men. What fraction of the students in the class are women?

Juli2301 [7.4K]

Answer:

Your answer is 15 Women

Step-by-step explanation:

33-18= 15

8 0

3 years ago

Whats the greatest common factor of 42,28, and 70

kobusy [5.1K]

Answer:

Step-by-step explanation:

1 * 70

5 * 14

7 * 10

1 * 42

3 * 14

7 * 6

1 * 28

2 * 14

7 * 4

pick the largest factor from 70 and check it they also work with the other two. 14 is the GCF.

7 0

3 years ago

Read 2 more answers

Solve the formula h=54t+12at2 h = 54 t + 1 2 a t 2 for a.

oee [108]

Hope this helps!!!!!

3 0

3 years ago

one adult ticket for a school play costs 10 dollars and one student ticket costs 6 dollars. one evening,750 people attended the

liraira [26]

The algebraic solution to the situation is as follows:

x + y = 750

10x + 6y = 6860

The number of adult and student are 590 and 160 respectively.

<h3>How to find and solve an algebraic equation?</h3>

One adult ticket for a school play costs 10 dollars and one student ticket costs 6 dollars.

One evening,750 people attended the play and the total receipts were 6860.

Therefore,

let

x = number of adult ticket

y = number of student tickets

Therefore,

x + y = 750

10x + 6y = 6860

10x + 10y = 7500

10x + 6y = 6860

4y = 640

y = 640 / 4

y = 160

Hence,

x = 750 - y

x = 750 - 160

x = 590

learn more on algebraic expression here: brainly.com/question/14934521

#SPJ1

4 0

2 years ago