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2 years ago

Given f(x) = 3x2 − 48 and g(x) = x − 4, identify (f/g)(x).

Mathematics

1 answer:

Ratling [72]2 years ago

3 0

The choose a. 3x+12

$( \frac{f}{g} )(x) = \frac{3 {x}^{2} - 48 }{x - 4} = \frac{3( {x}^{2} - 16) }{x - 4} \\ \\ = \frac{3(x - 4)(x + 4)}{x -4} \\ \\ = 3(x + 4) \\ = 3x + 12$

I hope I helped you^_^

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How to solve (g+2)(6g-3)

sergeinik [125]

Answer: 6g^2+9g-6

Step-by-step explanation:(g+2)(6g−3)

=(g+2)(6g+−3)

=(g)(6g)+(g)(−3)+(2)(6g)+(2)(−3)

=6g^2−3g+12g−6

=6g^2+9g−6

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2 years ago

A bag contains 12 red checkers and 12 black checkers. 1/randomly drawing a red checker 2/randomly drawing a red or black checker

8_murik_8 [283]

Answer:

(I suppose that we want to find the probability of first randomly drawing a red checker and after that randomly drawing a black checker)

We know that we have:

12 red checkers

12 black checkers.

A total of 24 checkers.

All of them are in a bag, and all of them have the same probability of being drawn.

Then the probability of randomly drawing a red checkers is equal to the quotient between the number of red checkers (12) and the total number of checkers (24)

p = 12/24 = 1/2

And the probability of now drawing a black checkers is calculated in the same way, as the quotient between the number of black checkers (12) and the total number of checkers (23 this time, because we have already drawn one)

q = 12/23

The joint probability is equal to the product between the two individual probabilities:

P = p*q = (1/2)*(12/23) = 0.261

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2 years ago

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Ymorist [56]

Answer:

Step-by-step explanation:

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3 years ago

Read 2 more answers

What the slope of a line

swat32

Answer:

The slope of a line is a number that measures its "steepness", usually denoted by the letter m. It is the change in y for a unit change in x along the line.

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3 years ago

A tank contains 60 kg of salt and 1000 L of water. Pure water enters a tank at the rate 6 L/min. The solution is mixed and drain

MissTica

Answer:

(a) 60 kg; (b) 21.6 kg; (c) 0 kg/L

Step-by-step explanation:

(a) Initial amount of salt in tank

The tank initially contains 60 kg of salt.

(b) Amount of salt after 4.5 h

$\text{Let A = mass of salt after t min}\\\text{and }r_{i} = \text{rate of salt coming into tank}\\\text{and }r_{0} =\text{rate of salt going out of tank}$

(i) Set up an expression for the rate of change of salt concentration.

$\dfrac{\text{d}A}{\text{d}t} = r_{i} - r_{o}\\\\\text{The fresh water is entering with no salt, so}\\ r_{i} = 0\\r_{o} = \dfrac{\text{3 L}}{\text{1 min}} \times \dfrac {A\text{ kg}}{\text{1000 L}} =\dfrac{3A}{1000}\text{ kg/min}\\\\\dfrac{\text{d}A}{\text{d}t} = -0.003A \text{ kg/min}$

(ii) Integrate the expression

$\dfrac{\text{d}A}{\text{d}t} = -0.003A\\\\\dfrac{\text{d}A}{A} = -0.003\text{d}t\\\\\int \dfrac{\text{d}A}{A} = -\int 0.003\text{d}t\\\\\ln A = -0.003t + C$

(iii) Find the constant of integration

$\ln A = -0.003t + C\\\text{At t = 0, A = 60 kg/1000 L = 0.060 kg/L} \\\ln (0.060) = -0.003\times0 + C\\C = \ln(0.060)$

(iv) Solve for A as a function of time.

$\text{The integrated rate expression is}\\\ln A = -0.003t + \ln(0.060)\\\text{Solve for } A\\A = 0.060e^{-0.003t}$

(v) Calculate the amount of salt after 4.5 h

a. Convert hours to minutes

$\text{Time} = \text{4.5 h} \times \dfrac{\text{60 min}}{\text{1h}} = \text{270 min}$

b.Calculate the concentration

$A = 0.060e^{-0.003t} = 0.060e^{-0.003\times270} = 0.060e^{-0.81} = 0.060 \times 0.445 = \text{0.0267 kg/L}$

c. Calculate the volume

The tank has been filling at 6 L/min and draining at 3 L/min, so it is filling at a net rate of 3 L/min.

The volume added in 4.5 h is

$\text{Volume added} = \text{270 min} \times \dfrac{\text{3 L}}{\text{1 min}} = \text{810 L}$

Total volume in tank = 1000 L + 810 L = 1810 L

d. Calculate the mass of salt in the tank

$\text{Mass of salt in tank } = \text{1810 L} \times \dfrac{\text{0.0267 kg}}{\text{1 L}} = \textbf{21.6 kg}$

(c) Concentration at infinite time

$\text{As t $\longrightarrow \, -\infty,\, e^{-\infty} \longrightarrow \, 0$, so A $\longrightarrow \, 0$.}$

This makes sense, because the salt is continuously being flushed out by the fresh water coming in.

The graph below shows how the concentration of salt varies with time.

3 0

3 years ago