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3 years ago

How do I find the inverse function of this equation

Mathematics

1 answer:

trapecia [35]3 years ago

4 0

Answer:

y=ln(x/(1-x))

Step-by-step explanation:

y=e^x/(1+e^x)

Cross multiply

y(1+e^x)=e^x

Distribute

y+ye^x=e^x

Put anything with x on with side and everything without x on opposing side:

y=e^x-ye^x

Factor right hand side

y=(1-y)e^x

Divide both sides by (1-y)

y/(1-y)=e^x

Use natural log.

ln(y/(1-y))=x

The inverse is

y=ln(x/(1-x))

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3 years ago

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The difference of three and the reciprocal of a number is equal to the quotient of 20 and the number. Find the number.

Monica [59]

Equation to find number: $\frac{1}{n}$ - 3 = $\frac{20}{n}$

Number's value: n = $-\frac{19}{3}$

Step-by-step explanation:

Let n be the unknown number.

The reciprocal basically makes the number (n in this case) a fraction. So, that being said, the reciprocal of n would be $\frac{1}{n}$ .

The difference of three and the reciprocal of a number ( $\frac{1}{n}$ ) would be $\frac{1}{n}$ - 3.

The quotient of 20 and the number (n) would be $\frac{20}{n}$ .

So, with this information we've gathered so far, we can come up with an equation to find what the number equals.

Equation: $\frac{1}{n}$ - 3 = $\frac{20}{n}$

To find what the number equals we must solve the equation.

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3 years ago

Janine babysits for $14.50 per hour. She also works as a dishwasher at her family's restaurant for $9.50 per hour. Her family ne

FrozenT [24]

The system of inequalities are
14.5·x + 9.5·y ≥ 140
7 ≤ y ≤ 10
x + y ≤ 15
2) 14.5·x + 9.5·y ≥ 140 represents the total amount of money Janine can earn
7 ≤ y ≤ 10 represents the range of values, Janine can spend dishwashing
x + y ≤ 15 represents the total number of hours Janine will like to work each week
3) 8 hours babysitting, 7 hours dishwashing
Step-by-step explanation:
The given parameters are;
The amount per hour Janine makes from babysits = $14.50
The amount per hour Janine makes from dishwashing = $9.50
The minimum number of hours Janine can spend dishwashing = 7 hours
The maximum number of hours Janine can spend dishwashing = 10 hours
The maximum number of hours Janine can work each week = 7 hours
The minimum amount she wants to make each week = $140
Let x represent the number of hours Janine spends babysitting and let y represent the number of hours Janine spends dishwashing
1) From the question, we have;
14.5·x + 9.5·y ≥ 140
7 ≤ y ≤ 10
x + y ≤ 15
2) Where
14.5·x + 9.5·y ≥ 140 represents the total amount of money Janine can earn
7 ≤ y ≤ 10 represents the range of values, Janine can spend dishwashing
x + y ≤ 15 represents the total number of hours Janine will like to work each week
Making, y, the subject of the formula of the above inequalities and plotting as functions is given as follows;
y ≥ 140/9.5 - (14.5/9.5)·x
y ≤ 15 - x
3) In order to earn as much money as possible given that the amount Janine earns from babysitting is more than the amount she earns from dishwashing, Janine should spend the least amount of time dishwashing, which is 7 hours, as given, and then spend the remaining 8 hours babysitting to receive $14.5 × 8 + $9.5×7 = $182.5

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3 years ago

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Minchanka [31]

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Answer: The answer is B

Step-by-step explanation:

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