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Serhud [2]
2 years ago
9

For the function f(x)=(x+6)^3, rind f^-1(x)

Mathematics
1 answer:
qaws [65]2 years ago
5 0

Answer:

f^{-1}(x)=\sqrt[3]{x}-6

Step-by-step explanation:

f(x)=(x+6)^3

y=(x+6)^3

x=(y+6)^3

\sqrt[3]{x}=y+6

\sqrt[3]{x}-6=y

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Jason did yard work for 3 hours and earned $18. What are the unit ratios in hours per dollar and dollars per hour?
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Answer:

1:6       One hour of work is worth $6

Step-by-step explanation:

$18/3= $6

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Consider the equality xy k. Write the following inverse proportion: y is inversely proportional to x. When y = 12, x=5.​
skelet666 [1.2K]

Answer:

y=\dfrac {60} {x}   or   xy=60   (depending on your teacher's format preference)

Step-by-step explanation:

<h3><u>Proportionality background</u></h3>

Proportionality is sometimes called "variation".   (ex. " 'y' varies inversely as 'x' ")

There are two main types of proportionality/variation:

  1. Direct
  2. Inverse.

Every proportionality, regardless of whether it is direct or inverse, will have a constant of proportionality (I'm going to call it "k").

Below are several different examples of both types of proportionality, and how they might be stated in words:

  • y=kx      y is directly proportional to x
  • y=kx^2     y is directly proportional to x squared
  • y=kx^3     y is directly proportional to x cubed
  • y=k\sqrt{x}}   y is directly proportional to the square root of x
  • y=\dfrac {k} {x}   y is inversely proportional to x
  • y=\dfrac {k} {x^2}   y is inversely proportional to x squared

From these examples, we see that two things:

  • things that are <u>directly proportional</u> -- the thing is <u>multipli</u>ed to the constant of proportionality "k"
  • things that are <u>inversely proportional</u> -- the thing is <u>divide</u>d from the constant of proportionality "k".

<h3><u>Looking at our question</u></h3>

In our question, y is inversely proportional to x, so the equation we're looking at is the following y=\dfrac {k} {x}.

It isn't yet clear what the constant of proportionality "k" is for this situation, but we are given enough information to solve for it:  "When y=12, x=5."

We can substitute this known relationship pair, and find the "k" that relates this pair of numbers:

<h3><u>Solving for k, and finding the general equation</u></h3>

General Inverse variation equation...

y=\dfrac {k} {x}

Substituting known values...

(12)=\dfrac {k} {(5)}

Multiplying both sides by 5...

(12)*5= \left ( \dfrac {k} {5} \right ) *5

Simplifying/arithmetic...

60=k

So, for our situation, k=60.  So the inverse proportionality relationship equation for this situation is y=\dfrac {60} {x}.

The way your question is phrased, they may prefer the form: xy=60

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2 years ago
Which linear inequality is represented by the graph?
Butoxors [25]
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If you know the area of a circular field is 6358.5 m2, what is the radius of the field?
diamong [38]

Answer:

r = 45 m.

Step-by-step explanation:

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r^2 = 6358.5 / pi

r = √(6358.5 / pi)

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