Find the area and the circumference of a circle with diameter 10 m.

please help! functions and relations. f(x)= square root of x-4. find the inverse of f(x) and it’s domain.

likoan [24]

ANSWER:

$\:D.\text{ }f^{-1}\left(x\right)=\left(x+4\right)^2;x\ge-4$

STEP-BY-STEP EXPLANATION:

We have the following equation:

$f(x)=\sqrt{x}-4$

The inverse is the following (we calculate it by replacing f(x) by x and x by f(x)):

$\begin{gathered} x=\sqrt{f^{-1}(x)}-4 \\ \\ \sqrt{f^{-1}(x)}=x+4 \\ \\ f^{-1}(x)=(x+4)^2 \end{gathered}$

The domain would be the range of the original equation, and it would be the range of values that f(x) could take, which was from -4 to positive infinity, that is, f(x) ≥ -4.

Therefore, the domain is x ≥ -4.

So the correct answer is D.

$\:f^{-1}\left(x\right)=\left(x+4\right)^2;x\ge -4$

4 0

1 year ago

Solve for x: (x-1)^3/2 = 27

Alex_Xolod [135]

(x-1)^3 / 2 = 27

For equations like this, we want to isolate x in order to get the value of it.

First, let's multiply both sides by 2 to eliminate the fraction.

(x-1)^3 = 27(2)

Now, let's take the cube root of both sides

(x-1) = ∛(27 * 2)

Now, simplify the root

x - 1 = 3∛2

Add both sides by 1

x = 1 + 3∛2

That's your answer.

Have an awesome day! :)

8 0

3 years ago

Read 2 more answers

A consumer affairs investigator records the repair cost for 4 randomly selected washers. A sample mean of $64.26 and standard de

Mashutka [201]

Answer:

Critical value: z = 1.28

The 80% confidence interval for the mean repair cost for the washers is between $46.487 and $82.033.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.80}{2} = 0.10$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$

So it is z with a pvalue of 1-0.1 = 0.9, so z = 1.28

Now, find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

So

$M = 1.28*\frac{27.77}{\sqrt{4}} = 17.773$

The lower end of the interval is the mean subtracted by M. So 64.26 - 17.773 = $46.487.

The upper end of the interval is M added to the mean. So 64.26 + 17.773 = $82.033.

The 80% confidence interval for the mean repair cost for the washers is between $46.487 and $82.033.

7 0

3 years ago

(c) The original function y= A(n) converted an input, the circle's radius, to an output, the circle's area.

timama [110]

Two functions f(x) and g(x) are inverses if and only if is true that each function evaluated in the other is equivalent to the identity.

This means that:

f( g(x)) = g( f(x)) = x

With this we can see that:

Input = area

Output = radius.

-------------------------------------

Let's see how we concluded that.

First, we know that the function:

y = A(n) converts an input, the radius of a circle into an output, the circle's area.

Let's assume that G(x) is the inverse function, and "n" is the variable that represents the radius.

By the definition of inverse functions we must have that:

G( A(n)) = n

and n is a radius, so the output of the inverse function is the radius of a circle.

And A(n) is the area of that circle, then the input for the inverse function is the area.

Finally, we can conclude that:

Input: Area

Output: Radius.

If you want to learn more, you can read:

brainly.com/question/2541698

3 0

2 years ago

A hyena can run 1/4 of a mile in 22.5 seconds. At this rate, which equation can be used to determine how fast a hyena runs in mi

morpeh [17]

40 miles an hour
60 [minutes] * 60 [seconds]= 3600
22.5[seconds for 1/4 of a mile]* 4[ one mile]= 90 [seconds per mile]
3600/90=40 [miles an hour]

4 0

3 years ago

Read 2 more answers