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1 year ago

Find f(g(x)) and g(f(x)). f(x)=x²-2 and g(x)=√x+1

Mathematics

1 answer:

Archy [21]1 year ago

6 0

Answer:

1. x - 1

2. $\sqrt{x^2-1}$

Step-by-step explanation:

$f(g(x)) = \sqrt{x+1}^2 - 2\\ = x + 1 - 2\\= x - 1$

$g(f(x)) =\sqrt{x^2-2+1}\\ = \sqrt{x^2-1}$

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A rectangular box which is open at the top can be made from an12-by-18-inch piece of metal by cutting a square from each corner

algol [13]

Answer:

h=2.35in, l=13.3in and w=7.3in

Step-by-step explanation:

In order to solve this problem, we must start by drawing a diagram that will represent the prolem. (Look at attached picture)

From the diagram we can see that the length ad the width of the box are found by using the following expressions:

L=18-2x

W= 12-2x

H=x

next, we can make use of the volume formula of a rectangular prism, which is the following:

V=WLH

so we can substitute the expressions we got before on the formula:

V=x(12-2x)(18-2x)

and for ease of calculation, we can multiply the terms, so we get:

$V=x(216-24x-36x+4x^{2})$

$V=x(4x^{2}-60x+216)$

$V=4x^{3}-60x^{2}+216x$

So now we can find the derivative of the volume:

$V'=12x^{2}-120x+216$

and set it equal to zero, so we get:

$12x^{2}-120x+216=0$

and now we can solve. We can start by factoring the left side of the equation, so we get:

$12(x^{2}-10x+18)=0$

which yields:

x^{2}-10x+18=0

This one can only be solved by using the quadratic formula:

$x=\frac{-b\pm \sqrt{-b^{2}-4ac}}{2a}$

so we substitute the corresponding values:

$x=\frac{-(-10)\pm \sqrt{-(-10)^{2}-4(1)(18)}}{2(1)}$

which yields:

x=7.65in or x=2.35in

we keep the 2.35in only, because the 7.65in returns an impossible box, since that would make the width a negative width.

So the 2.35in height would give us the greatest box. Now we can use it to find the height, the width and the length of the box.

Height=x=2.35

W=12-2x=12-2*2.35=7.3in

L=18-2x=18-2(2.35)=13.3in

5 0

2 years ago

37 1/2% of _________ is 36, Please help show work I am really confused.

klio [65]

Before you start working on this problem, make sure you know
how to use a couple of the tools in your toolbox:

Tool #1: 37-1/2 percent means 0.375

Tool #2: In math problems, "of" almost always means "times".

====================================

Your question says

   "37-1/2 percent of blank is 36".

Translate it with your tools:

      0.375 times blank = 36 .

Divide each side by 0.375:     Blank = 36 / 0.375 .

Now grab your pencil or your calculator, and find the value of that
fraction (do the division). Blank is equal to the value of the fraction.

To check your answer (find out whether it's correct):

Do exactly what the question says.

Multiply (0.375) times (your answer). If you get 36,
then your answer is correct. If not, it's not.

6 0

3 years ago

Which of the following circles have their centers in the second quadrant? Check all that apply.

erastova [34]

Answer:

B and C

Explanation:

Coordinates of A: (5,-5), which is in the 4th quadrant.

Coordinates of B: (-12,9), which is in the 2nd quadrant.

Coordinates of C: (-3,2), which is in the 2nd quadrant.

Coordinates of D: (2,-7), which is in the 4th quadrant.

6 0

3 years ago

In DEFG, what is DF?

vampirchik [111]

First you must find X by setting the sides equal to each other. from that you know x=4 then plug that into the w/ they give you the Equation to. = 6then multiply by 2 and you get 12

4 0

2 years ago

What are the potential zeros of f(x)=6x^4+ 2x^3 - 4x^2 +2?

Dmitry_Shevchenko [17]

The potential zeros of f(x)=6x^4+ 2x^3 - 4x^2 +2 are ±(1, 1/2, 1/3, 1/6, 2, 2/3)

<h3>How to determine the potential zeros of the function f(x)?</h3>

The function is given as:

f(x)=6x^4+ 2x^3 - 4x^2 +2

For a function P(x) such that

P(x) = ax^n +...... + b

The rational roots of the function p(x) are

Rational roots = ± Possible factors of b/Possible factors of a

In the function f(x), we have:

a = 6

b = 2

The factors of 6 and 2 are

a = 1, 2, 3 and 6

b = 1 and 2

So, we have:

Rational roots = ±(1, 2)/(1, 2, 3, 6)

Split the expression

Rational roots = ±1/(1, 2, 3, 6)/ and ±2/(1, 2, 3, 6)

Evaluate the quotient

Rational roots = ±(1, 1/2, 1/3, 1/6, 2, 1, 2/3, 1/3)

Remove the repetition

Rational roots = ±(1, 1/2, 1/3, 1/6, 2, 2/3)

Hence, the potential zeros of f(x)=6x^4+ 2x^3 - 4x^2 +2 are ±(1, 1/2, 1/3, 1/6, 2, 2/3)

The complete parameters are:

The function is given as:

f(x) = 3x^3 + 2x^2 + 3x + 6

The potential zeros of f(x)=6x^4+ 2x^3 - 4x^2 +2 are ±(1, 1/2, 1/3, 1/6, 2, 2/3)