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Question 1210395: What is the inverse of Y=(X+3)² ?
Answer by ikleyn(52776)

You can put this solution on YOUR website!
.
What is the inverse of Y=(X+3)² ?
~~~~~~~~~~~~~~~~~~~~~~~~

The direct function (which is the given function) does the following:

    - it adds the number 3 to the argument and then squares the value.


Therefore, the range of the given function is the set of all non-negative real numbers.



It means that the domain of the inverse function is the set of all non-negative real  numbers,
and at this set the inverse function makes the opposite operations in reverse order:

    - first, it takes square root from the value, and after that subtract 3 from the square root.


So, we can write an expression for the inverse function

    g(x) =  - 3.



But square root from a real number can be positive or negative.
Therefore, there are TWO possible expressions for "the" inverse function.


First  expression is  p(x) =  - 3,   using positive value of .


Second expression is  q(x) = - - 3,  using negative value of . 


These two possible expressions define two possible inverse functions.


Both inverse functions are defined over the set of non-negative real numbers.


First inverse function has the range [,).

Second inverse function has the range (-,].

At this point, the problem is solved completely, with detailed explanations, so everybody can understand.

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

It is important to note that the question in the problem is not precisely correct/accurate.

Indeed, it asks " what is the inverse function of Y = %28X%2B3%29%5E2

?"

To be correct, in this situaion, the question should ask " what are possible inverse functions of Y = %28X%2B3%29%5E2

?"

Now, after reading my post, you are armed to the teeth:
you know the right question and also know the right answer.

Come again to this forum soon to learn something new from the best source.

Question 1210394: What is the inverse of Y=(X+3)² ?
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52776)   (Show Source):
You can put this solution on YOUR website!
.
What is the inverse of Y=(X+3)² ?
~~~~~~~~~~~~~~~~~~~~~~~~

The direct function (which is the given function) does the following: - it adds the number 3 to the argument and then squares the value. Therefore, the range of the given function is the set of all non-negative real numbers. It means that the domain of the inverse function is the set of all non-negative real numbers, and at this set the inverse function makes the opposite operations in reverse order: - first, it takes square root from the value, and after that subtract 3 from the square root. So, we can write an expression for the inverse function g(x) = - 3. But square root from a real number can be positive or negative. Therefore, there are TWO possible expressions for "the" inverse function. First expression is p(x) = - 3, using positive value of . Second expression is q(x) = - - 3, using negative value of . These two possible expressions define two possible inverse functions. Both inverse functions are defined over the set of non-negative real numbers. First inverse function has the range [,). Second inverse function has the range (-,].

At this point, the problem is solved completely, with detailed explanations, so everybody can understand.

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

It is important to note that the question in the problem is not precisely correct/accurate.

Indeed, it asks   " what is the inverse function of Y = ?"

To be correct, in this situaion, the question should ask   " what are possible inverse functions of Y = ?"

        Now, after reading my post, you are armed to the teeth:
        you know the right question and also know the right answer.

Come again to this forum soon to learn something new from the best source.

Answer by josgarithmetic(39616)   (Show Source):
You can put this solution on YOUR website!
, but there are two of them. Try solve for Y and you'll see.

Question 1177104: Seth found 50 plants before adding volunteers to the search, and the rate of increase is 12% per volunteer.
PART A
The function n that models the situation is n(x) = ____ (____)^x
For 0 ≤ x ≤ 5, the domain of the function is whole numbers from ____ to ___ The y-intercept is ____
PART B What is the average rate of change from 0 to 5 volunteers? Round to the nearest whole number_____-

Answer by CPhill(1959)   (Show Source):
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**PART A**
* **The function:** n(x) = 50(1.12)^x
* The initial number of plants is 50.
* The rate of increase is 12%, which means each volunteer adds 12% to the previous total. This is represented by multiplying by 1.12 (100% + 12% = 112% = 1.12).
* **Domain:** Whole numbers from 0 to 5
* The domain represents the number of volunteers, and you can't have a fraction of a volunteer.
* **y-intercept:** 50
* The y-intercept is the starting value when x (number of volunteers) is 0. This represents the initial number of plants Seth found himself.
**PART B**
To find the average rate of change from 0 to 5 volunteers, we'll use the function we found in Part A:
1. **Calculate n(0) and n(5):**
* n(0) = 50(1.12)^0 = 50
* n(5) = 50(1.12)^5 ≈ 88.12
2. **Find the difference in the number of plants:**
* n(5) - n(0) ≈ 88.12 - 50 = 38.12
3. **Divide by the change in the number of volunteers:**
* Average rate of change = 38.12 / (5 - 0) = 7.624
4. **Round to the nearest whole number:**
* Average rate of change ≈ 8
**Therefore, the average rate of change from 0 to 5 volunteers is approximately 8 plants per volunteer.**

Question 1186214: One evening, while Mr. Cristobal's family is taking their dinner, a friend came and ask "if i will donate some of my wealth to you after i die and the condition is that I'll give it in staggered form, which scheme would you like ( arithmetic, geometric, harmonic)? Why?

Answer by ikleyn(52776)   (Show Source):
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.

Very unclear.

Not a Math problem and not a Math question.

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

There is a well known humoristic novel by famous American writer O'Henry about one combinator, Jeff Peters.
This combinator knew and used about 400 ways of taking money from people, but always within a law.

On the question, whether he wants to get everything by parts or in whole,
he always answered "In whole".

Question 1208376: How am I going to find it's inverse given:3x+5x=10
Found 2 solutions by ikleyn, Edwin McCravy:
Answer by ikleyn(52776)   (Show Source):
You can put this solution on YOUR website!
.
How am I going to find it's inverse given:3x+5x=10
~~~~~~~~~~~~~~~~~~~~~~~

This "problem" recalls me two-legged horse of Baron Munchausen.

It needs a major repair.
All the other legs need to be attached.
Otherwise it is only fit to be thrown in the trash.

Answer by Edwin McCravy(20054)   (Show Source):
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Did you mean 3x+5x=10 which is just 8x=10 or 4x=5 or x=5/4 which is a vertical line and not a function? If so, its inverse is simply found by replacing the x by a y and getting 4y=5 or y=5/4 which is a horizontal line and which is a function. But I'll bet your teacher is not trying to see whether you can add 3x and 5x to get 8x. I'll bet instead that you accidentally made a typo and one of those x's was supposed to be a y. Am I right? Check and see. Edwin

Question 1207380: Computing Hourly Wages Leigh is paid time-and-a-half for hours worked in excess of 40 hours and double-time for hours worked on Sunday.If Leigh had gross weekly wages of $456 for working 50 hours,4 of which were on Sunday, what is her regular hourly rate?

Let me see.

Let x = regular hourly rate

40x = 40 hours times x.

Leigh worked 10 additional hours beyond 40.

Leigh makes 1.2 for hours over 40 and double time on Sunday.

6(1.2x) = time and a half for 6 hours.

4(2x) = double time for 4 hours on Sunday.

Here is my equation set up:

40x + 6(1.2x) + 4(2x) = 456

You say?
Answer by ikleyn(52776)   (Show Source):
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.

Your setup is INCORRECT. A correct setup equation is 40x + 6*(1.5x) + 4*(2x) = 456.

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

Comment from student: I made a typo. My 6(1.2x) should be 6(1.5x). Everything else is correct.

My response: A correct answer from your side should sound like THIS:

        Thanks for your response and thanks for detecting/pointing my typo.

Question 1206902: Solve the following linear programming model geometrically, labeling all the corner points and shading the feasible or solution region
Maximize z = 200x+100y
Subject to: 3x+4y ≤ 24
X+y ≤ 16
X+3y≤30
X,y ≥0

Answer by Edwin McCravy(20054)   (Show Source):
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Maximize z = 200x+100y
Subject to: 3x+4y ≤ 24
X+y ≤ 16
X+3y≤30
X,y ≥0
Are you sure some of those first three ≤'s shouldn't have been ≥ ?. The graph seems funny because the first two restraints are irrelevant, So the feasible region is on or below all three lines, which means it's just on or below the green shaded region below the bottom line. That means there are only three corner points (0,0), (0,6), and (8,0) Substituting (x,y) = (0,0) in z = 200x+100y, z = 200(0)+100(0) = 0 + 0 = 0 Substituting (x,y) = (0,6) in z = 200x+100y, z = 200(0)+100(6) = 0 + 600 = 600 Substituting (x,y) = (8,0) in z = 200x+100y, z = 200(8)+100(0) = 1600 + 0 = 1600 So the maximum value for z is 1600 when x = 8 and y = 0. Edwin

Question 922297: The balances of two investments are changing at steady rates. One investment of $1450 is decreasing by $105.75 each month. The other investment of $825 is increasing by $144.25 each month. Write and solve an equation to find how many months it takes the balances of the investments to be the same. Let m represent the number of months.
Answer by mananth(16946)   (Show Source):
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The balances of two investments are changing at steady rates. One investment of $1450 is decreasing by $105.75 each month. The other investment of $825 is increasing by $144.25 each month. Write and solve an equation to find how many months it takes the balances of the investments to be the same. Let m represent the number of months.
One investment of $1450 is decreasing by $105.75 each month.
B1= 1450-(105.75m)
The other investment of $825 is increasing by $144.25 each month.
B2=825+144.25m
when will B1=B2
1450-105.75m=825+144.25m
Rearrange
1450-825=144.25m+105.75m
625=250m
m=625/250=2.5
Balances of the two investments will be the same at 2.5 month

Question 1205640: y = (3x) / (x + 2).
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!

It's not clear what your teacher wants here.
Please post the full instructions.

Since you posted this in the "inverses" section, I'll assume you want to find the inverse.
To do so, we will swap x and y, and then solve for y.
y = (3x)/(x+2)
x = (3y)/(y+2)
x(y+2) = 3y
xy+2x = 3y
2x = 3y-xy
2x = y(3-x)
(2x)/(3-x) = y
y = (2x)/(3-x)

Therefore, the inverse of y = (3x)/(x+2) is y = (2x)/(3-x)

y = (2x)/(3-x) is equivalent to y = (-2x)/(x-3) when we factor -1 out of the denominator.

Question 1205086: I am reading a Turn and Talk question in a math book.
It says "How do you know when a product
will be less than one of its factors?"
I thought products are always equal to or greater than its factors.
If a product will be less than one of its factors, I need to see
an example.
Answer by greenestamps(13198)   (Show Source):
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If you are only working with natural numbers (counting numbers -- 1, 2, 3, ...) then the product of two numbers is always equal to or greater than each factor.

But if we allow fractions and one of the factors is less than 1, then the product of that number and a second factor will be less than the second factor. For example,

(1/2)*4 = 2, which is less than 4.

or

(1/2)*(2/3) = 1/3

There the product is less than either of the factors, because both factors are less than 1.

And there are other examples if we allow different kinds of numbers. For example, if the first factor is positive and the second is negative, then the product is negative; and a negative number is less than any positive number.

Example: (3)*(-2) = -6, which is less than 3

Question 1205031: Hi!
I have been stuck on a few questions. My math teacher didn't go through enough examples for me to get these type of questions.
Find p when q=5.40 and r= 2.84 if p varies directly as the square of p and inversely as the cube of r and p=13.013 when q=4.30 and r=2.95.
thanks in advanced for your help.

Found 2 solutions by greenestamps, mananth:
Answer by greenestamps(13198)   (Show Source):
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Obviously there is a typo -- p can't vary directly as the square of p.

Equally obviously, as the problem is presented, the intent is that p varies directly as the square of q.

Given that, here is my choice of how to solve this kind of problem.

p varies directly as the square of q. In the given scenario, q=4.30, and in the new scenario q=5.40. Since p varies as the square of q, this increase in the value of q causes the value of p to increase by a factor of (5.40/4.30)^2.

p varies inversely as the cube of r. In the given scenario, r=2.95, and in the new scenario r=2.84. Since p varies inversely as the cube of r, this decrease in the value of r causes the value of p to increase by a factor of (2.95/2.84)^3.

Find the new value of p by multiplying the value of r in the given scenario by these two factors.

which evaluates to 23, correct to 3 decimal places.

ANSWER: 23

Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website!
Find p when q=5.40 and r= 2.84 if p varies directly as the square of p and inversely as the cube of r and p=13.013 when q=4.30 and r=2.95.
There appears to be a typo . error check and repost correctly (as the square of p)?
Find p when q=5.40 and r= 2.84 if p varies directly as the square of q and inversely as the cube of r and p=13.013 when q=4.30 and r=2.95.
Since you corrected the problem in your email here is the solution

First convert the variation into an equation by introducing a constant. We will put k as a constant

p=13.013 when q=4.30 and r=2.95. plug p q,r to find k
13.013 = k*( (4.3)^2/(2.95)^3)
= 18.0678
You know k

Find p when q=5.40 and r= 2.84 and k=18.0678

p= 23
which @greenstamps has already solved after editing your problem

Question 1203908: if m varies inversely as n when n=60, m=1.5, find m when n is 4.5

Found 2 solutions by josgarithmetic, mananth:
Answer by josgarithmetic(39616)   (Show Source):
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k, the variation constant

-

--------------now just use it for the question.

Answer by mananth(16946)   (Show Source):
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if m varies inversely as n when n=60, m=1.5, find m when n is 4.5

m1 * n1 = m2 * n2
1.5*60= m2*4.5
90 = 4.5m2
divide both sides of the equation by 4.5
m2 = 90 / 4.5
m2 = 20
So, m is 20.

Question 1203886: Suppose F(x) = f(g(x)) where
f(-2)=8
f'(-2)=4
f'(5)=3
g(5)=-2
g'(5)=6
Find F'(5)
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!

Answer: 24

Work Shown

F(x) = f(g(x))
F ' (x) = f ' (g(x)) * g ' (x) ...... chain rule
F ' (5) = f ' (g(5)) * g ' (5)
F ' (5) = f ' (-2) * 6
F ' (5) = 4 * 6
F ' (5) = 24

The relevant given info was
f'(-2)=4
g(5)=-2
g'(5)=6

While the following info wasn't needed
f(-2)=8
f'(5)=3
This likely was designed by your teacher to throw off the student (as a trick answer of sorts)

Question 932678: The volume of first cylinder is 12m^3. Second cylinder height is 3 time longer and base radus 2 times shorter than first cylynder parameters. Please, calculate the second cylinder volume.
A. 6.0m^3 B. 6.5m^3 c. 9.0m^3 D. 5.5m^3 E.7.5m^3
Found 5 solutions by Alan3354, ikleyn, josgarithmetic, greenestamps, mananth:
Answer by Alan3354(69443)   (Show Source):
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base radus 2 times shorter
----------------
1 time shorter would be zero (0).
2 times shorter is gibberish

Answer by ikleyn(52776)   (Show Source):
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.

Obviously, this post is a translation from other language,
but the person who translates it, does not know the standard rules
of presenting such problems in English (did not open and
did not read Math textbooks for middle schools in English).

It is a typical mistake of newcomers who start using English.

        My advise to the translator/composer:

In the Google search engine print

        " three times longer versus three times as long "

and read the info which Google will provide in response

https://forum.wordreference.com/threads/three-times-longer-than-three-times-as-long-as.1909017/

For other similar possible forms, print their analogs in Google again and learn
the responses from Google.

Doing this way, you will learn how not to fall into this trap in the future.

Answer by josgarithmetic(39616)   (Show Source):
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--------------------------------------------------------------------------
..., and base radus 2 times shorter than first cylynder parameters. ...
--------------------------------------------------------------------------

WHAT? Meaningless!

That is just bad. Maybe you or the material is trying to say,
...
Second cylinder height is an additional three of the first's length, and one half the radius of the first's
cylinder. Calculate the volume of the second cylinder.
...

First cylinder,

Second cylinder,

--------------but this is the same as left side equation of the First cylinder; so BOTH cylinders are still 12 cubic meters.

Answer by greenestamps(13198)   (Show Source):
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The author of this problem uses improper sloppy language which has no place in a serious math problem.

The other tutor interprets the given statement that the second cylinder is 3 time (sic) longer than the first cylinder to mean that the length of the second cylinder is 3 times the length of the first; and she interprets the statement that the base radus (sic) of the second cylinder is 2 times shorter than the base radius of the first cylinder to mean that the base radius of the second cylinder is 1/2 the base radius of the first cylinder.

Those interpretations are almost surely what the author of the problem intended; however, neither of those interpretations is grammatically correct. The second statement is in fact total nonsense.

If the length of the first cylinder is x, then the length of the second cylinders is 3x IF IT IS 3 TIMES AS LONG AS the first cylinder.

But if the length of the first cylinder is x and the second cylinder is 3 TIMES LONGER THAN the first, then the length of the second cylinder is x, PLUS 3 more times x -- or x+3x, which is 4x.

So "3 times longer than" means "4 times as long as".

Unfortunately, in sloppy everyday language, "3 times as long as" and "3 times longer than" are used (incorrectly!) to mean the same thing.

The given statement about the radius of the second cylinder is total nonsense. In everyday language, "2 times shorter than" is sloppily used to mean "1/2 as long as". But the grammatically correct interpretation of "2 times shorter than" is nonsensical.

If the radius of the first cylinder is y and the radius of the second cylinder is "2 times shorter than" the radius of the first, the correct interpretation of that statement is that the radius of the second cylinder is y, MINUS 2 times y -- which gives y-2y = -y....

A negative number for the radius of the second cylinder is absurd....

Presumably, you have shown the problem exactly how it was given to you, so my comments are not directed to you but rather to the author of the problem.

However, you have the unfortunate task of trying to guess what the given information really means....

Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website!

The volume of first cylinder is 12m^3.
pir^2h = 12
Second cylinder height is 3 time longer and base radus 2 times shorter than first cylynder parameters.
pi* (r/2)^2*(3h) =V
pi*(r^2/4)*3h= V
V/12= pi*(r^2/4)*3h/pir^2h
v/12 =3/4
V= 12*3/4 = 9 m^3

Question 1063818: y varies directly as x and inversely as the square of z calculator. y = 32 when x = 114 and z = 6. find y when x = 3 and z = 6
Found 3 solutions by josgarithmetic, greenestamps, mananth:
Answer by josgarithmetic(39616)   (Show Source):
You can put this solution on YOUR website!
---------------------------------------------------------------------------
y varies directly as x and inversely as the square of z .
---------------------------------------------------------------------------

k, variation constant

-

You were then given some values to find what is k value.

or better to try

--------which might be how you want it;

-------your variation model.

Answer by greenestamps(13198)   (Show Source):
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The other tutor goes to a lot of unnecessary work to get a decimal approximation of the answer.

From the given set of data to the new one, the value of z does not change, so the only change in the value of y is due to the change in the value of x.

y varies directly as x, so when the value of x changes by a factor of 3/114 = 1/38 the value of y changes by a factor of 1/38.

ANSWER: 32(1/38) = 32/38 = 16/19

Convert that to a decimal approximation if required or desired... but the answer in fraction form is exact.

Answer by mananth(16946)   (Show Source):
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y varies directly as x and inversely as the square of z calculator. y = 32 when x = 114 and z = 6. find y when x = 3 and z = 6

k = (32*36)/114= 10.1052

y = 10.1052*(3/36)= 0.8421

Question 1186213: Architect Cristobal made $35,000 during the first year of his job. Each year, he received a 20% raise. What were his total earnings during the first ten years on the job?

Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website!
Architect Cristobal made $35,000 during the first year of his job. Each year, he received a 20% raise. What were his total earnings during the first ten years on the job?
Sum of numbers in a G P= a1(r^n -1)/r-1
a1=35000
r=1.2
n=10
substitute with values in the formula
A= 35000*(1.2^10 -1)/(1.2-1)
=181710.774/0.2
= 908553.88

total earnings during the first ten years=$ 908553.88

Question 1202567: The sum of 2000 numbers is 2007. Find maximum product of these numbers. (There are more than one set of such numbers)
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52776)   (Show Source):
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.

The problem is worded, printed and presented INCORRECTLY in your post.

To be correct, it must say that all the considered numbers are positive.

Next incorrect statement is that "there are more than one set of such numbers ".

In OPPOSITE, there is ONLY ONE and UNIQUE such set of numbers.

        When a Math problem comes with such flagrant errors,
        a normal (and a natural) reaction of a reader is do not believe/(do not trust)
        to any of its word and to any of its number.

Answer by greenestamps(13198)   (Show Source):
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By a general principle, given a set of numbers with a particular sum, the maximum product of the numbers is when the numbers are all equal.

2000 numbers, all equal, with a sum of 2007, means each number is 2007/2000.

The maximum product is

ANSWER: .

Note the problem is not defined precisely enough. If some of the numbers are allowed to be negative, then there is no maximum product. Given a positive number x, the set consisting of -x, -1, 1997 1's, and x+11 has a sum of 2007, and the product of the numbers is x(x+11), which clearly has no maximum.

Question 1202004: Find the inverse of the matrix
[6 7]..........................
[2 3]
Use this inverse to find the coordinates of the point of intersection of the line 5c+7y=19 and 2x+3y=8 Explain why this method fail when applied to the lines 3x+4y=7 and 6x+8y=9
Answer by ikleyn(52776)   (Show Source):
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.
Find the inverse of the matrix
[6 7]..........................
[2 3]
Use this inverse to find the coordinates of the point of intersection of the line 5c+7y=19 and 2x+3y=8
Explain why this method fail when applied to the lines 3x+4y=7 and 6x+8y=9
~~~~~~~~~~~~~~~

Your matrix to inverse DOES NOT CORRESPOND to the system of equation in this post,
which you want to solve.

Extremely inaccurate writing/posting.

Question 1199111: The teachers at a middle school voted on one of two locations for the school party.
There were 30 votes for the skating rink and 13 votes for the bowling alley.
What is the ratio of the number of votes for skating to the number of votes for bowling?

Answer by Theo(13342)   (Show Source):
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30 votes for skating rink and 13 votes for bowling alley.
the ratio of number of votes for skating rink to the number of votes for bowling alley is 30 / 13.

Question 1197917: y varies directly as x and inversely as the square of z. y=30 when x=18 and z=3. Find y when x=64 and z=4.
Answer by josgarithmetic(39616)   (Show Source):
You can put this solution on YOUR website!

.
.

Question 1197463: Find inverse of the following function:
f(x)= (x² + 9)/(x - 5) x≠5
Answer by MathLover1(20849)   (Show Source):
You can put this solution on YOUR website!
Find inverse of the following function:

recall that

........swap variables

...........solve for

...complete square on right side

=> inverse is

'

Question 1197211: The stress on the material of a large circular metal pipe varies jointly with the internal pressure and the internal diameter of the pipe and inversely with the thickness of the material of the pipe. For a particular type of pipe, the stress is 103 pounds per square inch when the diameter is 4 inches, the thickness is 0.75 inches, and the internal pressure is 27 pounds per square inch.
Find the necessary thickness for a pipe if its diameter is 5 inches, the internal pressure is 32 pounds per square inch, and the pipe needs to be able to handle overall stress of 139 pounds per square inch.

The material of the pipe needs to be inches thick.
{Give at least 3 decimal places}

Answer by josgarithmetic(39616)   (Show Source):
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Joint & Inverse Variation Problem.

Stress, y
Internal pressure, p
Internal diameter, d
Thickness, x
Variation Constant, k

The first sentence in description gives ;
and the rest is uncomplicated.

Question 1197091: Solve for the inverse of the function
f (x)= (-2/3)x+5
Found 3 solutions by greenestamps, math_tutor2020, ewatrrr:
Answer by greenestamps(13198)   (Show Source):
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The response from the other tutor shows the traditional method for finding the inverse of a function: switch the x and y and solve for the new y.

For many relatively simple functions, an alternative which is often faster is to use the concept that an inverse function "un-does" what the function does.

For this example, the given function does this to the input:
(1) multiply by -2/3; and
(2) add 5

The inverse function, to undo that, needs to perform the opposite (inverse) operations in the opposite order:
(1) subtract 5; and
(2) divide by (-2/3) -- i.e., multiply by (-3/2)

ANSWER: y=(-3/2)(x-5)

Answer by math_tutor2020(3816)   (Show Source):
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The inverse notation should be instead of

Otherwise I agree fully with the other tutor.

Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!

Hi Solve for the inverse of the function: *Note: Notation f (x) =(-2/3)x+5 0r y = (-2/3)x+5 Replacing the y for x and x for y x = (-2/3)y + 5 Solving for y = (-3/2)(x-5) Wish You the Best in your Studies.

Question 1196895: The function defined by v(x)=3.8x converts a volume of x gallons into v(x) liters.
a. Find the equivalent volume in liters of 30 gallons of water.
b. Find and equation defining y=v^(-1) (x).
c.Use the inverse function in (b) to find the equivalent volume in gallons of 100-liter water.

Answer by ikleyn(52776)   (Show Source):
You can put this solution on YOUR website!
.

(a) To answer (a), substitute x= 30 into the given formula; then calculate. I sincerely hope that my help is not needed anymore in this step. (b) The inverse function is y = , converting liters x into gallons y. (c) To find the equivalent volume in gallons of 100-liter water, substitute x= 100 into my formula in (b); then calculate.

Solved, explained, and you are fully instructed.

Question 1196894: Arnel and Liza are playing a number guessing game. Arnel asks Tina to think of a positive number, double the number, square the result subtract 10, then add 8. If Tina’s answer is 254, what was then the original number? Use the concept of inverse function in your solution.
Answer by ikleyn(52776)   (Show Source):
You can put this solution on YOUR website!
.
Arnel and Liza are playing a number guessing game.
Arnel asks Tina to think of a positive number, double the number, square the result subtract 10, then add 8.
If Tina’s answer is 254, what was then the original number? Use the concept of inverse function in your solution.
~~~~~~~~~~~~~~~

Use the inverse operations in the inverse order. Consider it as a necessary exercise and complete the solution step by step on your own. The ANSWER is = 8.

Question 1195916: ((10^x)+(10^-x))/(10^x-(10^-x))

Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website!
Do you have a question?
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=
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Question 1194725: Please help! I need to be done with the course by June 20th! I have questions 1,2 and 3 done im just writing the first one down as it is needed for the next questions.
"You and your friend see kids playing on a seesaw. The two kids are balancing without their feet touching the ground. Your friend says that there is no way that a mother and daughter could do the same thing. You are not sure if that is true.
Use what you know about the different types of variation to figure out how a mother and child could balance. Use the Lever Tool to verify the data, and then use what you know about variation to model the relationship between weight and distance from the fulcrum.
1. Use the Lever Tool to verify each weight and distance pair given in the video for your seesaw. Write the values in the table below. (Note: The pan on the lever weighs 100 units!) (1 point)
A:
weight | distance
720|125
750|120
900|100
1000|90
1200|75
B: weight | distance
120|100
150|80
200|60
300|40
400|30
Analyzing your data
2. Use the data from the table to make a graph. (3 points: 1 point each for labels, coordinates, and sketch)
3. Does it look as though there is a relationship between the weight and its distance from the fulcrum? What type of variation is there (if any)? Support your answer. (1 point)
DONE no need to do these two thank you
4. Write an equation that models your data. Use variables of weight, W, and distance, D. (You will have to use one of your data points to find your constant of variation.) (3 points: 1 point for the general form of variation, 1 point for the constant of variation, and 1 point for the final equation)
5. The Lever Tool helps find values that will balance your seesaw, but it has limited range and precision. Use your graph to estimate a coordinate (W, D) that:
balances your seesaw
you could not simulate with the Lever Tool
To verify that your values are reasonable, substitute your coordinate into the equation you found in question 4. Is the coordinate you picked a good solution?
(3 points: 1 point for a value that cannot be shown on the Lever Tool, 1 point for the correct substitution, and 1 point for verification)
A new Balance
Your turn: Choose a new fixed weight and fixed difference that are different from the one for the seesaw you selected. (Reminder: Seesaw A has a fixed weight of 600 units and a fixed distance of 150 units. Seesaw B has a fixed weight of 100 units and a fixed distance of 120 units.)
6. What new values did you pick? (1 point)
7. With your new constant values on one side of the seesaw, use the Lever Tool to find 5 new pairs of weights and distances that balance the seesaw. Record these values in the table below. (Reminder: The pan on the lever weighs 100 units!) (2 points)
8. Now use the table to sketch a graph. (3 points: 1 point each for labels, coordinates, and sketch)
9. Write an equation that represents your data and graph. Write your equation in terms of weight, W, and distance, D. (You will have to use one of your data points or your fixed point to find your constant of variation.) (3 points: 1 point for the general form of variation, 1 point for the constant of variation, and 1 point for the final equation)"

Answer by ikleyn(52776)   (Show Source):
You can put this solution on YOUR website!
.

If you want to learn the basics, read the lesson
    - Using proportions to solve word problems in Physics
in this site.

Your assignment has many questions, but if you learn the basics from the referred lesson,
you will be able (will be in position) to solve/(to answer) many of these questions ON YOUR OWN.

After reading this lesson, let me know about your progress.

Question 1191049: Given f(x) = 2x +3 and g(x) = x2 + 3x - 1, find (f(g(x))).
Answer by josgarithmetic(39616)   (Show Source):
You can put this solution on YOUR website!
Just form the composition and simplify! Use g(x) as the input for f(x), and take any steps needed to put into a simpler form.

Question 1190886: four more than the quotient of a number and 3 is at least 9
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website!
four more than the quotient of a number and 3 is at least 9
---------------
(n/3) + 4 >= 9
n/3 >= 5

Question 1190608: field postulates
Answer by ikleyn(52776)   (Show Source):
You can put this solution on YOUR website!
.

See this Wikipedia article

https://en.wikipedia.org/wiki/Field_(mathematics)

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For studying common, general and basic knowledge use, in first turn,

                (a)   your textbooks

        and

                (b)   Wikipedia.

They SPECIALLY exist and are developed/created for these purposes.

To ask tutors to re-write from textbooks for you   is not ethical   and is not right way to study subjects.

+---------------------------------------------------------------+ | It is not ethical, because it DEMONSTRATES that | | you do not make your job and even do not want to make it. | +---------------------------------------------------------------+

In general, the Internet education is not intended to provide teaching from scratch.

It is intended to add and to develop your knowledge AFTER that as you just learned basics.

Question 1190548: 1/2e=1/4
1 1/2c=6
Answer by ikleyn(52776)   (Show Source):
You can put this solution on YOUR website!
.

To solve first equation, divide both sides by . You will get answer e = = = . ANSWER To solve second equation, divide both sides by 1 1/2 = . You will get answer c = = = 2*2 = 4. ANSWER

Solved and explained.

Question 1190100: determine their inverse function:
h(x)= 2x+1/x-3
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website!
it's ambiguous.
Add parentheses.