Posts by mathland

mathland · Help Me !

Bob wrote:

I think both the domain and the range are (-∞,∞)
First the domain.
All negatives real numbers have a negative, real cube root.
Say n is the cube root of t, n and t > 0, then -n is the cube root of -t. So all negative values of (t+4) have a cube root.
Range. f = cuberoot(t+4) is symmetrical about the point (-4,0)
proof: Suppose f = cuberoot(t+4) for t > -4
Then the vector from [-4,0] to [t , f] is [t+4, f]
Now consider the point [-t - 8, cuberoot(-t-8+4)]
The vector from this point to [-4,0] is [-4 -(-t-8) , -cuberoot(-t-4)] = [t + 4, +cuberoot(t+4)] = [t+4,f]
These two vectors are the same showing the required symmetry.
There is no upper bound to f.
Proof. Suppose N is the upper bound.
Form the number t = (N+1)^3 - 4
f(t) = cuberoot[(N+1)^3 - 4 + 4] = cuberoot[(N+1)^3] = N + 1 which is above the supposed upper bound. So there is no upper
bound. So the range extends to + ∞. But the graph has rotational symmetry. So the lower limit of the range is -∞.
Bob

Great math notes as always. I will explore this question more and more when time allows.

mathland · Help Me !

Bob wrote:

I'm still thinking about the range. Maybe more later.
In fact now:
Let t = 121 then f = cuberoot(121 + 4) = cuberoot 125 = 5 > 3
Bob

I'll wait to discuss the range further when you have time.

mathland · Help Me !

Bob wrote:

Let's work through some number cases first. Usually I find the algebra gets clearer when I do that.
x = 50
Cost = 50 x 60
Revenue = 50 x 90
Profit = R - C = 50 x(90-60)
I can see that for x less than 100 this is straight forward
R = 30x
What happens at exactly x = 100? Do we have a discount or not?
question wrote:
in excess of 100
So no discount for exactly 100.
Above 100.
It has taken me 30 minutes to make sense of this. I used a spreadsheet to backtrack the given profits to work out what the sale cost of a unit is for 120, 130, 140, 150, 160, 170. The wording doesn't make this clear at all.
Here's my attempt at clarity.
If x > 100, calculate how much above 100 it is. ie. calculate x -100
Multiply this by 0.15 to get the discount d = (x-100) times 0.15
Subtract this from 90 to get the lower price of a unit p = 90 - d
Work out the profit from one unit sold pr = p - 60
Finally multiply by the x value to get the revenue R = pr times x
Here's a couple of calculations to show this in practice:
x = 130 d = 30 times 0.15 = 4.5 p = 90 - d = 85.5 pr = 85.5 - 60 = 25.5 R = 25.5 times 130 = 3315
x = 170 d = 70 times 0.15 = 10.5 p = 90 - d = 79.5 pr = 79.5 - 60 = 19.5 R = 19.5 times 170 = 3315
Now your turn. Put the above algorithm together as a single formula in x
Best of luck,
Bob

I will work on this a bit more.

mathland · Help Me !

Bob wrote:

I'm trying to build up an equation from the information.
P = R - C
C is fixed. R depends on number sold ; let's call that x.
The discount only clicks in above an order of 100, so the term needed is (x-100)
So build up an R value using the percent reduction and (x-100)
Bob

You said:

"...build up an R value using the percent reduction and (x-100)."

What do you mean?

mathland · Help Me !

Bob wrote:

mathland,
You are being unnecessarily aggressive. I don't think the question is poorly stated. If you don't find a response helpful, then just ignore it.
I seem to remember helping with a similar question here:
http://www.mathisfunforum.com/viewtopic … 37#p418937
Bob

Ok. I updated my reply. I have been going back and forth with this guy after I was wrongly accused of posting an inappropriate thread.

mathland · Help Me !

Bob wrote:

I've just tried the graph and this confirms your answer.
But .... am I making a silly mistake here?:
Let t = -12
f(-12) = cuberoot (-12 +4) = cuberoot(-8) = -2
Instead of using the function grapher I tried the equation grapher at
https://www.mathsisfun.com/data/grapher-equation.html and used the equation y^3 = x + 4
This gives the complete graph including values of y below zero.
Bob

The range is [-3, 3].

Ever tried demos? It's a free online graphing calculator.

mathland · Help Me !

Bob wrote:

Yes. Well done!
B

This is pretty easy stuff. Once I solve the problem, it all comes back to me. This is review. I took precalculus in the Spring 1993 semester at Lehman College in the Bronx, NY.

mathland · Help Me !

Bob wrote:

All the things I would do are part of creating the graph. I cannot think of leaving that out.
You can differentiate to finds stationary points and look for asymptotes. Set x = 0 and y = 0. Let x tend to + / - infinity.
But in the end I would use all that to make a graph.
Bob

In other words, graphing is the best approach to find the range. After graphing this function, what should I be looking for to find the range in the picture? Also, the range is the y-coordinate of the point (x, y). If so, then I am searching for the height of the graph. Yes?

Do you sleep? The time in NYC is 4:28 am. I am currently on lunch break as I work overnight hours. I have a reason to be up now. Why are you up this time? Just curious....

mathland · Dark Discussions at Cafe Infinity

While there has been increasing interest in prophetic themes among the liberals and the neoorthodox, some conservatives have manifested a disposition to consider the study of prophecy as unimportant. In our
day, when the authority of the Bible is disputed and when
many have denied the infallibility of Scripture, some feel that
there is little profit in debating eschatology. In other words,
why improve the building if the foundation is not sure?

John F. Walvoord

mathland · Help Me !

mathland wrote:

Find the domain of f(x) = (x + 2)/[sqrt{x - 10}].
I see a radical in the denominator of the algebraic fraction. Disregarding the numerator, must I set the radicand (x - 10) to be greater than or equal to 0 and solve for x?

Let me see.

x - 10 >= 0

x >= 10...Domain?

mathland · Help Me !

Bob wrote:

if the question involved a square root I would agree.
But cuberoot(a negative) is possible without diving into complex numbers
Bob

Do I set the radicand to be greater than or equal to 0?

t + 4 >= 0

t >= -4...Domain?

mathland · Help Me !

Bob wrote:

hi Peccatrix123
I understand EA, BC, CD, I'm just confused by where point F is. Is F where the shape kind of slants?
Also, would FC be 12?
If you continue the line AB until it crosses CD, that is the point F.
The four points EAFD make a rectangle. It looks like you have got this, because FC is 12, well done.
And BCF is a right angled triangle.
So now use Pythagoras' theorem to calculate BF. You'll have all the measurements you need to calculate the two areas.
Bob

Hello Bob. About how many questions belong to the Unanswered section? Does it make sense to answer unanswered questions posted prior to the current year?

Thanks.

P. S. I really think this forum would benefit more if it was divided by courses. This is simply my opinion. Take a look at freemathhelp.com or mathhelpboard.com and others like it.

mathland · Help Me !

ganesh wrote:

See the link:
Distance Between 2 Points.

Ok.

mathland · Help Me !

The cost per unit in the production
of an MP3 player is $60. The manufacturer charges $90
per unit for orders of 100 or less. To encourage large
orders, the manufacturer reduces the charge by $0.15
per MP3 player for each unit ordered in excess of 100
(for example, the charge is reduced to $87 per MP3
player for an order size of 120).

(a) The table shows the profits P (in dollars) for
various numbers of units ordered, x. Use the table
to estimate the maximum profit.

Units x: Profit P

130................3315
140................3360
150................3375
160................3360
170................3315

When I look at this table and think of the word MAXIMUM, I quickly think of the largest Profit P number. If that is the case, I say the maximum profit is 3375. Yes?

(b) Plot the points (x, P) from the table in part (a). Does
the relation defined by the ordered pairs represent P
as a function of x?

The same value of x cannot be matched to 2 different P-values (in this example).
For this reason, I say the ordered pairs represent P as a function of x. Part (c) below confirms that P is a function of x.

(c) Given that P is a function of x, write the function
and determine its domain. (Note: P = R − C,
where R is revenue and C is cost.)

I need help with part (c).

mathland · Help Me !

I think the easiest way to find the range of functions that are not linear is to make a graph. Yes? What if I wanted to find the range without graphing? See below.

Find the range of each non-linear function below.

1. f(x) = (x + 2)/[sqrt{x - 10}]

2. f(x) = [sqrt{x + 6}]/(6 + x)

How is this done algebraically?

Note: sqrt = square root

mathland · Help Me !

Find the domain of f(x) = (x + 2)/[sqrt{x - 10}].

I see a radical in the denominator of the algebraic fraction. Disregarding the numerator, must I set the radicand (x - 10) to be greater than or equal to 0 and solve for x?

mathland · Help Me !

Find the domain of f(t) = cuberoot{ t + 4}.

Let me see.

I must set the radicand to be greater than or equal to 0 and solve for t. Yes?

mathland · Help Me !

Find a relationship between x and y such that (x, y) is equidistant
(the same distance) from the two points.

Two points: (6, 5), (1, −8)

The question is asking for a point that is the same distance from the two given points. Yes? If so, is there a formula to work out this question?

mathland · Help Me !

Not Dav wrote:

3 things,
1. This was from about 8 years ago
2. The question being asked right now is only asking for one of the questions not all.
3. I dont think the original poster is active anymore
Hope this helps

Thanks for clearing this up for me.

mathland · Dark Discussions at Cafe Infinity

Not Dav wrote:

I thought Dark discussions at cafe infinity can talk about almost any about life etc. This section do not have to be about math. If you want to talk about math, there are many other sub topics to talk in but here is not the place. You can make a new sub topic if you just want to talk about math or join into one.

Exactly. The title of the forum speaks for itself. Any topic outside of mathematics can be discussed here. I concur. However, I was criticized for talking about the rewards of no fab in a person's life.

mathland · Dark Discussions at Cafe Infinity

ganesh wrote:

mathland wrote:
ganesh wrote:
An average adult human can live up to about 3 billion seconds approximately! It can be more or less. This is a rough estimate. Therefore, time is invaluable. It is precious. One should make the best out of it.
Moving forward, we should discuss math only. Please, IGNORE my posts in this DARKNESS forum section. Take care....
Noted. And, it is 'Dark Discussions at Cafe Infinity' and not 'Darkness'.

So now you are correcting my English abbreviations? Of course, I know the entire name of the forum. I simply abbreviated, Einstein.

By the way, I have 3 college degrees in areas other than mathematics.

B. A. Sociology (1994)...Lehman College

A. A. Liberal Arts & Sciences (1990)...NYC Technical College

A. A. Religious Education...Family Radio School of the Bible

Are you still up for the Precalculus David Cohen textbook challenge? I want to see if you can handle David Cohen textbook questions.

mathland · Dark Discussions at Cafe Infinity

ganesh wrote:

mathland wrote:
ganesh wrote:
Do you expect I would answer these questions?
Regarding my science and mathematics background, go to all the earlier posts in the forum. Every post if you can.
Moving on to math. Let me make things easy for you. Math only as I search for a new site. I will ignore your replies to questions unrelated to mathematics.
If you really mean it, I will be happy. It makes things easier.
mathland wrote:
I will ignore your replies to questions unrelated to mathematics.
You started it first.

Since you know so much math, I have a very challenging Precalculus textbook by David Cohen that I can post from specifically for you and you alone. Are you willing to take the challenge? Are you daring?

mathland · Help Me !

demha wrote:

Just need some help understanding some of these math problems and checking the ones I already did (if right/wrong). Thank you for your time:
1. An equilateral triangle with a side of 1 inch - Answer: A
A 0.43 sq in
B 0.56 sq in
C 0.89 sq in
D 0.23 sq in
E 0.19 sq in
F 0.54 sq in

2. A square with a side of 2 feet - Answer: B
A 9 sq ft
B 4 sq ft
C 2 sq ft
D 7 sq ft
E 3 sq ft
F 8 sq ft

3. A regular pentagon with a side of 3 centimeters - Answer: F
A 23.01 sq cm
B 12.34 sq cm
C 39.17 sq cm
D 9.46 sq cm
E 34.21 sq cm
F 15.48 sq cm

4. A regular hexagon with a side of 10 cm - Answer: D
A 641.25 sq cm
B 194.45 sq cm
C 361.25 sq cm
D 259.81 sq cm
E 105.22 sq cm
F 453.01 sq cm

5. A regular heptagon with a side of 7 inches. ***need help understanding how to solve***
A 178.06 sq in
B 294.16 sq in
C 169.21 sq in
D 358.91 sq in
E 157.36 sq in
F 277.91 sq in

6. A trapezoid where the height is 18 cm, base 1 = 16 cm and b2 = 8 cm. - Answer: C
A 178.06 sq cm
B 122.5 sq cm
C 216 sq cm
D 230 sq cm
E 280.9 sq cm
F 510 sq cm

7. A trapezoid where the height = 7 mm, base 1 = 26 mm and base 2 = 9 mm. - Answer: B
A 178.06 sq mm
B 122.5 sq mm
C 216 sq mm
D 230 sq mm
E 28.9 mm
F 510 mm

Fill in the missing information for the following trapezoids:
8.
height = 19.8 cm
b1 = ________
b2 = 14.4 cm
area = 401.94 cm2 - Answer: A
A 26.2 cm
B 12.5 cm
C 216 cm
D 23 cm
E 28.9 cm
F 51 cm

9.
height = 23 mm
b1 = 23 mm
b2 = ________
area = 529 mm2 - Answer: D
A 78.06 sq mm
B 22.5 sq mm
C 21.6 mm
D 23 mm
E 28.9 mm
F 30 mm^2

10.
height = ________
b1 = 20 cm
b2 = 21 cm
area = 205 cm2 - Answer: D
A 17.06 cm
B 12.5 sq cm
C 26 cm
D 10 cm
E 28.9 cm
F 50 cm^2

11.
height = 28.9 m
b1 = 26.9 m
b2 = ________
area = 806.31 m^2 - Answer: E
A 17.06 sq m
B 15 m
C 46 m
D 23 m
E 28.9 m
F 51 m

12. If the area of a parallelogram is 690.84 m^2 and the height is 20.2 m, what is the length of the base? - Answer: D
A 78.06 m
B 22.5 m
C 216 m
D 34.2 m
E 28.9 m
F 51 m

13. If the base of a rectangle is 28 cm and the area is 588 cm^2, what is the height of the rectangle? - Answer: E
A 17.06 cm
B 122.5 sq cm
C 216 sq cm
D 23 cm
E 21 cm
F 51 cm^2

14. If the height of a rectangle is 26.1 m and the base is 17.3 m, what is the area of the rectangle? - Answer: A
A 451.53 m^2
B 122.5 m^2
C 216 m^2
D 430 m^2
E 289 m^2
F 510 m^2

15. If the height of a parallelogram is 34 cm and the base is 15 cm, what is the area of the parallelogram? - Answer: F
A 178.06 cm^2
B 122.5 cm^2
C 216 cm^2
D 230 cm^2
E 289 cm^2
F 510 cm^2

16. What is the area of a parallelogram with height 26 cm, base 16 cm, and side length 28 cm?***need help understanding how to solve***
A 178.06 sq cm
B 122.5 sq cm
C 216 sq cm
D 416 cm^2
E 28.9 cm
F 510 cm^2

17. What is the area of a regular octagon with a side of 6 cm? ***need help understanding how to solve***
A 178.06 sq cm
B 122.5 sq cm
C 216 sq cm
D 23 cm^2
E 173.82 cm^2
F 510 cm^2

18. What is the area of this polygon?***need help understanding how to solve***
http://www.compuhigh.com/linkme/admin/testeditor/upload/pics/geometry/lesson21/area1.gif

ls_XF = 53 mm ls_XV = 72 mm ls_VR = 16 mm
ls_FB = 31 mm ls_BT = 31 mm ls_EU = 47 mm
ls_UL = 31 mm ls_TL = 88 mm ls_DE = 16 mm
ls_RM = 70 mm ls_MC = 21 mm ls_DC = 70 mm

A 8014 mm2
B7030 mm2
C6027 mm2
D5478 mm2
E 1782 mm2
F 1225 mm2

19. What is the area of this rectangle?***need help understanding how to solve***
http://www.compuhigh.com/linkme/admin/testeditor/upload/pics/geometry/lesson21/area2.jpg

A 17.06 sq units
B60 sq units
C21.6 sq units
D53 sq units
E 28.9 sq units
F 51 sq units

20. What is the area of this polygon?***need help understanding how to solve***
http://www.compuhigh.com/linkme/admin/testeditor/upload/pics/geometry/lesson21/area3.jpg

A 178 sq units
B129 sq units
C230 sq units
D240 sq units
E 219 sq units
F 206 sq units

1. Post no more than two problems at a time. Give tutors a chance to reply.

2. Show your effort, your math work. By doing so, it helps the tutors here to know where you stand, mathematically speaking.

3. I like your questions but please be specific in terms of directions. For example, don't say this: y = mx + b. Help. What? Help in what way? This is just an example.

4. Give tutors a chance to reply. Many tutors work full-time and NO ONE HERE is getting paid to help out with hundreds of daily questions. I myself use the site as a tutor and as a person learning mathematics.

5. What grade are you in? What math course are you taking?

mathland · Help Me !

Bob wrote:

hi demha
I assume you are asked for the areas here.
1. An equilateral triangle with a side of 1 inch - Answer: A
A 0.43 sq in
B 0.56 sq in
C 0.89 sq in
D 0.23 sq in
E 0.19 sq in
F 0.54 sq in
Correct.
2. A square with a side of 2 feet - Answer: B
A 9 sq ft
B 4 sq ft
C 2 sq ft
D 7 sq ft
E 3 sq ft
F 8 sq ft
Correct.
3. A regular pentagon with a side of 3 centimeters - Answer: F
A 23.01 sq cm
B 12.34 sq cm
C 39.17 sq cm
D 9.46 sq cm
E 34.21 sq cm
F 15.48 sq cm
Correct.
4. A regular hexagon with a side of 10 cm - Answer: D
A 641.25 sq cm
B 194.45 sq cm
C 361.25 sq cm
D 259.81 sq cm
E 105.22 sq cm
F 453.01 sq cm
Correct.
5. A regular heptagon with a side of 7 inches. ***need help understanding how to solve***
A 178.06 sq in
B 294.16 sq in
C 169.21 sq in
D 358.91 sq in
E 157.36 sq in
F 277.91 sq in
How did you do the previous ones? I'm doing them like this: (i) 360/7 to get the central angle for one of 7 identical triangles. (ii) Split this angle in half to create a right angled triangle (iii) Use tan to get the height of the triangle (iv) half base x height for the area of one (v) x by 7 to get area of heptagon

6. A trapezoid where the height is 18 cm, base 1 = 16 cm and b2 = 8 cm. - Answer: C
A 178.06 sq cm
B 122.5 sq cm
C 216 sq cm
D 230 sq cm
E 280.9 sq cm
F 510 sq cm
Correct.
7. A trapezoid where the height = 7 mm, base 1 = 26 mm and base 2 = 9 mm. - Answer: B
A 178.06 sq mm
B 122.5 sq mm
C 216 sq mm
D 230 sq mm
E 28.9 mm
F 510 mm
Correct.
Fill in the missing information for the following trapezoids:
8.
height = 19.8 cm
b1 = ________
b2 = 14.4 cm
area = 401.94 cm2 - Answer: A
A 26.2 cm
B 12.5 cm
C 216 cm
D 23 cm
E 28.9 cm
F 51 cm
Correct.
9.
height = 23 mm
b1 = 23 mm
b2 = ________
area = 529 mm2 - Answer: D
A 78.06 sq mm
B 22.5 sq mm
C 21.6 mm
D 23 mm
E 28.9 mm
F 30 mm^2
Correct.
10.
height = ________
b1 = 20 cm
b2 = 21 cm
area = 205 cm2 - Answer: D
A 17.06 cm
B 12.5 sq cm
C 26 cm
D 10 cm
E 28.9 cm
F 50 cm^2
Correct.
11.
height = 28.9 m
b1 = 26.9 m
b2 = ________
area = 806.31 m^2 - Answer: E
A 17.06 sq m
B 15 m
C 46 m
D 23 m
E 28.9 m
F 51 m
Correct.
12. If the area of a parallelogram is 690.84 m^2 and the height is 20.2 m, what is the length of the base? - Answer: D
A 78.06 m
B 22.5 m
C 216 m
D 34.2 m
E 28.9 m
F 51 m
Correct.
13. If the base of a rectangle is 28 cm and the area is 588 cm^2, what is the height of the rectangle? - Answer: E
A 17.06 cm
B 122.5 sq cm
C 216 sq cm
D 23 cm
E 21 cm
F 51 cm^2
Correct.
14. If the height of a rectangle is 26.1 m and the base is 17.3 m, what is the area of the rectangle? - Answer: A
A 451.53 m^2
B 122.5 m^2
C 216 m^2
D 430 m^2
E 289 m^2
F 510 m^2
Correct.
15. If the height of a parallelogram is 34 cm and the base is 15 cm, what is the area of the parallelogram? - Answer: F
A 178.06 cm^2
B 122.5 cm^2
C 216 cm^2
D 230 cm^2
E 289 cm^2
F 510 cm^2
Correct.
16. What is the area of a parallelogram with height 26 cm, base 16 cm, and side length 28 cm?***need help understanding how to solve***
A 178.06 sq cm
B 122.5 sq cm
C 216 sq cm
D 416 cm^2
E 28.9 cm
F 510 cm^2
You only need two measuements. They have given you an extra measurement just to make sure you know which two to multiply together.
17. What is the area of a regular octagon with a side of 6 cm? ***need help understanding how to solve***
A 178.06 sq cm
B 122.5 sq cm
C 216 sq cm
D 23 cm^2
E 173.82 cm^2
F 510 cm^2
Split this into 8 triangles. The angle at the top of each triangle is 360/8 and then you need to half this to make a right angle for the tangent calculation.
18. What is the area of this polygon?***need help understanding how to solve***
You can split this polygon onto three rectangles. (see picture below) You will have to use the information to work out the length and width of each part and then add up the areas.
ls_XF = 53 mm ls_XV = 72 mm ls_VR = 16 mm
ls_FB = 31 mm ls_BT = 31 mm ls_EU = 47 mm
ls_UL = 31 mm ls_TL = 88 mm ls_DE = 16 mm
ls_RM = 70 mm ls_MC = 21 mm ls_DC = 70 mm

A 8014 mm2
B7030 mm2
C6027 mm2
D5478 mm2
E 1782 mm2
F 1225 mm2

19. What is the area of this rectangle?***need help understanding how to solve***
Use Pythagoras to work out the height of the rectangle.
A 17.06 sq units
B60 sq units
C21.6 sq units
D53 sq units
E 28.9 sq units
F 51 sq units

20. What is the area of this polygon?***need help understanding how to solve***
My picture below shows how you can split this shape into a rectangle and a triangle. You will also need to use Pythag. to get the length of the red line.
A 178 sq units
B129 sq units
C230 sq units
D240 sq units
E 219 sq units
F 206 sq units

Hope that helps
Bob

This person posted a Bible load of math questions. The other day, I was criticized for posting 4 or 5 problems.

mathland · Help Me !

Bob wrote:

hi mathland,
I do my best. If someone asks for help, they may get back a single reply or they may get several. It's the Op's choice about which to use and which to ignore. You don't need to make any comment at all to a reply that you don't think was helpful.
I joined in 2010 and began offering help. A member (I'll call them A), who was also helping a poster, was very rude to me about my help. I spent some thinking time constructing replies, some sarcastic, some rude, some just protesting my case. In the end I decided not to reply at all.
Unknown to me at the time the moderators were having a private discussion about this. They threatened member A with expulsion and the 'offending' post was edited. Then MIF asked me if I would become a moderator. His reason for choosing me was that I had maintained a polite and non heated position in the face of provocation.
Moderators are able to do the following: (1) edit a post to remove unsuitable comments (2) delete a post entirely (3) close down a thread so that no subsequent posts can be made (4) ban a member (for a period or permanently) (5) delete all records of a member.
Administrators can do all that and also control the structure of the forum in a number of ways.
If you are unhappy about a post you should click the 'Report' button below the post, on the right. This generates a report for moderators so they can consider what action to take. Ordinary members cannot block other members.
This morning I have removed a number of unpleasant comments from the forum and deleted some posts entirely. I have closed some threads. It is my hope that the members effected will take this as a warning that they have made unacceptable comments and avoid this in future. That way we can keep the forum as a pleasant and safe place for all.
Best wishes,
Bob

1. Thank you, Bob

2. I accidentally clicked on "Report" at the bottom of your most recent reply (this one). It was an error.

3. You have no idea how many math sites I have joined and left due to troublemakers, you know, people picking fights and arguments.

4. I have idea how many countless times I posted my main reason for joining MIF.
Some "know it all" stated that my questions are too easy. The person went on to say that he does understand what my problem is in terms of math. I feel like challenging this fool by posting the toughest textbook problems specifically for him to help me with. This may teach him some humility.

5. How do I become a moderator here?

6. I still don't know how to upload pictures. Can you show me step-by-step?

7. I hope my contribution to MIF will help others who may be struggling and/or facing the same problems in their math class.

8. As you know, I am 56 years old. I have three college degrees in areas other than math. I took Precalculus in the Spring 1993 semester at Lehman College. I earned an A minus. Of course, this is long ago. So, I decided to revisit this course as I study Calculus 1 (also for the sake of learning). All this is just for fun. How do you think I made through the pandemic?

9. I love Precalculus. It is one of my favorite courses.

10. I will also contribute here as a math tutor by answering prealgebra, algebra 1, algebra 2, geometry and trigonometry questions (at the middle school and high school levels). Thus far, I have not seen too many recent middle school and high school math questions here (MIF).

Math Is Fun Forum

#26 Re: Help Me ! » Domain of Cube Root Function » 2021-05-14 11:07:54

#27 Re: Help Me ! » Domain of Cube Root Function » 2021-05-14 06:19:43

#28 Re: Help Me ! » Maximum Profit » 2021-05-14 06:18:22

#29 Re: Help Me ! » Maximum Profit » 2021-05-13 20:46:59

#30 Re: Help Me ! » Relationship Between x and y » 2021-05-13 20:44:06

#31 Re: Help Me ! » Domain of Cube Root Function » 2021-05-13 20:40:13

#32 Re: Help Me ! » Find Domain of Algebraic Fraction » 2021-05-13 20:33:00

#33 Re: Help Me ! » Find Range Algebraically » 2021-05-13 20:30:37

#34 Dark Discussions at Cafe Infinity » Is Bible Prophecy Important? » 2021-05-13 19:26:35

#35 Re: Help Me ! » Find Domain of Algebraic Fraction » 2021-05-13 19:23:09

#36 Re: Help Me ! » Domain of Cube Root Function » 2021-05-13 19:22:03

#37 Re: Help Me ! » Polygons and Review » 2021-05-13 18:02:13

#38 Re: Help Me ! » Relationship Between x and y » 2021-05-13 17:57:50

#39 Help Me ! » Maximum Profit » 2021-05-13 15:33:43

#40 Help Me ! » Find Range Algebraically » 2021-05-13 15:06:52

#41 Help Me ! » Find Domain of Algebraic Fraction » 2021-05-13 15:02:17

#42 Help Me ! » Domain of Cube Root Function » 2021-05-13 14:57:53

#43 Help Me ! » Relationship Between x and y » 2021-05-13 14:50:13

#44 Re: Help Me ! » Polygons and Review » 2021-05-13 10:37:52

#45 Re: Dark Discussions at Cafe Infinity » Loneliness » 2021-05-13 10:34:44

#46 Re: Dark Discussions at Cafe Infinity » Loneliness » 2021-05-13 09:09:39

#47 Re: Dark Discussions at Cafe Infinity » An Autograph Means Nothing To Me » 2021-05-13 09:03:50

#48 Re: Help Me ! » Polygons and Review » 2021-05-13 08:58:19

#49 Re: Help Me ! » Polygons and Review » 2021-05-13 08:51:05

#50 Re: Help Me ! » Testing For Function » 2021-05-13 08:47:28

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