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59. Write the area A of a square as a function
of its perimeter P.
60. Write the area A of a circle as a function
of its circumference C.
61. Path of a Ball You throw a baseball to a child
25 feet away. The height y (in feet) of the baseball is
given by y = − (x^2)/10 x^2 + 3x + 6 where x is the horizontal
distance (in feet) from where you threw the ball.
Can the child catch the baseball while holding a baseball glove
at a height of 5 feet?
Enjoy.
In Exercises 9 and 10, which sets of ordered pairs represent
functions from A to B? Explain.
9. A = {0, 1, 2, 3} and B = {−2, −1, 0, 1, 2}
(a) {(0, 1), (1, −2), (2, 0), (3, 2)}
(b) {(0, −1), (2, 2), (1, −2), (3, 0), (1, 1)}
(c) {(0, 0), (1, 0), (2, 0), (3, 0)}
(d) {(0, 2), (3, 0), (1, 1)}
10. A = {a, b, c} and B = {0, 1, 2, 3}
(a) {(a, 1), (c, 2), (c, 3), (b, 3)}
(b) {(a, 1), (b, 2), (c, 3)}
(c) {(1, a), (0, a), (2, c), (3, b)}
(d) {(c, 0), (b, 0), (a, 3)}
NOTE: THIS IS EXTRA PRACTICE FOR MEMBERS. I AM NOT ASKING FOR HELP WITH 9 AND 10.
mathland wrote:Find the distance between the points.
17. (−2, 6), (3, −6)
18. (8, 5), (0, 20)
19. (1, 4), (−5, −1)
20. (1, 3), (3, −2)
21. (1/2, 4/3) (2, −1)
22. (9.5, −2.6), (−3.9, 8.2)
___________________
would the formula be √ (x1 - x2)² + (y1 -y2)² ? edit: oop the link already said so
I posted the problems as extra practice for members.
mathland wrote:ganesh wrote:I did take tuitions for middle school students (home tuition) as an amateur.
When I said Mathematics has provided me bread and butter, I meant I got a good job only because of my math and science background.
1. What is your math and science background?
2. How much math do you know?
3. Can you help me with calculus 1, 2, and 3 moving forward?
4. Do you know math beyond calculus?
5. How much science do you know?
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.
All correct!
B
Thank you Bob for not putting me down or picking fights. How do I block members on this site? I need to block two troublemakers.
Thanks.
mathland
Both correct.
B
Very good.
Well, yes; but it's a two step process. First change the equation to one that you know how to differentiate, then implicit is forced on you.
B
Thank you. [comment removed by Admin] I do use your hints and steps to solve the posted questions on paper. [comment removed by Admin}
mathland wrote:ganesh wrote:Being alone is some times gives more time to attend to other things.
One is left with an advantage : Time!
I concur. Alone time means more time to think about things that really matter.
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....
mathland wrote:ganesh wrote:There are things you know at some to or the other.
There are also things you may never know.
One is, life and death.
I live and let live. I tell you about Jesus. It is your choice to accept the gospel message or to reject it. What happens next is between you and God.
You can't just tell people about Jesus if you don't live like Jesus.
I concur.
mathland wrote:ganesh wrote:There are things you know at some to or the other.
There are also things you may never know.
One is, life and death.
I live and let live. I tell you about Jesus. It is your choice to accept the gospel message or to reject it. What happens next is between you and God.
'Live and Let Live' is a wonderful principle.
I concur. I hate to argue. I hate the anxiety that develops when trying to convince someone that my view is right. My job is to tell you what Jesus said happens to those who reject Him. If you decide that worshipping a cow is the right way to go, then this is your choice. The problem is then between you and God.
mathland wrote:ganesh wrote:Mathematics is a hobby as well as bread and butter.
Without it, I would have never been a complete person.
So, are you a math teacher or simply a math enthusiast?
I did take tuitions for middle school students (home tuition) as an amateur.
When I said Mathematics has provided me bread and butter, I meant I got a good job only because of my math and science background.
REST IN PEACE...What?
What in the world does that mean? How do we know for sure that our departed loved ones are resting in peace? Do we know for sure they are resting in the peace of paradise? The reason we say "rest in peace" after someone dies is basically because we assume that the soul of the departed left this world to be with God in Heaven.
Again, how do you know the departed went to Heaven? Believe it or not, RIP is not biblical. Jesus said there are two places after death: Heaven and Hell. Let me put it this way: if there is no Heaven, there is no Hell and vice-versa. If everyone goes to Heaven after death, then Jesus lied. If Jesus lied, then He is not the Messiah, the Son of God. Something for you to think about.
mathland
People around the world erroneously think that the only ticket to a guaranteed life in Heaven is death. So, if I die, I immediately go into the presence of God. My friends, nothing can be further from the truth. The sad reality is that not everyone goes to Heaven after physical death. In fact, Jesus said that there are more people on the broad road to destruction than the narrow road into the kingdom of God. Something to think about, right?
mathland
Yes, I know that the site has links to math notes. The idea for posting threads is to get people involved in mathematical discussion.
Determine whether the equation represents y
as a function of x.
1. x^2 + y^2 = 4
2. x^2 − y = 9
Let me see.
Question 1
I will solve for y.
x^2 + y^2 = 4
y^2 = -x^2 + 4
sqrt{y^2} = sqrt{-x^2 + 4}
When taking the square root, two answers is the result: one is positive, the other negative.
y = -sqrt{-x^2 + 4}
y = sqrt{-x^2 + 4}
For 1, the equation does not represent y as a function of x.
You say?
Question 2
x^2 - y = 9
Solve for y.
-y = -x^2 + 9
y = (-x^2 + 4)/(-1)
y = x^2 - 4
I see that y does not lead to two different values (positive & negative) on the right side. I say the equation for 2 represents y as a function of x.
You say?
Determine whether the table relation represents y as a function of x. Identify the domain and range.
Values of x.............Values of y
2..................................11
2..................................10
3....................................8
4....................................5
5....................................1
Let me see.
I know the following:
(x, y) = (input, output) = (domain, range).
From this, I can see that x = input = domain.
I also see that y = output = range.
If the input x has two different output y-values, there is no function.
I see that 2 is matched with 11 and 10. I say the above table does not represent a function. The table relationship does not represent y as a function of x.
Domain = {2, 2, 3, 4, 5}
Range = {11, 10, 8, 5, 1}
eg.
Differentiate wrt x:
This last step (to get the answer as a function of x) uses
Bob
The idea is to use implicit differentiation.
Yes, from the 3rd law:
or alternatively
You can check this out with an example.
Let a = 64
(root 64)^3 = 8^3 = 512
root (64^3) = root(262144) = 512
Bob
Honestly, math is simply never-ending education.
mathland wrote:ganesh wrote:Being alone most of the time isn't wrong at all.
Some have many friends, some a few, and some have none at all.
There is nothing wrong in it, I think.
]0⁹[(lļ
More alone time works for me.
Being alone is some times gives more time to attend to other things.
One is left with an advantage : Time!
I concur. Alone time means more time to think about things that really matter.
mathland wrote:ganesh wrote:Yes, it was a hobby at that point of time.
But, as we grow, priorities shift.
Fortunately, learning has been a top priority.
Math is a hobby for me at this stage in my life. I don't think I'll ever stop learning new mathematical ideas.
Mathematics is a hobby as well as bread and butter.
Without it, I would have never been a complete person.
So, are you a math teacher or simply a math enthusiast?
mathland wrote:ganesh wrote:True. Complicated and difficult to judge.
I have been a faker for too long. I preach A bit do B instead. It's getting dull and old.
It is never too old to change habits. Provided, it is change for the better.
I'll keep you posted.
mathland wrote:ganesh wrote:That is the bottom line.
Exactly. I say Jesus is the way to Heaven. All religions have their own way to Heaven.
Who's right? We'll just have to wait and see. We long to see Heaven but refuse to accept death as a door into the afterlife.
.There are things you know at some to or the other.
There are also things you may never know.
One is, life and death.
I live and let live. I tell you about Jesus. It is your choice to accept the gospel message or to reject it. What happens next is between you and God.
mathland wrote:ganesh wrote:Understandable!
A double life is too complicated to deal with. Be the person you were meant to be.
True. Complicated and difficult to judge.
I have been a faker for too long. I preach A bit do B instead. It's getting dull and old.
mathland wrote:ganesh wrote:I feel the COVID-19 pandemic has been a lesson! Life is like a soap bubble! Anytime, anything, anywhere can happen! Therefore, be good to all!
The pandemic attacked the good, the bad, the ugly, the rich, the poor, etc.
It is good or bad for all, in a way. Bad - lives lost, good - all fight for a united cause.
There has not been much unity in America before, during and after the pandemic leaves. The democrats have turned the USA into a battlefield.
mathland wrote:ganesh wrote:Yes! None to distub or distract!
I am passionate about my alone to such a degree that people think I am antisocial. Well, I am not antisocial. I just prefer being alone most of the time.
Being alone most of the time isn't wrong at all.
Some have many friends, some a few, and some have none at all.
There is nothing wrong in it, I think.
More alone time works for me.