CPhill

56 Questions
43886 Answers

+19

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Blocked Posts

I just wrote to the site manager to let him know that this is happening....I'll try to "unblock" as many posts as possible ( but realize that I can't stay on here all day )
CPhi lire plus ..

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CPhill 7 août 2023

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HAPPY BIRTHDAY , MELODY !!!

I baked you a cake.....be sure to share !!!!!

lire plus ..

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CPhill 16 avr. 2022

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HAPPY BIRTHDAY, MELODY !!!!

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CPhill 16 avr. 2021

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Gotta take a break folks !!!!

I'll come back a little later and try to answer as many questions as I can [ or as many as I know how to do !!! ]

lire plus ..

CPhill 26 mars 2020

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HAPPY BIRTHDAY, HECTICTAR !!!

She is one of the best "answerers" on this site [ even though she IS from Alabama....well.....everyone can't be perfect !!!! (Hehehe!!) ]
lire plus ..

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CPhill 14 oct. 2019

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'Waiting For Moderation'

I see that this has been happening quite a bit.....

If you "right click" on the image and select "Copy Image Address".....you can open up a new browser window and paste this address into it.....hit "Enter" lire plus ..

CPhill 21 oct. 2018

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4th Anniversary For Me !!!

Been on this site for 4 years now.....my thanks to Melody (and Andrew) for recommending me as a "mod".....I've learned quite a bit and "met" a lot of good people on here.....I've even managed (somehow) to help some of them....!!! lire plus ..

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CPhill 13 mars 2018

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Hey, guys.....I'm going to be gone for awhile....If you can hang on....I'll answer as many questions as I know how in just a bit....

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CPhill 6 mars 2018

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I'm Out Until This Afternoon...You Kids Have Fun !!!

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CPhill 13 févr. 2018

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HAPPY BIRTHDAY, HECTICTAR !!!!

You are a real asset to the forum.....!!!!!

Here's your cake.....enjoy.....!!!!
lire plus ..

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CPhill 14 oct. 2017

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Going To The Picnic

This one isn't too difficult....give it a try.....!!!!!

lire plus ..

CPhill 25 sept. 2017

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How Much Do They Weigh ????

This is another problem from American puzzle-maker Sam Lloyd.....

Five little girls taken in couples weigh 129 pounds, 125 pounds, 124 pounds, 123 pounds, 122 pounds, 121 pounds, 120 pound, 118 pounds, 116 lire plus ..

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CPhill 23 sept. 2017

+26

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The Width Of The River.....

Here is a problem I've always liked...it was devised by one of the great American "puzzleists" of all time, Sam Lloyd

It has been posted on the forum before, but not in a while.....maybe we have some new people who would like lire plus ..

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CPhill 20 sept. 2017

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ReCaptcha Verification

I don't know if others are having this problem or not......when using Opera or Firefox I had to do the ReCaptcha thing when submitting answers.......however.......using Google Chrome seems to solve this problem - for me anyway....

Comments??? lire plus ..

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CPhill 19 mars 2017

+35

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Happy Pi Day..(3.14)....Everybody.....!!!!!

hectictar ●●●●●●

CPhill 14 mars 2017

+130556

+3

The diameter is 2

To see this, note that the circumference is given by C = 2πR, or C=2Rπ. But 2R = D, where D is the diameter.

Therefore, C=Dπ

So 6.28 = Dπ

And if we let π = 3.14

Then, 6.28 = D * 3.14

So D = 6.28 / 3.14 = 2

CPhill26 mars 2014

+130556

+2

Example:

Twice a number = 2n

So, 5 less than twice would be

2n - 5

CPhill25 mars 2014

+130556

+2

Take a look at this website, Stu. I've found that his explanations are pretty good. He also gives some examples.

http://tutorial.math.lamar.edu/Classes/CalcI/DerivativeIntro.aspx

If you have any specific questions, post them to the forum.

Hope this helps.

CPhill25 mars 2014

+130556

+2

Although I'm not the most "technical" user of the calculator, it will add and subtract fractions (and reduce them to simplest form). It will also convert an "unknown" decimal to a fraction.

Examples

0.1752055660974067

I'm not sure what you might be after, but if you have more specific questions, post them to the forum and we'll see if we can answer them.

CPhill25 mars 2014

+130556

+2

First, let sin(x) = x

So

3SIN(x)^2-7SIN(x)-3=0

= 3x^2 - 7x - 3 = 0

Solving, we have.....

3x^2 - 7x - 3 = 0

This implies that sin(x) = (7 - √85) / 6 and sin(x) = (7 + √85) / 6

The second answer is impossible, since it implies that sin(x) > 1

Solving for the first, we have

asin(((7-sqrt(85))/6))

Hope this helps

CPhill25 mars 2014

+130556

+2

Bertie

Your method of substituting cos(pi/3) for 1/2 and sin (pi/3) for (√3)/2 is quite ingenious!!!!

I like that MUCH BETTER !!!

CPhill25 mars 2014

+130556

+2

sqrt(3)cos(x) - sin(x)= 1

Let's see if this works

(add sin(x) to both sides and square both sides)

3(cos(x)^2 = 1 + 2sin(x) +sin(x)^2

(using cos(x)^2 = 1 - sin(x)^2, we have)

3*(1 - sin(x)^2) = 1 + 2sin(x) +sin(x)^2

(Simplify)

4*sin(x)^2 + 2*sin(x) - 2 = 0

(Divide through by 2)

2*sin(x)^2 = sin(x) -1 = 0

(Factor)

(2sin(x) -1) (sin(x) +1 ) = 0

Solving, we get x = (pi/6 + 2*pi*n , 3*pi/2 +2*pi*n)

Another 2nd quad angle, 5*pi/6, solves (2sin(x) -1 = 0), but it doesn't "work in the original problem) (due to "squaring," we get an extraneous solution??)

I think that may be it.....but check my work and method!!

CPhill25 mars 2014

+130556

+2

This is an interesting one........

For all real numbers x,

√(x)^2 = IxI = x if {x ≥ 0 and -x if x < 0}

So, √(-1)^2 = I-1I = -(-1) = 1

Now, many people assume that the result could be "-1" - due to following faulty "proof."

Step 1 √(-1)^2 =

Step 2 √(-1) * √(-1) =

Step 3 ( i * i ) =

Step 4 ( -1 )

The problem comes in the transition from Step 1 to Step 2.

In general, √(a * a) = √(a) * √(a) only if a ≥ 0. (Thus, we can't "split" the radicals in this manner.)

I think that's it !!!

CPhill22 mars 2014

+130556

+2

How do you Solve this?
2(x+3) - 2x^2(x+3) = 0
In my answer sheet they rewrite it to (x+3) * (2-2x^2) = 0
Im unsure what happens to the other (x+3)

They (almost) took the greatest common factor, (x + 3), out of both terms......... !!!!

We can also take a "2" out !!!

Doing this, we get

2 * (x + 3) * (1 - x^2) = 0

We can get rid of the 2 by dividing through, so this becomes

(x + 3) * (1 - x^2) = 0

To solve, set each factor = 0

The first one is easy

x + 3 = 0

Subtracting 3 from both sides, we get

x = -3 and that's one solution

Now, setting the other factor to 0 we get

1 - x^2 = 0

This can be factored as

(1 - x) * (1 + x) = 0

And setting these two things to 0 (as before), we get the other two solutions of 1 and -1

Hope this helps

CPhill22 mars 2014

+130556

+2

how do i do a problem like this 1/2(w-4)??

I assume you just want to "distribute" the 1/2 over the terms in the parentheses.

This would just give us

1/2w - 2

CPhill21 mars 2014