CPhill

56 Questions
43866 Answers

+18

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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 mehr ..

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CPhill 07.08.2023

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HAPPY BIRTHDAY , MELODY !!!

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

mehr ..

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CPhill 16.04.2022

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HAPPY BIRTHDAY, MELODY !!!!

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CPhill 16.04.2021

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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 !!! ]

mehr ..

CPhill 26.03.2020

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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!!) ]
mehr ..

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CPhill 14.10.2019

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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" mehr ..

CPhill 21.10.2018

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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....!!! mehr ..

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CPhill 13.03.2018

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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 06.03.2018

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

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CPhill 13.02.2018

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HAPPY BIRTHDAY, HECTICTAR !!!!

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

Here's your cake.....enjoy.....!!!!
mehr ..

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CPhill 14.10.2017

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Going To The Picnic

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

mehr ..

CPhill 25.09.2017

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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 mehr ..

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CPhill 23.09.2017

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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 mehr ..

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CPhill 20.09.2017

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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??? mehr ..

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CPhill 19.03.2017

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

hectictar ●●●●●●

CPhill 14.03.2017

+130491

+2

This represents 52 ! where the "!" is known as "factorial"

In this case.....it's a REALLY BIG number !!

52!

See....I told you so !!!!

CPhill27.03.2014

+130491

+2

Isn't your equation

y = 3.75 + .75(x)

where 3.75 is the "fixed cost" part and .75(x) the "variable cost" part ???

If so, we have

14.50 = 3.75 + .75(x)

Subtracting 3.75 from both sides, we have

11.25 = .75(x)

Dividing both sides by .75, we have

x =

11.25/.75

(This usually represents some variable quantity like hours worked, etc.)

CPhill27.03.2014

+130491

+2

The sum of the first N positive integers is given by N * (N+1) / 2

So we have......

401* 402 / 2

Notice that we could also see a pattern here.....
400 + 1 = 401
399 + 2 = 401
398 + 3 = 401
.
.
.
201 + 200 = 401

So, we have 200 pairs that add to 401, or

200(401) plus the lone remaining "unpaired" 401 = 80601

That's it !!!

CPhill27.03.2014

+130491

+2

At the end of the first year, you get 100% of the 3300 plus 5% more.

In decimal terms, this equates to 1.00 + .05 = 1.05.

So, to find the amount of the raise after the first year, we just multiply 3300 * (1.05)

To find the amount after two years, we take what we had at the end of the first year (3300 * (1.05)) and multiply THAT by 1.05.

So we have........(3300 * 1.05) * (1.05 or 3300 * (1.05) ^2

Then, the "formula" to find the amount after N years is just........... 3300*(1.05)^N

I'll let you finish this one.....(remember to do the exponent part first and then multiply by 3300, unless you're putting the whole thing in a calculator to evaluate it all at once)

CPhill27.03.2014

+130491

+2

This isn't the most "mathematical" explanation.....but it might help anyway.

Let us suppose that something originally costs $100.

Now, let's suppose that we take 10% off. Well, looking at it another way, it must now just be "worth" 90% of what its original price was, i.e., $90.

Now, let's suppose that we take 15% off of that. Well, then the "new" price must just be 85% of the $90 (since we took 15% off), i.e., $76.50.

Well, the "final" price is just 76.5% of the original $100 price........thus we "took off" $23.50.....or 23.5% of 100 !!!

In terms of "math-speak," we could express this in the following way........100 - (100*.90*.85)......100 - (76.50)........Original Price - (Final Price) = "Discount"

This is simplistic, but I hope it helps you see it.......

CPhill27.03.2014

+130491

+2

We could use some fancy math here, but let's not.

Since a boy 6 feet tall casts a shadow 4 times his height (24 ft.), the flagpole must do the same.

Then the flagpole's shadow must be 4 times its height.

Then dividing 200 by 4, the height of the flagpole must be 50 ft.

And that it. No fuss, no muss.

CPhill27.03.2014

+130491

+2

We could use some fancy math here, but let's not.

Since a boy 6 feet tall casts a shadow 4 times his height (24 ft.), the flagpole must do the same.

Then the flagpole's shadow must be 4 times its height.

Then dividing 200 by 4, the height of the flagpole must be 50 ft.

And that it. No fuss, no muss.

CPhill27.03.2014

+130491

+2

X = 36 degrees

Call the apex point of the triangle A
Call the angle bisector AD, where D is the point where the bisector intersects the base of the triangle.

Let the vertexes counterclockwise from A be labeled B and C.

Then, in triangle ADC, AD = DC. And in any triangle having equal sides, the angles opposite those sides are equal, too. Therefore, < DCA (angle "X") = < DAC (one of the angles formed by the bisector).

And in triangle ABD, AB = AD, so the measure of angles ABD and ADB are equal.

And by the exterior angle theorem, angle ADB = DAC + DCA. Therefore, ABD = BAD + DCA.

And, because of bisection, angle BAD = DAC. And angle BAC equals their sum.

Therefore, ABD + BAC + DCA = 180.

Therefore, by substitution, BAD + DCA + BAD + DAC + DCA = 180 or, simplifying, 2BAD + 2DCA + DAC = 180.
But DCA = DAC., And DAC = BAD.
Therefore, DCA = DAC = BAC = BAD.

And substituting again......2DCA + 2DCA + DCA = 180

Therefore, 5DCA=180
Therefore DCA = 36 = X

Let's check that this is true. In triangle ABD....ABD = 72 angle ADB =72 and BAD = 36....these sum to 180
And, in triangle ADC, angle ADC is supplemental to angle ADB (i.e., 108) and DAC = 36 and DCA = 36...so these sum to 180, as well.

CPhill27.03.2014

+130491

+2

Have you tried the calculator on this site??

Hit the "2nd" button on the calculator and find the "asin" function.

You also have the option to express this in degrees or radians.

If you still have trouble - let us know.

CPhill27.03.2014

+130491

+2

what is 526923076.923 in scientific notation?

5.26923076923 × 10^8

CPhill26.03.2014