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That is not correct

But you are right you can get a pattern going.

To determine the pattern you draw lines and COUNT!

That is not going to help.  It has nothing to do with this question. Asinus got confused.

You have 

f(x)=x^2   

And you know that

$g'(x)=\frac{-1}{2x}$

NOW can you integrate that to get the value of g(x)???

What is the

$\int \frac{-1}{2x}\;dx$       ?

Normally, if you do not know the answer, you might do this :

$\int \frac{-1}{2x}\;dx=\frac{-1}{2}\int x^{-1}\;dx = \frac{-1}{2}\int x^{-1+1}\;dx$

But that leaves us with a power of 0 and that definitely is not right!   

So this should remind you that the answer is a natural log !

Now can you or Asinus  do this integral and get the function g  ?

$g(x)=\int \frac{-1}{2x}\;dx$

Possible: ${8 \choose 2} = 28$

Favorable: $4$

$\frac{1}{7}$

I do not know how to share my graph but i plugged in g as -1/4x^2 

1/  Use the law of cosines to calculate all 3 angles.

2/  If AB=15,  BC=10, and AC=20 then DC is what you're looking for.

3/  By using the law of sines, calculate the length of DC.

a)

$\text{total pizza ate}\ =\ \frac13\ \text{of a pizza}\ +\ \frac14\ \text{of a pizza} \\~\\ \text{total pizza ate}\ =\ (\frac13+\frac14)\ \text{of a pizza} \\~\\ \text{total pizza ate}\ =\ (\frac{1\times4}{3\times4}+\frac{1\times3}{4\times3})\ \text{of a pizza} \\~\\ \text{total pizza ate}\ =\ (\frac{4}{12}+\frac{3}{12})\ \text{of a pizza} \\~\\ \text{total pizza ate}\ =\ \frac{7}{12}\ \text{of a pizza}$

b)

Technicallyyyy there could be any number of slices in the pizza. But 12 would be a good number of slices. That way Khalid could eat 4 full slices and his sister could eat 3 full slices.

12/13

Hi asinus,

I did not see your edit till a moment ago.

your   g'(x) is now correct  but you have not integrated it to get g

What did you get for g ?

What did you plot, if you provided me with a link to your plot I could comment a lot better.

Note: Asinus's answer is not correct.   (Although it is better than before)

$g'(x)=\frac{-1}{2x}\qquad \text{That is true}$

But what do you get when you integrate that?

what are all the values of a?

please help

This means 

(11 + 8 + 14 + 14 + x)/5 = 13

Can you rearrange this to find x?

Hi asinus,

Thank you for you help!

I have plotted in f and g onto Desmos but I am unsure what to do now. How should I continue?

There's a better way than drawing and counting, I can't keep track of it all.

But I noticed that for every 2 lines, they add 6 new angles.

The area of the   red-blue-green triangle here:

https://www.desmos.com/calculator/xlgcebrsji

The forces are equal.....    if either force were greater the car would deccelerate (due to friction) or accelerate (due to greater motiv power).

What is the ceiling of the numbers you want to check? Because there are an infinite number of integers which will have 3 distinct prime factors, such as: 9971  x  123457  x 1000003 =1,230,993,439,969,241. You can simply reverse the digits:1429699343990321

First of all, either that dog is seriously overweight, or he/she is going through a growth spurt. If Amar's dog east 114 pounds of dry dog food every day, a 45-pound bag of dog food will only last 45/114 of a day.

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If this is not the answer you are looking for, or it is incorrect, don't hesitate to ask, and I can look at the question again :D

There are $\binom{10}{3} = 120$ different combinations of 3 meerkats that have to stand guard. Therefore each meerkat has to stand guard $\frac{120}{10} = 12$ nights. That means each meerkat gets 108 nights of sleep.

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If this answer is incorrect, or you are looking for a different answer, feel free to ask me and I can look at the question again :D

If this is what you are asking: Ms. Cole has 4 yards of string. She cuts the string into pieces that are each 12 yards long. How many pieces of string does Ms. Cole have?

Then your answer is: She has 1/3 of a piece of string.

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If this is what you are asking: Ms. Cole has 4 yards of string. She cuts the string into pieces that are each 12 feet long. How many pieces of string does Ms. Cole have?

Then your answer is: She has 1 piece of string.

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If this is what you are asking: Ms. Cole has 4 yards of string. She cuts the string into pieces that are each 12 inches long. How many pieces of string does Ms. Cole have?

Then your answer is: She has 12 pieces of string.

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I am not exactly sure if this is what you are looking for. If you need anything else, don't hesitate to ask :D

If the area of the original square is $64$ square inches, then the perimeter is $32$ inches, and each side is $8$ inches. Each triangle will have an area of $32$ square inches. The perimeter of the triangles is $16$ + the hypotenuse. The length of the hypotenuse is given by the Pythagorean theorem: $a^2 + b^2 = c^2$ so we have $8^2 + 8^2 = c^2$ therefore the length of the hypotenuse is $\sqrt{128}$  so your answer is $16 + \sqrt{128} = 16 + 8\sqrt{2}$. 

I'm not 100% sure this is the answer you want, if you need anything else, just ask :D

The volume of a cone $V$ can be calculated by the equation $V = \frac{bh}{3}$ where $b$ is the area of the base. If the cone has a radius of $5.5$ then the area of the base is $30.25\pi$ therefore the volume of the cone is $\frac{12 \times 30.25\pi}{3} = 121\pi \approx 380.132711084$ units^3.

No, 4 sqrt 5 is correct.

Out of the five people, there is a $\frac{2}{5} \cdot \frac{1}{4} = \frac{2}{20} = \frac{1}{10}$ chance that the commitee will have exactly two women and one man. And there is a $\frac{1}{10} \cdot \frac{1}{3} = \frac{1}{30}$ chance that the chairperson will be a man.

I'm not 100% sure this answer is correct, someone should double check it :D

If we plug in $-5$ to the function $f(x) = |x + 1|$ we get $|-5 + 1|$ which simplifies to $|-4| = 4$

instead of 4sqrt(5)