GYanggg

The root of the problem is not one who gives to answers, but the ones who take it.

I agree with x^2 that his answers include brilliant solutions to helped users not only get the answer, but understand it. 

When supplying an answer, you should always include a solution. Whether or not they look at it, is completely up to them. Answering someone's math question is not cheating if you help them understand. It is them, who do not look at the solutions which is considered cheating. 

Hi Melody!
 

In that case, then this is possible. 

Using the same logic, a sphere is composed of mulitple cones. 

This is because a cone is considered a pyrimaid. 

Thank you for correcting my mistake,

Gavin

Hey Guest!

I have answered a few chemistry questions on this website.

It is supposed to be for math (I think).

If you want to ask a chemistry problem, ask away!

I will give it a go, no guarantees it will know how to do it. 

Hey ant101!

x = speed of frog

y = speed of current

We use (distance)=(rate)*(time) 

We can set up the system of equations:

\((x+y)\cdot2=8\\ (x-y)\cdot14=8\)

Solving for x, we get:

\(x=\frac{16}7\)

I hope this helped,

Gavin

If a knight can storm a castle in 15 days, he can storm 1/15 of a castle in one day. 

If he and his partner can do it in 10 days, they can storm 1/10 of a castle in one day. 

We can set up the equation: 

\(\frac{1}{15}+\frac{1}{x}=\frac{1}{10}\\x=30\)

It will take his partner 30 days to storm the castle alone. 

I hope this helped,

Gavin

\(\frac12\le\frac x8\le\frac79\)

We commonize the denominator:

\(\frac{36}{72}\le\frac{9x}{72}\le\frac{56}{72}\)

This works out when x=4, 5, and 6

I hope this helped,

Gavin

Please don't just type in the answer, read the solution and try to understand the problem. Try to do other problems like this on your own. Then you can actually improve. 

There are two methods to do this problem.

Method 1: Pattern Finding

There are 9 palindromes with 2 digits 

There are 90 palindromes with 3 digits

There are 90 palindromes with 4 digits

Method 2: Counting

The 4 digit palindrome is in this format:

ABBA

There are 9 choices for A

10 for B

9*10=90

I hope this helped, 

Gavin

I totally agree with you.

One way to remedy this issue is to post the full solution but leave out the last steps, so the person asking the question can have time to read the solution and must understand it to figure out the answer. 

Gavin.

4. Expand

\(ay^3+by^2+cy+d=3x^3-8x^2+7\\ \ \\ a(x-2)^3+b(x-2)^2+c(x-2)+d=3x^3-8x^2+7\\ \ \\ ax^3−6ax^2+12ax−8a+bx^2−4bx+4b+cx-2c+d=3x^3-8x^2+7\\ \ \\ ax^3-6ax^2+bx^2+12ax-4bx+cx-8a+4b-2c+d=3x^3-8x^2+7 \)

We get:

\(ax^3=3x^3 \\ bx^2-6ax^2=-8x^2\\ 12ax-4bx+cx=0\\ 4b-8a-2c+d=7\)

We get the systems:

\(a=3\\ b-6a=-8\\ 12a-4b+c=0\\ 4b-8a-2c+d=7\)

\(a=3\\ b-6\cdot3=-8\Rightarrow b=10\\ 12\cdot3-4\cdot10+c=0\Rightarrow 36-40+c=0 \Rightarrow c=4\\ 4\cdot10-8\cdot3-2\cdot4+d=7\Rightarrow40-24-8+d=7 \Rightarrow d=-1\)

\(a+b+c+d=3+10+4-1=\boxed{16}\)

I hope this helped,

Gavin