RiemannIntegralzzz

$(0.\overline{6})(0.\overline{06})=(6/9)*(6/99)=4/99=0.\overline{04}$

The sum of the first $15$ digits will be $0+4+0+4+0+4...+4+0$. This has length $15$, with $8$ zeroes and $7$ fours. So it is equal to $8(0)+7(4)=\boxed{28}$

The area of a rhombus is given by $\frac{pq}{2}$, where p and q are the diagonals. Plugging in gives $\frac{18*12}{2}=\boxed{108}$

Cheerios$=99$ cents

Tasteeos$=8/9$(Cheerios)$=8/9(99)=8*11=\boxed{89}$ cents

Just listing out the terms, we get:

1/2+1/3=5/6

1/2+1/3+1/4=13/12

1/2+1/3+1/4+1/5=77/60

1/2+1/3+1/4+1/5+1/6=87/60

1/2+1/3+1/4+1/5+1/6+1/7=223/140

1/2+1/3+1/4+1/5+1/6+1/7+1/8=481/280

1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9=4609/2520

1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10=4861/2520

1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11=55991/27720(first number greater than 2)

From this, we can see the smallest integer value of x is 11. However, this way of listing out terms is slow, and if anybody else has an algebraic way, it would be much appreciated.

Because line AC splits angle ZAB into two equal angles, so ZAC=23, then ZAB=46. But because ZAB is a half of a rhombus, ABZ and AZB must be equal. Let's denote them: $x$. We have x+x+46=180, which gives 2x+46=180, which gives 2x=134, which gives $\boxed{x=ABZ=67^\circ}$

Hi Guest! It says the answer is incorrect, but it hasn't given me the correct answer yet, can you show your full work and I can look for errors? Thanks!

When you triple the distance, the gravitational attraction goes down by $9$, because it is inversely proportional to $3^2=9$. But because it is directly proportional to the mass of each body, when the mass of each is doubled, it goes up by $4$, because $2$(for the first body)$*2$(for the second body)$=4$. So in total, the gravitational attraction is now $\boxed{4/9}$ of the original gravitational attraction between the two bodies.

Happy problem solving!

Using the sum of angles of a triangle formula on the leftmost triangle, we find that $36+63+x=180$. Solving gives $\boxed{x=81}$

Knowing now that $x=81$, we see that since $x$ and $z$ lie on the same line, $x+z=180$. We already know what $x$ is, so we have $81+z=180$. Solving gives $\boxed{z=99}$

Now using the sum of angles of a triangle formula again on the rightmost triangle, we find that $13+z+y=180$. But we already know what $z$ is! $z=99$! So we have $13+99+y=180$. Solving gives $\boxed{y=68}$.

FINAL ANSWERS: $\boxed{x=81, y=68, z=99}$

Let us denote the interior angle(not 114, not x) as y. Because the exterior angle plus the interior angle sum to $180^\circ$, we have $164+y=180$, which gives $y=16^\circ$. Now, we use the formula for the sum of the angles of a triangle. It states that the sum of all the angles in a triangle is equal to $180^\circ$, so we have $16+114+x=180$, which gives $x=180-16-114$, which gives $\boxed{x=50}$

$10^{-10}=\frac{1}{10^{10}}$, so we have $12345678*10^{-10}=\frac{12345678}{10^{10}}$. But $10^{10}$ is 1 with 10 zeroes after it, so we have $\frac{12345678}{10^{10}}=\frac{12345678}{10000000000}$, which is equal to $\boxed{0.0012345678}$