1. In parallelograms, opposite sides are congruent. Therefore EV=16
2. In parallelograms, adjacent angles add up to 180°, so measure of angle V = 100°
3. Opposite angles are equal so measure of angle L = 95°
4. Diagonals of parallelograms bisect each other. DE=10
5. Same rule as #4. LV=18
Answer:
Step-by-step explanation:
You can split the coins into 3 groups, each of them has 3 coins. Weigh group 1 vs group 2, if one is lighter, that group has the fake coin. If both groups weigh the same, then group 3 has the fake coin.
Continue to split the group that has the fake coin into 3 groups, each group has 1 coin. Now apply the same procedure and we can identify the fake coin.
Total of scale usage is 2
b) if you have
coins then you can apply the same approach and find the fake coin with just n steps. By splitting up to 3 groups each step, after each step you should be able to narrow down your suspected coin by 3 times.
Step 1: you narrow down to group of
coins
Step 2: you narrow down to group of
coins
Step 3: you narrow down to group of
coins
...
Step n: Step 1: you narrow down to group of
coin
Notice the picture below
just use the pythagorean theorem to ge the diagonal

The rows add up to

, respectively. (Notice they're all powers of 2)
The sum of the numbers in row

is

.
The last problem can be solved with the binomial theorem, but I'll assume you don't take that for granted. You can prove this claim by induction. When

,

so the base case holds. Assume the claim holds for

, so that

Use this to show that it holds for

.



Notice that






So you can write the expansion for

as

and since

, you have

and so the claim holds for

, thus proving the claim overall that

Setting

gives

which agrees with the result obtained for part (c).
If it's not 6 cubic feet (because by the wording the answer is given).
If one dimension of the amount of soil they remove is 6, then you have to do 6*6*6= 216
If the total amount of soil removed is 6 cubic feet, then the dimensions of the cube would be ![\sqrt[3]{6}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B6%7D)