61 × 1000 = ?
61 × 1 = 61
61 × 10 = 610
61 × 100 = 6100
61 × 1000 = 61000
Answer:
ln(5/256)
Step-by-step explanation:
Step 1, do the stuff in parenthesis:
1/5 (2ln5 + 3ln5) - 8ln2 = 1/5 (5ln5) - 8ln2
Step 2, remove parenthesis and simplify:
1/5 (5ln5) - 8ln2 = ln5 - 8ln2
Step 3, use this formula-
8*ln2 = ln2^8 = ln256
-to get:
ln5 - 8ln2 = ln5 - ln256
Step 4, use another formula:
ln(A) - ln(B) = ln(A/B), so the answer is ln(5/256) TADA!
<u>650 cannonballs
</u>
Explanation step by step:
upper layer = 1 ^ 2
second layer = 2 ^ 2
third layer = 3 ^ 2
layer 12 is 12 ^ 2
<u>The formula is:
</u>
<u>n * (n + 1) * (2n + 1) / 6
</u>
<u>n = 12
</u>
<u>12 (12 + 1) (2 * 12 + 1) / 6
</u>
<u>12 * 13 * 25/6 =
</u>
<u>650
</u>
<u>
</u>
There are 650 cannonballs in this pyramid.
For the equation y - x < 0,
y < x
The shaded portion will be under the dashed line joining points (-2, -2) and (3, 3).
for the equation x - 1 > 0,
x > 1
The shaded portion will be to the right of the dashed line joining points (1, 5) and (1, -3).
The portion affected by the two shadings will be the portion common to the right of the dashed line joining points (1, 5) and (1, -3) and under the dashed line joining points (-2, -2) and (3, 3).
Therefore the correct answer is option c.
2x + 7 ≤ 3x - 5
Start by keeping the variable x on the left side of the inequality, and move everything else to the right side.
We can do this by subtracting 3x from both sides and subtracting 7 from both sides.
-x ≤ -12
Divide both sides by -1 to make x a positive; when dividing by a negative number you will flip the inequality sign, so ≤ becomes ≥.
x ≥ 12
Possible solutions for x are any number equal to or greater than 12.
