We use the formula: ( a - b )^3 = a^3 - b^3 - 3ab( a - b);
a = 1000; b = 1;
999^3 = 1000^3 - 1^3 - 3·1000·1( 1000 - 1 ) = 1000000000 - 1 - 3000·999 = 1000000000 - 1 - 2997000 = 997002999;
Answer:
Depends on how many people each table holds
Step-by-step explanation:
Answer: the height in inches, of the pile after 3 weeks is 34 11/12 inches
Step-by-step explanation:
Each consecutive week for the next 5 weeks the height of pile increase by 8 7/12 inches. Converting 8 7/12 inches to improper fraction, it becomes 103/12 inches. The height is increasing in an arithmetic progression. The formula for determining the nth term of an arithmetic sequence is expressed as
Tn = a + (n - 1)d
Where
a represents the first term of the sequence.
d represents the common difference.
n represents the number of terms in the sequence.
From the information given,
a = 17 3/4= 71/4 inches
d = 103/12 inches
n = 3 weeks
the height in inches, of the pile after 3 weeks, T3. Therefore,
T3 = 71/4 + (3 - 1)103/12
T3 = 71/4 + 2 × 103/12 = 71/4 + 103/6
T3 = 419/12 inches = 34 11/12 inches
Answer:
Aidan is 2 miles far from the ending point when he reaches the water station.
Step-by-step explanation:
The locations of the starting point, water station and ending point are (3, 1), (3, 7) and (3, 9), all expressed in miles. First we determine the distances between starting and ending points and between starting point and water station by the Pythagorean Theorem:
From starting point to ending point:
(Eq. 1)
From starting point to water station:
(Eq. 2)
The distance between the water station and the ending point is:
(Eq. 3)
Hence, Aidan is 2 miles far from the ending point when he reaches the water station.
Answer:
5 and 13
Step-by-step explanation:
