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:
C) 2,6,24,120,720
Step-by-step explanation:
Here the n-th term An = 
A1 is the first term
A1 = (1 + 2)!/(1 + 2)
= 3!/3
A1 = 2
A2 is the second term
A2 = (2 +2)!/(2 +2)
= 4!/4
A2 = (1*2*3*4) /4
A2 = 6
A3 is the third term
A3 = (3 + 2)!/(3 +2)
A3 = 5!/5
A3 = 24
A4 is the fourth term
A4 = (4 + 2)!/(4 + 2)
A4 = 6!/6
A4 = 120
A5 is the fifth term
A5 = (5 + 2)!/(5 +2)
A5 = 7!/7
A5 = 720
Answer: C) 2,6,24,120,720
Thank you.
Answer:
16.03
Step-by-step explanation:
Answer: 46.90mins
Step-by-step explanation:
The given data:
The diameter of the balloon = 55 feet
The rate of increase of the radius of the balloon when inflated = 1.5 feet/min.
Solution:
dr/dt = 1.5 feet per minute = 1.5 ft/min
V = 4/3·π·r³
The maximum volume of the balloon
= 4/3 × 3.14 × 55³
= 696556.67 ft³
When the volume 2/3 the maximum volume
= 2/3 × 696556.67 ft³
= 464371.11 ft³
The radius, r₂ at the point is
= 4/3·π·r₂³
= 464371.11 ft³
r₂³ = 464371.11 ft³ × 3/4
= 348278.33 ft³
348278.333333
r₂ = ∛(348278.33 ft³) ≈ 70.36 ft
The time for the radius to increase to the above length = Length/(Rate of increase of length of the radius)
The time for the radius to increase to the
above length
Time taken for the radius to increase the length.
= is 70.369 ft/(1.5 ft/min)
= 46.90 minutes
46.90mins is the time taken to inflate the balloon.
