In the number 987,164.302, the digit 9 occupies the hundred thousands position, 8 is in the ten thousands position, 7 is placed in the thousands position, 1 is located in the hundreds position, 6 is in the tens position, and 4 is in the ones position.
The sphere's radius is calculated as 18 divided by 2, giving 9 cm.
Using the formula for the volume of a sphere, we find it to be 4/3 πr^3, resulting in 4/3 x π x (9)^3 which equals 972 π cubic centimeters.
If we halve the diameter, the new volume can be calculated as: 4/3 x π x (9/2)^3 equals 4/3 x π x (9)^3 x (1/2)^3, simplifying down to 1/8 of 972.
Thus, the new volume will only be 1/8 of the original volume.
What recursive formula applies to generate the following sequence where f(1) = 3 and n ≥ 1?
3, –6, 12, –24, 48
The applicable recursive formula for this sequence is
f(n + 1) = –2 f(n)
When n=1, f(n) equals 3
Now when n = 2
f(2) = -2 (3) = -6
When n = 3
f(3) = -2 (-6) = 12, and this pattern continues.
The total water used for a bath is half the tub's full capacity. Volume of water used = (volume)/2 = (5×3×2.8)/2 = 42/2 = 21 cubic feet. For a shower, the total water used is calculated as: total water = rate × time = 1.52 × 12 = 18.24 gallons. To convert gallons to cubic feet, since 1 cubic foot equals 7.5 gallons: amount = 18.24/7.5 = 2.432 cubic feet. Therefore, the conclusion reached is that bathing consumes more water than showering.
