A(w) = -w² + 100w
Step-by-step explanation: Initially, we need to express the length (l) of the rectangular area in terms of the width (w). Given that the total perimeter of the rectangle is 200 feet implies that 2(w + l) = 200, leading to l = 100 - w. Hence, the area A can be given as width multiplied by length: A = w * l = w * (100 - w) = -w² + 100w. Consequently, A(w) = -w² + 100w.
In this problem the number we are working with is:
105,159
By definition we note:
thousand place: a five-digit quantity greater than zero.
Moreover, the rounding rule is:
if the digit being removed is 5 or more, increase the kept digit by one.
Therefore, rounding to the nearest ten thousand yields:
105,159 = 110,000
Answer:
105,159 rounded to the nearest ten thousand is:
105,159 = 110,000
Answer: a) 1791 seconds
b) 29701 seconds
Step-by-step breakdown:
1 US gallon = 0.134 cubic feet
It takes 20 seconds to fill a 2-gallon watering can with the garden hose. Converting 2 gallons into cubic feet results in
2 × 0.134 = 0.268 cubic feet
a) The inflatable pool has dimensions of 3 feet wide, 8 feet long, and 1 foot deep.
Volume = 3 × 8 × 1 = 24 cubic feet
If it takes 0.268 cubic feet = 20 seconds
Then 24 cubic feet = (24 × 20)/0.268
= 1791 seconds
b) The formula for the volume of a cylinder is πr²h
Diameter = 13 feet
Radius = diameter/2 = 13/2 = 6.5
The circular pool's volume calculates to
3.14 × 6.5² × 3 = 397.995 cubic feet
If it takes 0.268 cubic feet = 20 seconds
Then 397.995 cubic feet = (397.995 × 20)/0.268
= 29701 seconds
3 distinct arrangements - 1 x 9 (or 9 x 1) and 3 x 3
Thus, the total number of arrangements = 2 x 2 = 4 = an even count
Initially, we identify pairs of different factors of 9.
The pairs of factors for 9 are:
(1, 9) and (3, 3)
For each of these pairs, Mr. Deets can create 2 arrangements.
This means the total arrangements Mr. Deets can construct = 2 x 2 = 4, confirming that the overall number is even.
