Answer:
3.75cm 44.16cm²
20cm 314cm²
42cm 1384.74cm²
Step-by-step explanation:
Area of a circle = πr²
Where : = π = pi = 3.14
R = radius
the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.
A radius is half of the diameter
16. Radius = 7.5 / 2 = 3.75
Area = 3.14 x 3.75² = 44.16
17. Diameter = 10 x 2 = 20
Area = 10² x 3.14 = 314
18. Diameter = 21 x 2 = 42
Area = 21² x 3.14 = 1384.74
You need to find the volumes of the the two containers.
Then subtract the smaller volume from the larger volume.
Volume of Cylinder = pi * r^2 * h
radius = diameter/2
Container A:
radius = 38 ft/2 = 19 ft
Volume = pi * r^2 * h = 3.14159 * (19 ft)^2 * 19 ft = 21,548.2 ft^3
Container B:
radius = 32 ft / 2 = 16 ft
Volume = 3.14159 * (16 ft)^2 * 20 ft = 16,084.9 ft^3
Difference in volumes:
21,548.2 ft^3 - 16,084.9 ft^2 = 5,463.2 ft^3
2x + 3x = 90
5x = 90
x = 18
Analysis to obtain the function that models the polulaiton ob bees:
1) First year 9,000 bees
2) Second year: decrease 5% => 9,000 - 0.05* 9,000 = 9,000 * (1 - 0.05) = 9,000 * 0.95
3) Every year the population decreases 5% => 9,000 * 0.95)^ (number of years)
4) if you call x the number of years, and f(x) the function that represents the number of bees, then: f(x) = 9,000 (0.95)^ x.
Analysis of the statements:
<span>1) The
function f(x) = 9,000(1.05)x represents the situation.
FALSE: WE DETERMINED IT IS f(x) = 9,000 (0.95)^x
2) The function
f(x) = 9,000(0.95)x represents the situation.
TRUE: THAT IS WHAT WE OBTAINED AS CONCLUSION OF THE PREVIOUS ANALYSIS.
3) After 2 years, the farmer
can estimate that there will be about 8,120 bees remaining.
Do the math:
f(2) = 9,000 * (0.95)^2 = 9,000 * 0,9025 = 8,122
So, the statement is TRUE
4) After 4
years, the farmer can estimate that there will be about 1,800 bees
remaining.
f(4) = 9,000 * (0.95)^4 = 9,000 * 0.81450625 = 7,330
So, the statement is FALSE
5) The domain values, in the context of the situation, are
limited to whole numbers.
FALSE: THE DOMAIN VALUES ARE ALL NON NEGATIVE REAL VALUES. FOR EXAMPLE THE FUNCTION IS WELL DEFINED FOR X = 5 AND HALF
6) The range values, in the context of the
situation, are limited to whole numbers.
TRUE: THERE CANNOT BE FRACTIONS OF BEES
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