Please help, I need to get this done!I need to get number 16, 17, and 18 done please help!!!!
1 answer:
Answer:
16) 62.8 m²
17) 19.4 m²
18) 103.5 m²
Step-by-step explanation:
The formula to find area of a circle is: . To find radius, find the half of the diameter.
To solve number 16, first find the area of the unshaded circle using the formula: . This is also 3.14*16. Multiply to get 50.24 m². Now find the area of the larger circle using the formula:
. This is also 3.14*36. Multiply to get 113.04 m². Now subtract 113.04 - 50.24 to get the shaded area or 62.8 m².
To solve number 17, first find the area of the square using the formula: side x side. In this case multiply: 5.25 x 5.25 to get 27.5625. Round to the nearest tenth to get 27.6 m². Now find the area of the circle using the formula: . This is also 3.14*2.625. Multiply to get 8.2425. Round to the nearest tenth to get 8.2. Subtract 27.6 - 8.2 to get 19.4 m².
To solve number 18, find the area of one unshaded circle using the formula: . This is also 3.14*3.0625. Multiply to get 9.61625. Round to the nearest tenth to get 9.6 m². Add 9.6 + 9.6 to find the area of both unshaded circles. You get 19.2 m². Now find the area of the shaded circle using the formula:
. This is also 3.14*39.0625. Multiply to get 122.65625. Round to the nearest tenth: 122.7. Subtract 122.7 - 19.2 to get 103.5 m².
Hope it helps and is correct!
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Answer:
84 feet
Step-by-step explanation:
This problem involves several steps. The first step is to realize that the given figure does not show the required number of vertical stringers. It shows 5, but there will be 7 of them. The given diagram is helpful in that it shows a vertical stringer on the centerline of the arches.
The second step is to write a function that will tell you how long the stringer will be. I find it convenient to write the equation for an arch shape such as this using the parent function h(x) = 1-x^2. This parent function gives an arch of height 1 and width 1 from center (a total width of 2). You want an arch that is 16 ft high and 40 ft wide (one side from center), so you must scale this parent function both horizontally (by 40) and vertically (by 16). It becomes ...
H(x) = 16(1 -(x/40)^2)
The taller arch is twice this height, so the length of a vertical stringer at position x is
vertical length = 2H(x) -H(x) = H(x)
That is, the function H(x) we defined can be used to find the length of the stringers.
The third step is to find the stringer lengths. It can save some energy if you realize that the problem is symmetrical, so that the stringer at x=-30 is the same length as the one at x=30. We need to find stringer lengths every 10 feet from -40 feet to +40 feet. Of course, the ones at ±40 feet are zero length, because that is where the two arches meet.
H(-30) = 16(1 -(3/4)^2) = 7
H(-20) = 16(1 -(1/2)^2) = 12
H(-10) = 16(1 -(1/4)^2) = 15
H(0) = 16
Then the fourth step is to add up the stringer lengths, rounding the result as required.
7 +12 +15 +16 +15 +12 +7 = 16 + 2(34) = 84 . . . . feet (no rounding needed)
Finally, you need to answer the question asked:
The sum of vertical stringer lengths is 84 feet.
